Download Shell-Model calculations for astrophysics

Shell-Model calculations for
astrophysics
Gabriel Martı́nez Pinedo
Institut d’Estudis Espacials de Catalunya
K. Langanke (Århus)
D. J. Dean (ORNL)
E. Caurier (Strasbourg)
J. Sampaio (Lisbon)
A. Juodagalvis (ORNL)
F. Nowacki (Strasbourg)
M. Rampp (Garching)
W. R. Hix (ORNL)
O. E. B. Messer (ORNL)
H.-Th. Janka (Garching)
A. Mezzacappa (ORNL)
M. Liebendörfer (Toronto)
P. von Neumann-Cosel (Darmstadt)
A. Richter (Darmstadt)
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 1
Semileptonic Weak Processes in Stars
kλ
νλ
1111
0000
0000
1111
0000
1111
0000
1111
e−
orbital
e−
e− capture
qλ = νλ − kλ
e−
e−
−
+
β decay
1111e
0000
0000
1111
0000
1111
−
−
111
000
000
111
000
111
νl
l
−
111
000
000
111
000
111
kλ
1111
0000
0000
1111
0000
1111
−
νl
l
OF ∼ eiqr τ
OGT ∼ eiqr στ
l+
−
νl
νλ
+
1111
0000
0000
1111
0000
1111
ν′l
νl
νλ
ν′λ
1111
0000
0000
1111
0000
1111
0000
1111
−
ν′l
−
νl
νλ
(anti)neutrino capture (anti)neutrino scattering
kλ
bound-state β decay continuum charged (anti)lepton capture
qλ = νλ + kλ
νl
kλ
νλ
νλ
kλ
l−
νλ
qλ = νλ + kλ
νλ
−
νe
111
000
000
111
000
111
000
111
β decay
qλ = νλ + kλ
ν′λ
kλ
νe
111
000
000
111
000
111
000
111
111
000
000
111
000
111
kλ
νλ
e+
−
000 νe
111
νe
kλ
νλ
qλ = kλ − νλ
qλ = ν′λ − νλ
qλ = νλ − kλ
• Low energies (. 20 MeV), rates are sensitive to
nuclear correlations. The model of choice is the
shell-model, guided by experimental information.
• At intermediate energies, rates are determined by
excitations of collective resonances. RPA or the
continuum RPA are the methods of choice.
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 2
Presupernova Evolution
• T = 0.1–0.8 MeV, ρ = 107 –1010 g cm−3 .
Composition of iron group nuclei (A = 45–65)
• Important processes:
➢ electron capture:
e− + (N, Z) → (N + 1, Z − 1) + νe
➢ β − decay:
(N, Z) → (N − 1, Z + 1) + e− + ν̄e
• Dominated by allowed transitions (Fermi and
Gamow-Teller).
• GT resonance determined by charge exchange
reactions: (n, p) (TRIUMF), (d, 2 He) (KVI),
(t, 3 He) (MSU)
Methods for determining rates:
• Independent Particle Model (Fuller, Fowler, & Newman, 1982–1985).
• Shell-Model Diagonalization Calculations (Langanke & Martínez-Pinedo,
2001). Calculations possible for all pf-shell nuclei. Maximum dimension 109
slater determinants.
