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N. Paar
Physics Department Faculty of Science
University of Zagreb Croatia
Self-consistent description of supernova electron capture and neutrino-nucleus processes
International Workshop XLI on Gross Properties of Nuclei and Nuclear Excitations, “Astrophysics and Nuclear Structure”, Jan 26 – Feb 1, 2013, Hirschegg, Austria
Periodic Table of Elements 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1 1
Hydrogen 1.00794
H1 Atomic #
Name Atomic Mass
SymbolC Solid
Hg Liquid
H Gas
Rf Unknown
Metals NonmetalsAlkali m
etals
Alkaline
earth metals
Lanthanoids Transition m
etals
Poor m
etals
Other
nonmetals
Noble gases
Actinoids
2
Helium 4.002602
He2 K
2 3
Lithium 6.941
Li2 1 4
Beryllium 9.012182
Be2 2 5
Boron 10.811
B23 6
Carbon 12.0107
C24 7
Nitrogen 14.0067
N25 8
Oxygen 15.9994
O26 9
Fluorine 18.9984032
F27 10
Neon 20.1797
Ne2 8
KL
3 11
Sodium 22.98976928
Na2 8 1
12
Magnesium 24.3050
Mg2 8 2
13
Aluminium 26.9815386
Al283
14
Silicon 28.0855
Si284
15
Phosphorus 30.973762
P285
16
Sulfur 32.065
S286
17
Chlorine 35.453
Cl287
18
Argon 39.948
Ar2 8 8
KLM
4 19
Potassium 39.0983
K2 8 8 1
20
Calcium 40.078
Ca2 8 8 2
21
Scandium 44.955912
Sc2 8 9 2
22
Titanium 47.867
Ti2 8
10 2
23
Vanadium 50.9415
V2 8
11 2
24
Chromium 51.9961
Cr28
131
25
Manganese 54.938045
Mn28
132
26
Iron 55.845
Fe28
142
27
Cobalt 58.933195
Co28
152
28
Nickel 58.6934
Ni28
162
29
Copper 63.546
Cu2 8
18 1
30
Zinc 65.38
Zn28
182
31
Gallium 69.723
Ga28
183
32
Germanium 72.64
Ge28
184
33
Arsenic 74.92160
As28
185
34
Selenium 78.96
Se28
186
35
Bromine 79.904
Br28
187
36
Krypton 83.798
Kr2 8
18 8
KLMN
5 37
Rubidium 85.4678
Rb2 8
18 8 1
38
Strontium 87.62
Sr2 8
18 8 2
39
Yttrium 88.90585
Y2 8
18 9 2
40
Zirconium 91.224
Zr2 8
18 10
2
41
Niobium 92.90638
Nb2 8
18 12
1
42
Molybdenum95.96
Mo28
1813
1
43
Technetium (97.9072)
Tc28
1814
1
44
Ruthenium 101.07
Ru28
1815
1
45
Rhodium 102.90550
Rh28
1816
1
46
Palladium 106.42
Pd28
1818
0
47
Silver 107.8682
Ag2 8
18 18
1
48
Cadmium 112.411
Cd28
1818
2
49
Indium 114.818
In28
1818
3
50
Tin 118.710
Sn28
1818
4
51
Antimony 121.760
Sb28
1818
5
52
Tellurium 127.60
Te28
1818
6
53
Iodine 126.90447
I28
1818
7
54
Xenon 131.293
Xe2 8
18 18
8
KLMNO
6 55
Caesium 132.9054519
Cs2 8
18 18
8 1
56
Barium 137.327
Ba2 8
18 18
8 2
57–7172
Hafnium 178.49
Hf2 8
18 32 10
2
73
Tantalum 180.94788
Ta2 8
18 32 11
2
74
Tungsten 183.84
W28
183212
2
75
Rhenium 186.207
Re28
183213
2
76
Osmium 190.23
Os28
183214
2
77
Iridium 192.217
Ir28
183215
2
78
Platinum 195.084
Pt28
183217
1
79
Gold 196.966569
Au2 8
18 32 18
1
80
Mercury 200.59
Hg28
183218
2
81
Thallium 204.3833
Tl28
183218
3
82
Lead 207.2
Pb28
183218
4
83
Bismuth 208.98040
Bi28
183218
5
84
Polonium (208.9824)
Po28
183218
6
85
Astatine (209.9871)
At28
183218
7
86
Radon (222.0176)
Rn2 8
18 32 18
8
