Embed Size (px)
DESCRIPTION
The Nuclear Symmetry Energy and Neutron Star Crusts. Collaborators ： Wei-Zhou Jiang (South-East U.) Che Ming Ko and Jun Xu (TAMU) Bao-An Li (TAMU-Commerce) - PowerPoint PPT Presentation
Citation preview
The Nuclear Symmetry Energy and Neutron Star Crusts
Lie-Wen Chen (陈列文 )
(Department of Physics Shanghai Jiao Tong University)
Compact stars in the QCD phase diagram IIMay 20‐24 2009 Beijing
Collaborators Wei-Zhou Jiang (South-East U)Che Ming Ko and Jun Xu (TAMU)Bao-An Li (TAMU-Commerce) Gao-Chan Yong (IMPCAS)Hong-Ru Ma (SJTU) Zhi-Gang Xiao and Ming Zhang (Tsinghua U)
Outline
EOS of asymmetric nuclear matter and the nuclear symmetry energy
Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
The nuclear symmetry energy and neutron star crusts
Summary and outlook
Main References LW Chen CM Ko BA Li and GC Yong Front Phys China 2(3) 327 (2007)
[arXiv07042340]BA Li LW Chen and CM Ko Phys Rep 464 113-281 (2008) [arXiv08043580]J Xu LW Chen BA Li and HR Ma Phys Rev C 79 035802 (2009) [arXiv08074477]J Xu LW Chen BA Li and HR Ma Astrophys J 697 1549-1568 (2009) [arXiv09012309]
I EOS of Asymmetric Nuclear Matter and the Nuclear Symmetry Energy
Neutron Stars hellip
Structures of Radioactive Nuclei SHE hellip
Isospin Effects in HICrsquos hellip
Many-Body Theory
Many-Body Theory
Transport Theory General Relativity
Nuclear Force
EOS for Asymmetric
Nuclear Matter
Density Dependence of the Nuclear Symmetry Energy
HICrsquos induced by
neutron-rich nuclei
(CSRLanzhouFRIBGSIRIKENhelliphellip)
Most uncertain property of an asymmetric
nuclear matter
What is the isospin dependence of the in-medium nuclear effective interactions
Isospin Physics in medium energy nuclear physics
Radioactive beam facilities are being built around the world
IMP CIAE
Providing new opportunities for both nuclear physics and astrophysics
World status of Rare Isotope Accelerators
Many-Body Approaches to Nuclear Matter EOS
Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Greenrsquos Function (SCGF) Theory Variational Many-Body (VMB) approach helliphellip Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) helliphellip Phenomenological Approaches Relativistic mean-field (RMF) theory Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations Phenomenological potential models helliphellip
Equation of State of symmetric nuclear matter is relatively well determined
(1) EOS of symmetric matter around the saturation density ρ0
Giant Monopole Resonance 0
22
0 0 2Incompressibility K =9 ( )
d E
d
K0=231plusmn5 MeVPRL82 691 (1999)Recent resultsK0=240plusmn20 MeVG Colo et al U Garg et al
__
GMR 0Frequency f K
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Outline
EOS of asymmetric nuclear matter and the nuclear symmetry energy
Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
The nuclear symmetry energy and neutron star crusts
Summary and outlook
Main References LW Chen CM Ko BA Li and GC Yong Front Phys China 2(3) 327 (2007)
[arXiv07042340]BA Li LW Chen and CM Ko Phys Rep 464 113-281 (2008) [arXiv08043580]J Xu LW Chen BA Li and HR Ma Phys Rev C 79 035802 (2009) [arXiv08074477]J Xu LW Chen BA Li and HR Ma Astrophys J 697 1549-1568 (2009) [arXiv09012309]
I EOS of Asymmetric Nuclear Matter and the Nuclear Symmetry Energy
Neutron Stars hellip
Structures of Radioactive Nuclei SHE hellip
Isospin Effects in HICrsquos hellip
Many-Body Theory
Many-Body Theory
Transport Theory General Relativity
Nuclear Force
EOS for Asymmetric
Nuclear Matter
Density Dependence of the Nuclear Symmetry Energy
HICrsquos induced by
neutron-rich nuclei
(CSRLanzhouFRIBGSIRIKENhelliphellip)
Most uncertain property of an asymmetric
nuclear matter
What is the isospin dependence of the in-medium nuclear effective interactions
Isospin Physics in medium energy nuclear physics
Radioactive beam facilities are being built around the world
IMP CIAE
Providing new opportunities for both nuclear physics and astrophysics