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 3
Stellar EC rates
11111
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11111
000000
111111
00000
11111
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111111
00000
11111
000000
111111
00000
11111
000000
111111
00000
11111
000000
111111
00000
11111
000000
111111
00000
11111
000000
111111
00000
11111
000000
111111
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11111
000000
111111
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111111
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111111
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111111
000000
111111
15
15
10
• Location GT resonance
10
• Fragmentation over excitation
energy
Supernova
5
0
5
• Total GT Strength
0
Gamow−Teller
Resonance
electron
distribution
(Z−1,A)
(Z,A)
0
even-even
1
0
1
0
2 3 4 5 6 7 8 9
FFN GT resonance energy (MeV)
1
0
even neutrons
LMP
FFN
10
10
ρ7=10.7
10
55
0
10
Co
57Fe
0 1 2 3 4 5 6 7 8 9
FFN GT resonance energy (MeV)
10
ρ7=4.32
10
54
60
Mn
Co
0
10
10
10
10
10
10
ρ7=33
10
10
ρ7=10.7
1
4
7
T9
Japanese-German Nuclear Structure and Astrophysics Workshop
Co
10
10
odd neutrons
ρ7=4.32
10
10
10
53Cr
59
10
10
61Ni
Ni
10
10
odd A
56
1
1
2
4
4
3
2
1
3
2
15
6
3
9
6
4
26
5
4
3
2
1
3
2
1
odd-odd
8
7
6
5
4
3
2
10
Fe
10
−1
8
7
6
5
4
3
2
10
λec (s )
even A
SM GT resonance centroid (MeV)
SM GT resonance centroid (MeV)
SM and FFN comparison
56
from:
Langanke, Martinez-Pinedo
Nucl.Phys. A 673, 481 (2000)
10
10
10
1
ρ7=33
4
7
10
T9
Shell-Model calculations for astrophysics – p. 4
Experimentally known GT+ strengths
Nucleus Uncorrelated
51
V
54
Fe
55
Mn
56
Fe
58
Ni
59
Co
62
Ni
20
Ne
5.15
10.19
7.96
9.44
11.9
8.52
7.83
5.0
Correlated
Unquenched Q = 0.74
2.42
5.98
3.64
4.38
7.24
3.98
3.65
0.55
Japanese-German Nuclear Structure and Astrophysics Workshop
1.33
3.27
1.99
2.40
3.97
2.18
2.00
0.30
Expt.
1.2 ± 0.1
3.3 ± 0.5
1.7 ± 0.2
2.8 ± 0.3
3.8 ± 0.4
1.9 ± 0.1
2.5 ± 0.1
0.400 ± 0.017
Shell-Model calculations for astrophysics – p. 5
51
Shell-Model vs experiment ( V)
C. Baümer et al. PRC 68, 031303 (2003)
10−2
LMP
(d,2He)
0.4
10−4
51V(d,2He)51Ti
0.3
λ (s−1)
B(GT+)
10−3
10−5
1.4
1.2
10−6
0.2
1
0.8
10−7
0.1
0.6
0
10
2
4
6
8
10
−8
0
2
4
6
8
10
T (109 K)
Old (n, p) data
0.1
0.5
51
V(n,p) Alford et al. (1993)
0.4
0.3
large shell model
calculation
B(GT+)
B(GT+)
0.2
0.4
0
1
2
3
4
5
6
7
Ex [MeV]
0.3
0.2
0.1
0
Japanese-German Nuclear Structure and Astrophysics Workshop
0
2
4
6
8
10
Shell-Model calculations for astrophysics – p. 6
58
Shell-Model vs experiment ( Ni)
M. Hagemann, et al., PLB 579, 251 (2004)
10−1
+
(d,2He)
KB3G
LMP
FFN
GXPF1
Experiment: Bexp(GT )
2
(d, He) 170 MeV
idem binned per 1 MeV
(n,p) 198 MeV
10−2
λec (s−1)
1.0
GT strength
0.5
0.0
10−3
10−4
0.5
10−5
101
+
Theory: Bth(GT )
1.0
this work KB3G
Caurier et al.
0
2
4
6
8
10
Ex (MeV)
λec/λec,exp
1.5
GT Strength
Expt.
KB3G
GXPF1
1.0
100
0.5
0.0
0
10−1
2
4
6
Energy (MeV)
8
10
Japanese-German Nuclear Structure and Astrophysics Workshop
2.0
4.0
6.0
T (10 K)
8.0
9
Shell-Model calculations for astrophysics – p. 7
Collapse phase
Important processes:
• Neutrino transport (Boltzmann
equation):
ν + A ⇄ ν + A (trapping)
ν + e− ⇄ ν + e− (thermalization)
cross sections ∼ Eν2
• electron capture on protons:
e− + p ⇄ n + νe
What is the role of electron capture on nuclei?
e− + (N, Z) ⇄ (N + 1, Z − 1) + νe
What is the role of inelastic neutrino-nucleus scattering?
