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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 00000 00000 11111 000000 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 00000 11111 000000 111111 00000 11111 000000 111111 000000 111111 000000 111111 000000 111111 000000 111111 000000 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