World status of Rare Isotope Accelerators
Many-Body Approaches to Nuclear Matter EOS
Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Greenrsquos Function (SCGF) Theory Variational Many-Body (VMB) approach helliphellip Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) helliphellip Phenomenological Approaches Relativistic mean-field (RMF) theory Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations Phenomenological potential models helliphellip
Equation of State of symmetric nuclear matter is relatively well determined
(1) EOS of symmetric matter around the saturation density ρ0
Giant Monopole Resonance 0
22
0 0 2Incompressibility K =9 ( )
d E
d
K0=231plusmn5 MeVPRL82 691 (1999)Recent resultsK0=240plusmn20 MeVG Colo et al U Garg et al
__
GMR 0Frequency f K
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
I EOS of Asymmetric Nuclear Matter and the Nuclear Symmetry Energy
Neutron Stars hellip
Structures of Radioactive Nuclei SHE hellip
Isospin Effects in HICrsquos hellip
Many-Body Theory
Many-Body Theory
Transport Theory General Relativity
Nuclear Force
EOS for Asymmetric
Nuclear Matter
Density Dependence of the Nuclear Symmetry Energy
HICrsquos induced by
neutron-rich nuclei
(CSRLanzhouFRIBGSIRIKENhelliphellip)
Most uncertain property of an asymmetric
nuclear matter
What is the isospin dependence of the in-medium nuclear effective interactions
Isospin Physics in medium energy nuclear physics
Radioactive beam facilities are being built around the world
IMP CIAE
Providing new opportunities for both nuclear physics and astrophysics
World status of Rare Isotope Accelerators
Many-Body Approaches to Nuclear Matter EOS
Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Greenrsquos Function (SCGF) Theory Variational Many-Body (VMB) approach helliphellip Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) helliphellip Phenomenological Approaches Relativistic mean-field (RMF) theory Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations Phenomenological potential models helliphellip
Equation of State of symmetric nuclear matter is relatively well determined
(1) EOS of symmetric matter around the saturation density ρ0
Giant Monopole Resonance 0
22
0 0 2Incompressibility K =9 ( )
d E
d
K0=231plusmn5 MeVPRL82 691 (1999)Recent resultsK0=240plusmn20 MeVG Colo et al U Garg et al
__
GMR 0Frequency f K
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Radioactive beam facilities are being built around the world
IMP CIAE
Providing new opportunities for both nuclear physics and astrophysics
World status of Rare Isotope Accelerators
Many-Body Approaches to Nuclear Matter EOS
Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Greenrsquos Function (SCGF) Theory Variational Many-Body (VMB) approach helliphellip Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) helliphellip Phenomenological Approaches Relativistic mean-field (RMF) theory Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations Phenomenological potential models helliphellip
Equation of State of symmetric nuclear matter is relatively well determined
(1) EOS of symmetric matter around the saturation density ρ0
Giant Monopole Resonance 0
22
0 0 2Incompressibility K =9 ( )
d E
d
K0=231plusmn5 MeVPRL82 691 (1999)Recent resultsK0=240plusmn20 MeVG Colo et al U Garg et al
__
GMR 0Frequency f K
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Many-Body Approaches to Nuclear Matter EOS
Microscopic Many-Body Approaches Non-relativistic Brueckner-Bethe-Goldstone (BBG) Theory Relativistic Dirac-Brueckner-Hartree-Fock (DBHF) approach Self-consistent Greenrsquos Function (SCGF) Theory Variational Many-Body (VMB) approach helliphellip Effective Field Theory Density Functional Theory (DFT) Chiral Perturbation Theory (ChPT) helliphellip Phenomenological Approaches Relativistic mean-field (RMF) theory Relativistic Hartree-Fock (RHF) Non-relativistic Hartree-Fock (Skyrme-Hartree-Fock) Thomas-Fermi (TF) approximations Phenomenological potential models helliphellip