ν + A ⇄ ν + A∗
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 8
Collapse abundances
3
T= 17.84 GK, ρ= 3.39e+11 g/cm , Ye=.0.379
Z (Proton Number)
40
30
20
Log (Mass Fraction)
10
−5
−4
−3
−2
0
0
10
20
30
40
50
60
N (Neutron Number)
Japanese-German Nuclear Structure and Astrophysics Workshop
70
80
90
Shell-Model calculations for astrophysics – p. 9
Blocking electron capture at N=40
• Standard treatment of weak interaction
rates (Bruenn 85): Electron capture on
nuclei suppressed for N ≥ 40. Electron
capture takes place only in protons.
g9/2
N=40
Blocked
GT
f5/2
p1/2
p3/2
f7/2
neutrons
protons
111111111111
000000000000
Core
000000000000
111111111111
000000000000
111111111111
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 10
Unblocking electron capture at N=40
• Standard treatment of weak interaction
rates (Bruenn 85): Electron capture on
nuclei suppressed for N ≥ 40. Electron
capture takes place only in protons.
g9/2
Unblocked
Correlations
Finite T
• Unblocking due to finite temperature
(Fuller 1982, Cooperstein & Wambach
1984) and Correlations.
p1/2
• Electron capture rates computed ShellModel Monte Carlo plus RPA calculations.
f7/2
GT
f5/2
p3/2
neutrons
protons
111111111111
000000000000
Core
000000000000
111111111111
000000000000
111111111111
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 11
Electron capture: nuclei vs protons
Energetics
Electron capture rates
40
106
105
104
30
101
1
H
68
Ni
69
Ni
76
Ga
79
Ge
89
Br
100
10
10
10
10
10
1010
1011
µe
20
Qp
1012
0
ρ (g cm )
1010
1011
ρ (g cm−3)
1012
Abundances
0
Yn
P
Yh
10−2
Rh = i Yi λi = Yh hλh i
R p = Yp λ p
Yα
10
〈Q〉 = µn−µp
10
−3
10−1
Abundance
(MeV)
102
2
1
4
3
λec (s−1)
103
−3
Yp
10−4
10−5
1010
1011
1012
ρ (g cm−3)
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 12
Reaction rates
104
103
30
〈Eνe〉 (MeV)
Rec (s−1)
102
101
100
10−1
10
10−2
protons
nuclei
protons
nuclei
10−3
10−4
20
1010
1011
ρ (g cm−3)
1012
0
1010
1011
ρ (g cm−3)
1012
Electron capture on nuclei dominates over capture on protons
Langanke,et al., PRL 90, 241102 (2003).
Hix, et al., PRL 91, 201102 (2003)
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 13
Consequences
With Rampp & Janka (General Relativistic model)
15 M⊙ presupernova model from A. Heger & S. Woosley
0.30
0.25
2.0
s
1.5
1.0
11
10
12
10
10
ρc (g cm−3)
14
10
0.0 10
10
103
50
102
40
1
10
30
20
0
10
Bruenn
LMSH
13
104
10
0.5
Bruenn Y
e
LMSH
Bruenn
LMSH
〈Eν〉 (MeV)
0.35
105
Eν−emission (MeV s−1)
sc (kB), Tc (MeV)
Ylep
Ye,c, Ylep,c
T
2.5
0.40
0.20 10
10
106
3.0
0.45
11
10
0
1010
1012
1014
ρc (g cm−3)
12
10
13
10
ρc (g cm−3)
Japanese-German Nuclear Structure and Astrophysics Workshop
14
10
10−1 10
10
1011
1012
1013
ρc (g cm−3)
1014
Shell-Model calculations for astrophysics – p. 14
Neutrino interactions in the collapse
• Elastic scattering:
ν + A ⇄ ν + A (trapping)
• ν-e scattering:
ν + e− ⇄ ν + e− (thermalization)
• Absorption:
νe + (N, Z) ⇄ e− + (N − 1, Z + 1)
• Inelastic ν-nuclei scattering:
ν + A ⇄ ν + A∗
➢ Currently not considered in collapse simulations.
➢ Cross sections determined by Gamow-Teller (Shell-Model)
plus Forbidden (RPA) transitions.