KLMNOP
7 87
Francium (223)
Fr2 8
18 32 18
8 1
88
Radium (226)
Ra2 8
18 32 18
8 2
89–103104
Ruherfordium (261)
Rf2 8
18 32 32 10
2
105
Dubnium (262)
Db2 8
18 32 32 11
2
106
Seaborgium (266)
Sg28
18323212
2
107
Bohrium (264)
Bh28
18323213
2
108
Hassium (277)
Hs28
18323214
2
109
Meitnerium (268)
Mt28
18323215
2
110
Darmstadtium (271)
Ds28
18323217
1
111
Roentgenium (272)
Rg2 8
18 32 32 18
1
112
Ununbium (285)
Uub28
18323218
2
113
Ununtrium (284)
Uut28
18323218
3
114
Ununquadium (289)
Uuq28
18323218
4
115
Ununpentium (288)
Uup28
18323218
5
116
Ununhexium(292)
Uuh28
18323218
6
117
Ununseptium
Uus118
Ununoctium (294)
Uuo2 8
18 32 32 18
8
KLMNOPQ
For elements with no stable isotopes, the mass number of the isotope with the longest half-life is in parentheses.
Periodic Table Design and Interface Copyright © 1997 Michael Dayah. http://www.ptable.com/ Last updated: May 27, 2008
57
Lanthanum 138.90547
La2 8
18 18
9 2
58
Cerium 140.116
Ce2 8
18 19
9 2
59
Praseodymium 140.90765
Pr28
1821
82
60
Neodymium 144.242
Nd28
1822
82
61
Promethium (145)
Pm28
1823
82
62
Samarium 150.36
Sm28
1824
82
63
Europium 151.964
Eu28
1825
82
64
Gadolinium 157.25
Gd2 8
18 25
9 2
65
Terbium 158.92535
Tb28
1827
82
66
Dysprosium 162.500
Dy28
1828
82
67
Holmium 164.93032
Ho28
1829
82
68
Erbium 167.259
Er28
1830
82
69
Thulium 168.93421
Tm28
1831
82
70
Ytterbium 173.054
Yb28
1832
82
71
Lutetium 174.9668
Lu2 8
18 32
9 2
89
Actinium (227)
Ac2 8
18 32 18
9 2
90
Thorium 232.03806
Th2 8
18 32 18 10
2
91
Protactinium 231.03588
Pa28
183220
92
92
Uranium 238.02891
U28
183221
92
93
Neptunium (237)
Np28
183222
92
94
Plutonium (244)
Pu28
183224
82
95
Americium (243)
Am28
183225
82
96
Curium (247)
Cm2 8
18 32 25
9 2
97
Berkelium (247)
Bk28
183227
82
98
Californium (251)
Cf28
183228
82
99
Einsteinium (252)
Es28
183229
82
100
Fermium (257)
Fm28
183230
82
101
Mendelevium (258)
Md28
183231
82
102
Nobelium (259)
No28
183232
82
103
Lawrencium (262)
Lr2 8
18 32 32
9 2
Michael Dayah For a fully interactive experience, visit www.ptable.com. michael@dayah.com
OUTLINE
1. Inelastic neutrino-nucleus reactions involving supernova neutrinos. Large-scale calculations for charge-exchange reactions 2. Electron capture on nuclei at finite temperature in stellar environment 3. Nuclear equation of state – constraints on the symmetry energy from theory of collective nuclear motion and experimental data
The goal is self-consistent microscopic description inspired by EDFs, of nuclear structure, excitations, weak interaction processes, and nuclear equation of state of relevance for astrophysics and nucleosynthesis
Charged-current neutrino-nucleus reactions
The properties of nuclei and their excitations govern the neutrino-nucleus cross sections. Nuclear transitions induced by neutrinos involve operators with finite momentum transfer.