Equation of State of symmetric nuclear matter is relatively well determined
(1) EOS of symmetric matter around the saturation density ρ0
Giant Monopole Resonance 0
22
0 0 2Incompressibility K =9 ( )
d E
d
K0=231plusmn5 MeVPRL82 691 (1999)Recent resultsK0=240plusmn20 MeVG Colo et al U Garg et al
__
GMR 0Frequency f K
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Equation of State of symmetric nuclear matter is relatively well determined
(1) EOS of symmetric matter around the saturation density ρ0
Giant Monopole Resonance 0
22
0 0 2Incompressibility K =9 ( )
d E
d
K0=231plusmn5 MeVPRL82 691 (1999)Recent resultsK0=240plusmn20 MeVG Colo et al U Garg et al
__
GMR 0Frequency f K
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
(2) EOS of symmetric matter for 1ρ0lt ρ lt 3ρ0 from K+ production in HICrsquosJ Aichelin and CM Ko
PRL55 (1985) 2661C Fuchs
Prog Part Nucl Phys 56 (2006) 1
Transport calculations indicate that ldquoresults for the K+ excitation function in Au + Au over C + C reactions as measured by the KaoS Collaboration strongly support the scenariowith a soft EOSrdquo
C Fuchs et al PRL86 (2001) 1974
Equation of State of symmetric nuclear matter is relatively well determined
See also C Hartnack H Oeschler and J Aichelin
PRL96 012302 (2006)
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
(3) Present constraints on the EOS of symmetric nuclear matter for 2ρ0lt ρ lt 5ρ0 using flow data from BEVALAC SISGSI and AGS
Use constrained mean fields to predict the EOS for symmetric matter
bull Width of pressure domain reflects uncertainties in comparison and of
assumed momentum dependence
P Danielewicz R Lacey and WG Lynch Science 298 1592 (2002)
2Pressure P( )s
E
The highest pressure recorded under laboratory controlled conditions in nucleus-nucleus collisions
y
px
High density nuclear matter2 to 5ρ0
Equation of State of symmetric nuclear matter is relatively well determined
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Liquid-drop model
Symmetry energy term
W D Myers WJ Swiatecki P Danielewicz P Van Isacker A E L Dieperinkhelliphellip
Symmetry energy including surface diffusion effects (ys=SvSs)
The Nuclear Symmetry Energy
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
EOS of Asymmetric Nuclear Matter
s2 4
ym ( )( ) ( ) ( )0) ( n pE OE E (Parabolic law)
The Nuclear Symmetry Energy2
sym 2
1 ( )( )
2
EE
The Nuclear Matter Symmetry Energy
0
sym
sy
2
0 0
0 0
s
sy
0
msym 0
0
0
y
m
m
( )3 18
30 MeV (LD mass formula )
( )3 (Many-Body Theory
( )
Exp
( )
50 200 e )M
( )
V
E Myers amp Swiatecki NPA81 Pomorski amp Du
EL
KL
dek PRC67
L
K
E E
0
2sym2
0 sym2
asy sym
sym
(Sharma et al
isobaric incompressiblity
( )9 (Many-Body Theory Exp )
The isospin part of the of asymmetric nuclear matter
700 466 MeV
320 180 6 GMR( M eV
K
K K K
K
L
E
ShlomoampYoungbloodPRC47529(93)
PRC38 2562 (88))
566 1350 34 159 M eV
550 1
(
(T Li et al PRL99162503(2007))00 MeV )
Symmetry energy termSymmetric Nuclear Matter
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
ChenKoLi PRC72 064309(2005) ChenKoLi PRC76 054316(2007)
The Nuclear matter symmetry energy
ZH Li et al PRC74 047304(2006) Dieperink et al PRC68 064307(2003)
BHF
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
II Constraining the density dependence of the nuclear symmetry energy in heavy-ion collisions
Promising Probes of the Esym(ρ) in Nuclear Reactions (an incomplete list )
At sub-saturation densities (亚饱和密度行为) Sizes of n-skins of unstable nuclei from total reaction cross sections Proton-nucleus elastic scattering in inverse kinematics Parity violating electron scattering studies of the n-skin in 208Pb np ratio of FAST pre-equilibrium nucleons Isospin fractionation and isoscaling in nuclear multifragmentation Isospin diffusiontransport Neutron-proton differential flow Neutron-proton correlation functions at low relative momenta t3He ratio Hard photon production