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 15
′
Neutrino Scattering from (e, e )
E*
(v, v'), GT0
(e, e'), M1
S
ISOVECTOR
PIECE
DOMINATES
S
L
T(GT0) ~ Σtz(i)Si
i
T(M1) =
1
2
(L p - L n)+(gp - gn)Σ tz(i)Si µN
i
M1 data give GT0 information
if Orbital contribution can be removed
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 16
′
Neutrino Scattering from (e, e )
DECOMPOSITION OF
M1 STRENGTH
(SHELL MODEL)
M1 DATA
(A. Richter)
0.3
Orbital
0.2
0.1
B(M1) (µN2)
0
Spin
0.6
0.4
0.2
0
Total
0.6
0.4
0.2
0
0
5
10
15
20
E (MeV)
USUALLY ORBITAL AND SPIN PARTS WELL SEPARATED
Usually orbital and spin parts well separated.
Spherical nuclei: Orbital part strongly suppressed.
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 17
′
Neutrino Scattering from (e, e )
0.1
0.08
52
Orbital
Cr
0.06
E
E
0.04
0.02
0
1.5
GT0 resonance
ν
ν′
Spin
Finite T
2
B(M1) (µN)
1.0
Nν
0.5
0.0
1.5
103
Total
10
σ (10−42 cm2)
1.0
0.5
0.0
1.5
(Z,A)
Expt.
52
Cr
Only GS (SDalinac data)
Only GS (Theory)
T = 0.8 MeV
2
101
100
10−1
10−2
1.0
10−3
0.5
10−4
0
0.0
5
10
15
20
25
30
35
40
Neutrino Energy (MeV)
6
8
10
12
14
Excitation Energy (MeV)
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 18
Neutrinos from supernovae
Neutrino emission after bounce:
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 19
Neutrino nucleosynthesis
A. Heger et al, astro-ph/0307546
p
12
′ 11
C(ν, ν p) B
12
C(ν, ν ′ n)11 C
Product
11
B
19
F
138
La
ν′
ν
ν
180
ν′
Ta
Parent
12
C
20
Ne
138
Ba
139
La
180
Hf
181
Ta
Reaction
(ν, ν ′ n), (ν, ν ′ p)
(ν, ν ′ n), (ν, ν ′ p)
(νe , e− )
(ν, ν ′ n)
(νe , e− )
(ν, ν ′ n)
n
• Improved treatment progenitor
star evolution.
• Reaction network extended from
zinc to bismuth.
• Improved treatment of spallation
cross sections.
101
Production Factor relative to 16O
Improvements over Woosley et
al. (1990) classical work:
100
10−1
15 M⊙ without ν
15 M⊙ with ν
25 M⊙ without ν
25 M⊙ with ν
10−2
10−3
Japanese-German Nuclear Structure and Astrophysics Workshop
11
B
19
F
138
La
180
Ta
Shell-Model calculations for astrophysics – p. 20
20
GT Strength in Ne
0.2
Exp
0.2
SM
GT Strength
0.15
0.1
0.1
0
0.05
−0.1
0
[Y2⊗σ]1
−0.05
0
4
8
12
−0.2
16
Energy (MeV)
Japanese-German Nuclear Structure and Astrophysics Workshop
GTeff
0
4
8
12
16
Energy (MeV)
Shell-Model calculations for astrophysics – p. 21
Conclusions
• Electron capture on nuclei dominates over electron capture on
protons during the collapse.
• Neutrino-nucleus inelastic scattering important for supernova
dynamics, iron group nucleosynthesis, neutrino
nucleosynthesis, . . .
• Cross-sections can be determined from (e, e′ ) or (p, p′ ) data.
In N = Z nuclei also by charge exchange reactions.
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 22
Presupernova abundances
3
T= 9.01 GK, ρ= 6.80e+09 g/cm , Ye=.0.433
Z (Proton Number)
40
30
20
10
Log (Mass Fraction)
−5
−4
−3
−2
0
0
10
20
30
40
50
60
N (Neutron Number)
70
80
90
µe = 7.14 MeV
Japanese-German Nuclear Structure and Astrophysics Workshop
Shell-Model calculations for astrophysics – p. 23