LOW-ENERGY NEUTRINO-NUCLEUS PROCESSES
NEUTRINO-NUCLEUS CROSS SECTIONS
Transition matrix elements are described in a self-consistent way using relativistic Hartree-Bogoliubov model for the initial (ground) state and relativistic quasiparticle random phase approximation for excited states (RHB+RQRPA)
DD-ME2 density-dependent effective interaction + Gogny pairing
Multipole composition of the neutrino-nucleus cross sections: RNEDF (DD-ME2) vs. shell model + RPA (SGII)
CHARGED-CURRENT NEUTRINO-NUCLEUS CROSS SECTIONS
Remarkable agreement between models based on completely different foundations and effective interactions !
In addition to GT, at larger neutrino energies exitations of higher multipolarities (forbidden transitions) contribute.
56Fe(νe,e-) 56Co <σ>(10-42cm2)
QRPA(SIII) (Lazauskas et al.) 352 Shell model (GXPF1J) + RPA (SGII) (T. Suzuki et al.)
259
RPA (Kolbe, Langanke) 240 QRPA (Cheoun et al.) 173 RNEDF (DD-ME2) 263 EXP. (KARMEN) 256±108±43
Neutrino-nucleus cross sections for 56Fe target, averaged over the electron neutrino from µ+ decay at rest (DAR)
⇥�⇤th = (258± 57) � 10�42cm2
UNCERTAINTIES IN MODELING ν-NUCLEUS CROSS SECTIONS
νe FLUX (Michel)
Present theoretical uncertainty from all models appear considerably smaller than the experimental one.
0 50 100 150 200 250
0
2000
4000
6000
8000
10000pool OPb
stable nuclei
<!"
e>
[10
-42 c
m2]
A
12C & 56Fe12C & 56Fe (Exp.)
LARGE-SCALE CALCULATIONS OF νe-NUCLEUS CROSS SECTIONS
The cross sections are averaged over the neutrino spectrum from muon DAR.
The model calculations reasonably reproduce the only two experimental cases, 12C and 56Fe.
Model calculations include all multipoles (both parities) up to J=5.
50 100 150 200 250
0
400
800
1200
1600 pool OPb
stable nuclei
neutron-rich (N/Z > 1.5)
neutron-deficient (N/Z < 1)
<!"
e>
[10
-42 c
m2]
A
T=4 MeV
LARGE-SCALE CALCULATIONS OF ν-NUCLEUS CROSS SECTIONS
The cross sections averaged over supernova neutrino spectrum.
The cross sections become considerably enhanced in neutron-rich nuclei, while those in neutron-deficient and proton-rich nuclei are small (blocking).
ADVANTAGES: 1) self-consistent parameter-free microscopic description of the cross sections (apart from the effective interactions that are fixed) 2) Complete calculations including all transition operators at finite momentum transfer and transitions up to J=5 (both parities)
50 100 150 200 2500
2
4
6
8
10
allneutron-deficient (N/Z<1)neutron-rich (N/Z > 1.5)stable nuclei
<!"e>
(RQ
RPA
) /
<!"e>
(ET
FS
I+C
QR
PA
)
A
T=4 MeV
LARGE-SCALE CALCULATIONS OF ν-NUCLEUS CROSS SECTIONS
How the RNEDF results (up to J=5) compare to ETFSI+CQRPA (only IAS & GT transitions; Borzov, Goriely) ?
50 100 150 2000
0.5
1
1.5
2
2.5
3
all
neutron-deficient (N/Z < 1)
neutron-rich (N/Z > 1.5)
stable nuclei
<!"e>
(RQ
RPA
) /
<!"e>
(RPA
-LM
)
A
T=4 MeV
LARGE-SCALE CALCULATIONS OF ν-NUCLEUS CROSS SECTIONS
How the RNEDF results compare to RPA (Woods-Saxon + Landau-Migdal Force) by Kolbe, Langanke et al. ?
0
2
4
6
8
10
RQRPA (DD-ME2)
QRPA (Balasi et al.)
