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