Towards high densities reachable at CSRChina FAIRGSI RIKEN GANIL and FRIB (高密度行为) π -π + ratio K+K0 ratio Neutron-proton differential transverse flow np ratio at mid-rapidity Nucleon elliptical flow at high transverse momenta np ratio of squeeze-out emission
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Solve the Boltzmann equation using test particle method Isospin-dependent initialization Isospin- (momentum-) dependent mean field potential
Isospin-dependent N-N cross sections a Experimental free space N-N cross section σexp
b In-medium N-N cross section from the Dirac-Brueckner approach based on Bonn A potential σin-medium
c Mean-field consistent cross section due to m Isospin-dependent Pauli Blocking
0 sym
1(1 )
2 z CV V V V
Phase-space distributions ( ) satify the Boltzmann equation
( ) ( )p r r p c NN
f r p t
f r p tf f I f
t
Isospin-dependent BUU (IBUU) model
Transport model for HICrsquos
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Isospin- and momentum-dependent potential (MDI)
30
0
0
0
016 fm
( ) 16 MeV
MDI Interaction
( ) 316 MeV
211 MeV
06
g( o )
8
G ny
sym
E A
E
K
m m
ChenKoLi PRL94032701
(2005)LiChen PRC72 064611
(2005)
DasDas GuptaGaleLi
PRC67034611 (2003)
Transport model IBUU04
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
2
NNmedium free
NN
in neutron-rich mattermedium free
NN is the reduced mass of the
colliding pair NN in mediumJW Negele and K Yazaki PRL 47 71 (1981)VR Pandharipande and SC Pieper PRC 45 791 (1992)M Kohno et al PRC 57 3495 (1998)D Persram and C Gale PRC65 064611 (2002)
1 In-medium cross sections are reduced2 nn and pp cross sections are splitted due to the neutron-proton effective
mass slitting in neutron-rich matter
LiChen PRC72 (2005)064611
Medium effects effective mass on the incoming current in initial state and level density of the final state
Neglecting medium effects on the transition matrix
In-medium Nucleon-nucleon cross sectionsEffective mass scaling model
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
0
0
( ) 316( ) MeV
(From
Fit the symmetry ene
0 ) we obtain
rgy w
1
069 for
0
ith
5 f 1
0
or
sym
x
x
E
(1) Isospin diffusion
(2) Isospin scaling
ChenKoLi PRL94(05) PRC72(05) LiChen PRC72(05)
Shetty et alPRC75(07)PRC76(07)
Zhang et alPLB664(08)
(3) Double np ratio
0( )
with 05
ipotsym
i
E
Symmetry Energy Sub-saturation density behaviors
IBUU04
ImQMD
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
IBUU04 S~316(o)
ImQMD Double np ratios and two isospin diffusion measurements
Consistent constraints from the 2 analysis of three observables
S=125(o)23 + 176 (o)
i
i
i
i i
TsangZhangDanielewiczFamianoLiLynchSteiner PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
105
00
069 316( 316( ) )( )
Symmetry energy constrained at -saturation densities
between the and lines agrees extremely well with the
sub
-1 0 PR
AsymE
x x
(IBUU04)
(ImQMD)
X=-1
ChenKoLi PRL 94 032701 (2005) Tsang et al PRL 102 122701 (2009)
Symmetry Energy Sub-saturation density behaviors
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Subthreshold K0K+ yield may be a sensitive probe of the symmetry energy at high densities
AichelinKo PRL55 2661 (1985) Subthreshold kaon yield is a sensitive probe of the EOS of nuclear matter at high densities (ZX Li QF Li et al M Di Toro et al hellip)
Theory Famiano et al PRL97 052701 (2006)Exp Lopez et al FOPI PRC75 011901(R) (2007)
96 9644 44
96 9640 40
Ru+ Ru and
Zr+ Zr1528 AGeV
K0K+ yield is not so sensitive to the symmetry energy Lower energy and more neutron-rich system
High density behaviors Kaon Probe
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
IBUU04 XiaoLiChenYongZhang PRL102 062502(2009) A Quite Soft Esym at supra-saturation densities
M Zhang et al arXiv09040447
High density behaviors Pion Probe