0-
0+
1-
1+
2-
2+
!"
e[10
-40 c
m2]
E"e
=100 MeV
3-
3+
4-
4+
5-
5+
J#
96Mo("e,"e')96Mo*
NEUTRAL-CURRENT NEUTRINO-NUCLEUS CROSS SECTIONS
⌫e +Z XN ! ⌫e +Z X⇤N
• Inelastic neutrino-nucleus scattering through the weak neutral-current plays important role in neutrino transport in stellar environment
STELLAR ELECTRON CAPTURE
• The core of a massive star at the end of hydrostatic burning is stabilized by electron degeneracy pressure (as long as its mass does not exceed the Chandrasekhar limit) • Electron capture reduces the number of electrons available for pressure support (in opposition to nuclear beta decay) • Electron capture initiates the gravitational collapse of the core of a massive star, triggering a supernova explosion
Electron capture e� +Z XN �Z�1 X⇥
N+1 + �e
ELECTRON CAPTURE (EC) CROSS SECTIONS
For 56Fe the electron capture is dominated by the GT+ transitions, while for neutron-rich nuclei (76Ge) forbidden transitions play more prominent role)
• Model based on finite temperature (RMF + RPA) Finite temperature effects are described by Fermi-Dirac occupation factors for each single-nucleon state at the level of RMF, the same occupation factors are transferred to the RPA
STELLAR ELECTRON CAPTURE ON NEUTRON RICH Ge ISOTOPES
DEPENDENCE OF THE ELECTRON CAPTURE CROSS SECTIONS ON TEMPERATURE
Unblocking effect: electron-capture threshold energy decreases with temperature.
STELLAR ELECTRON CAPTURE RATES ON Fe ISOTOPES
�ec =1
⇥2�3
� �
E0e
peEe⇤ec(Ee)f(Ee, µe, T )dEe
FTRRPA - present LSSM – large scale shell model K. Langanke and G. Martınez-Pinedo, At. Data Nucl. Data Tables 79, 1 (2001). TQRPA A.A. Dzhioev et al., PRC 81, 015804 (2010)
Nuclear matter energy per part.:
E(⇢,↵) = E(⇢, 0) + S2(⇢)↵2 + . . .
S2(⇢) = J � L✏+ ...
✏ = (⇢0 � ⇢)/(3⇢0)
L = 3⇢0dS2(⇢)
dr|⇢0
↵ = (N � Z)/A
Symmetry energy term:
In order to explore the evolution of the excitation spectra as a function of the density dependence of the symmetry energy, a set of interactions is used, that span a broad range of values for the symmetry energy at saturation density (J) and the slope parameter (L).
5 10 15 20 25 30E[MeV]
0
2
4
6
8
10 J=30, L=30.0 MeV
J=32, L=46.5 MeV
J=34, L=62.1 MeV
J=36, L=85.5 MeV
J=38, L=110.8 MeV
R[e
2 fm
2 /M
eV]
132Sn
DD-ME
E1
Neutron skin thickness (ΔRpn) in nuclei is strongly correlated with symmetry energy at saturation density (J) & slope of the symmetry energy (L)
NUCLEAR EOS - CONSTRAINING THE SYMMETRY ENERGY
CONSTRAINING THE SYMMETRY ENERGY
J=(32.6±1.4) MeV
• Theoretical constraints on the symmetry energy at saturation density [J] and slope of the symmetry energy [L] from dipole polarizability [αD=(8π/9)e2m-1] using relativistic nuclear energy density functionals
• Exp. data from polarized proton inelastic scattering, αD=18.9(13)fm3/e2 A. Tamii et al., PRL. 107, 062502 (2011)
L=(50.9±12.6) MeV
30 32 34 36 38
J [MeV]
18
20
22
24
208Pb
αD [fm
3]
0 20 40 60 80 100 120
L [MeV]
18
20
22
24208Pb
αD [fm
3]
DD-ME
CONSTRAINING THE SYMMETRY ENERGY
Also see M. B. Tsang et al., PRC 86, 015803 (2012)
• Constraining the symmetry energy at saturation density (J) and slope of the symmetry energy (L) from various approaches:
28 30 32 34 36 38
J [MeV]
20
40
60
80
100
120HIC
QMC & neutron star
FRDM
IAS
PDR (Carbone 2010)
L [
Me
V]
PDR - 68Ni,132Sn
αD - 208Pb
208Pb(p,p)
+0 ,T
1 ,Tï
1 , T ï1ï
+0 , T
T = T
T =T ï1
z
z
Daughter nucleus
Target nucleus
6L=1, 6S=1
6L=1
GDR
E1
0
0
0 , 1 , 2 , T ï1ï ï ï
0
0
0
0+1 , T ï1
IVSGDR
GT
AGDR
IAS
0
0
S=16
Strong(p,n)
8
9
10
11
12
13
14
15
110 112 114 116 118 120 122 124Mass number (A)
E DR
-EIA
S (M
eV)
Sn isotopes
AGDR
IVSGDR
ANTI-ANALOG GDR AND NEUTRON-SKIN THICKNESS
10
10.5
11
11.5
12
0.12 0.16 0.2 0.24 0.28 0.326Rpn (fm)
E(A
GD
R)-E
(IA
S) (M
eV)
124Sn
*
6Rpn=0.205(50)
E(A
GD
R)-
E(IA
S) [
MeV
]
neutron skin thickness
METHOD ΔRpn (fm) (p,p) 0.8 GeV 0.25 ± 0.05 (α,α’) IVGDR 120 MeV 0.21 ± 0.11 Antiproton absorption 0.19 ± 0.09 (3He,t) IVSGDR 0.27 ± 0.07
Pygmy dipole resonance 0.19 ± 0.05 (p,p) 295 MeV 0.185 ± 0.05 AGDR - present result 0.21 ± 0.05
ANTI-ANALOG GDR AND NEUTRON-SKIN THICKNESS
TEST CASE: 124Sn
CONCLUDING REMARKS
ü We have established self-consistent framework based on the relativistic nuclear energy density functional to describe
� neutrino-nucleus cross sections, both for neutral-current and charged current reactions
� electron capture rates at finite temperature
o Includes complete set of transition operators and transitions of all relevant multipoles (forbidden transitions)
o This framework allows universal modeling of neutrino-nucleus cross sections (OPb pool completed), electron capture rates, and beta decays
ü Studies (both theoretical and experimental) of dipole polarizability and AGDR provide useful constraints on the nuclear symmetry energy and neutron skin thickness
NEUTRINO-NUCLEUS REACTIONS:
● N. Paar, T. Suzuki, M. Honma, T. Marketin, and D. Vretenar, PRC 84, 047305 (2011).
● A. R. Samana, F. Krmpotic, N. Paar, C. A. Bertulani, PRC 83, 045807 (2011).
● H. Đapo, N. Paar, PRC 86, 035804 (2012).
● N. Paar, H. Tutman, T. Marketin, T. Fischer, submitted to PRC (2012). ELECTRON CAPTURE: ● Y. F. Niu, N. Paar, D. Vretenar, and J. Meng, PRC 83, 045807 (2011).
● A. F. Fantina, E. Khan, G. Colo, N. Paar, and D. Vretenar, PRC 86, 035805 (2012).
NEUTRON-SKIN THICKNESS & SYMMETRY ENERGY:
● J. Piekarewicz et al., PRC 85, 041302(R) (2012).
● A. Krasznahorkay, N. Paar, D. Vretenar, M. Harakeh, submitted to PLB (2012).
ACKNOWLEDGEMENTS & PUBLICATIONS
0 10 20 30 40 500.01
0.1
1
10
Exp.
DD-ME2
GXPF1J
Ex[MeV]
B(GT- )
Gamow-Teller (GT) transitions calculated in two models: �RQRPA (DD-ME2) �Shell model (GXPF1J) T. Suzuki et al.
Shell model includes important correlations among nuclei, accurately reproduces the experimental GT strength. However, already in medium mass nuclei the model spaces become large, many nuclei and forbidden transitions remain beyond reach. RQRPA reproduces total GT strength and global properties of transition strength. Allows systematic calculations of high multipole excitations (forbidden transitions), enables extrapolations toward nuclei away from the valley of stability.
GAMOW-TELLER TRANSITION STRENGTH FOR 56Fe
Recommended