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
LattimerPrakash Science 304 536 (2004)
Neutron star has solid crust over liquid coreRotational glitches small changes in period from sudden unpinning of superfluid vortices Evidence for solid crust 14 of Vela moment of
inertia glitches Needs to know the
transition density to calculate the fractional moment of inertia of the crustLink et al PRL833362 (99)
III The Nuclear Symmetry Energy and Neutron Star Crusts
core-crust transition
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
2 Thermodynamic approach
Or similarly one can use 3 the RPA
If one uses the parabolic approximation (PA)
Then the stability condition is
gt0
Onset of instability in the uniform n+p+e matter
1 Dynamical approachk0 (neglecting Coul)
Stability condition
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Core-Crust Transition Density Parabolic Law fails
(1) It is NOT enough to know the symmetry energy one almost has to know the exact EOS of n-rich matter
WhyBecause it is the determinant of the curvature matrixthat determines the stability condition Example
Not so surprise
ZhangChen CPL 18 (2000) 142Steiner PhysRev C74 (2006) 045808
Higher-order term effects on direct URCA
XuChenLiMa PRC79 035802 (2009)
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
(2) Locating the inner edge of neutron star crust
Kazuhiro Oyamatsu Kei Iida
Phys Rev C75 (2007) 015801
pasta
XuChenLiMa PRC79 035802 (2009)
XuChenLiMa ApJ 697 1547 (2009) arXiv09012309
Parabolic Approximation has been assumed
Significantly less than their fiducial valuesρ t=007-008 fm-3 and Pt=065 MeVfm3
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
(3) Constraints on M-R relation of NS
(Isospin Diff)
(Empirical estimate Link et al PRL833362(99))
LattimerPrakash
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
(4) Properties of neutron star crusts
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
Larger L leads to thicker neutron-skin but thinner neutron star crust
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
(5) Inner Crust EOS Dependence
XuChenLiMa ApJ 697 1549 (2009) arXiv09012309
The mass is insensitive to the inner crust EOSThe radius is sensitive to the inner crust EOS for a softer symmetry energyThe inner crust EOS has tiny effects on the dII when dII is small
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
The softest symmetry energythat the TOV is still stable is x=093 giving M_max=011 solar mass and R=gt28 km
For pure nucleonic matterNew PhysicsSoft symmetry energy at HD
K0=211 MeV is used higher incompressibility
for symmetric matter will lead to higher masses systematically
(6) HD Esym and properties of neutron stars
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
The isospin diffusion data Isoscaling and Isotope dependence of GMR seem to give a stringent constraint for the sub-saturation density behavior of the symmetry energy (L=86plusmn25 MeV and Kasy=-500plusmn50 MeV)
Probing the high density behavior of the symmetry energy remains a big challenge and the pion ratio data from FOPI favor a quite soft Esym at high densities
Significant constraints on inner edge and crust properties of neutron stars have been already obtained from present knowledge on symmetry energy at sub-saturation density region
Crosscheck is definitely needed
IV Summary and Outlook
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Thanks
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
Institute of Nuclear Particle Astronomy and Cosmology-INPAC Shanghai Jiao Tong University
httpphysicssjtueducniwdd09indexhtml
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
International workshop on nuclear dynamics in heavy-ion reactionsand the symmetry energy (IWND2009)
August 22ndash25 Shanghai China
OrganizersShanghai Institute of Applied Physics CAS
Shanghai Jiao Tong UniversityBeijing Normal University
Institute of Modern Physics CAS
