Neutrino-Nucleus Reactions Based on Recent Progress of Shell Model Calculations

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1 Neutrino-Nucleus Reactions Based on Recent Progress of Shell Model Calculations Toshio Suzuki (Nihon University) New shell model calculations in p-shell modified shell model Hamiltonian (SFO) with improved spin-dependent transitions and moments Suzuki, Fujimoto, Otsuka Neutrino-nucleus reactions on 12 C, 4 He Suzuki, S. Chiba (JAEA), O. Iwamoto (JAEA), Kajino (NAO) New shell model Hamiltonian in fp-shell by Honma et al. Neutrino-nucleus reactions on Fe and Ni isotopes Suzuki, Higashiyama, Otsuka, Kajino, Balantekin

2 New Shel-Model interaction in p-shell: SFO Suzuki, Fujimoto & Otsuka, PR C67, (2003) = (0p 1/2 ) (0p 3/2 ) (0.3 MeV 3.92 MeV) V T=0 M n-p spin-flip M=monopole 0p 1/ p 3/2 p n N=8

3 Spin-tensor decomposition of nuclear effective interactions V = k V k k = 0: central, k = 1: spin orbit, k = 2: tensor < abjt V LSJ S' L' k J < a' b' J' T where k cdjt>= ( ) J' LSJ' ( ) (2J' + 1) ' S' L' k V c' d' J' T > a = { n l a a j a }, J (2k + 1) a' = { n l a j' a LLSS ' ' a j j' a b j' c '} < ab LSJ>< cd L' S' J > < a' b' LSJ' >< c' d' L' S' J' > j' d etc.

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5 Effects of Tensor Force on Shell Evolution

6 Effective Single-Particle Energy Neutron E 1s1/2 0p1/2 0p3/2 orbit p E 20 Proton 16 0d3/2 1s1/2 0d5/2 0p1/2 0p3/2 < orbit

7 Energy levels of B and C isotopes

8 B(GT) values for 12 C -> 12 N Magnetic moments of p-shell nuclei present = SFO

9 s.p. [ p 1/2 p 3/2 ] 1 1 (-g / / g Mixing of p1/2 and p3/2

10 Charge-Exchange Neutrino-Nucleus Reactions µ µ µ ν µ µ µ µ + = γ + γ = = A V J u u j J j G H h e h ) ( l l s s r r r r r r r A g A p p m q m i V + + ) ' ( ± W e e n p n

11 Spin-dependent excitations Gamow-Teller (1 + ): Spin-diole (0 -, 1 -, 2 - ): s r t r r [ s r ] J t ± ± Multipoles 1 + : E 5 1, M1, C 5 1, L : E 5 2, M2, C 5 2, L : M 5 1, E1, C1 0 - : C 5 0, L 5 0

12 Folding over neutrino spectrum σ σ E E x x DAR = ( E ) ν e σ + + p m e E m e + n + x ( E ) f ( E ) de d E x = d Ω n n m d spectrum <E( e )> 35 MeV m σ Ω

13 WBT: Warburton-Brown Volpe, Auerbach, Colo, Suzuki, Van Giai, PR C62 (2000) HT: Hayes-Towner, PR C62, (2000) p:cohen-kurath (8-16)2BME, sd: USD of Wildenthal, pf: KB3, p-sd and others: Millener-Kurath SFO*: g eff A /g A =0.95 NCSM: Hayes-Navratil-Vary, PRL 91 (2003) AV8 (2-body) + TM (99) (3-body) CRPA: Kolb-Langanke-Vogel, NP A652, 91 (1999) Allenet.al. (1990) Exp: LSND PR C64 (2001) Exp.

14 Inclusive = Exclusive (1 + ) + Excited state g.s. 3 h w Exp: LSND PR C64 (2001) * 0.75 *0.70

15 Supernovae Spectra E 2 E / T f ( E ) = N <E> & tail part 1+ exp[ E / T a] n m, n t : < 2 3 E >= 25 ( T, a) = ( 8MeV, 0) ( 6. 26MeV, 3) MeV n n e : < E >= 11 MeV ( T, a ) = ( 3. 5MeV, 0 ) e : < E >= 16 MeV ( T, a ) = ( 5MeV, 0 )

16 Charge-exchange Neutral-Current SFO* PSDMK2* SFO* PSDMK2*

17 Proton and eutron emissions BR: Hauser-Feshbach model

18 Spin-dipole strength in 4 He

19 Charge-exchange Neutral-Current

20 K. Yoshida

21 Neutrino Nucleus Reactions on Fe and Ni Isotopes + ( ν, e ), ( ν, e ) Charge-exchange reactions; e e Gamow-Teller transitions GT strength: shell model calculation by Honma Emissions of proton, neutron,, e e e e e ( ν, ep),( ν, en),( ν, eα),( ν, e γ),( ν, epn), + e e e ( ν, epp),( ν, eαp), ( ν, en)

22 New features in GXPF1 by Honma et al. KB3G A = KB + monopole corrections G: improved gap, 3: fine tuning in V fr (A = 50-52) GXPF1 A = More attraction for T=0 m.e. than G-matrix E(1p 3/2 ) E(0f 7/2 ) 3 MeV cf. 2 MeV for KB3, FPD6 New magic number at N = 34 cf. N = 32 for KB3, FPD6 r.m.s deviations from observed values GXPF1 vs KB3G Z, N <28; Z<28, N>28: similar Z or N =28 ( 56 Ni, 55 Co, 57 Ni); Z, N>28: smaller for GXPF1 Core excitations are not well described by KB3G Monopoles GXPF1 vs KB3G 1p-1p part differ GXPF1: not a constant shift (J-dependence) Systematic description of 2 1+ energies in Ni, Ca, Ti, Cr, Fe isotopes cf. KB3G 56 Ni : E cal E exp 2 MeV 56 Ni-core (f 7/2 ) 16 : 69% (GXPF1), 49% (FPD6) B(GT + ): 11.3 (GXPF1), 10.1 (KB3), 13.7 (closed core)

23 Cross Sections for GT (J=1 + ) transitions d σ G cos θ 4π 2 θ ( ) (, ) cos d F C + = E (, e ) (, e ) 2 e p ef Z f E ν ν f Ω π J i + mag 2 el,5 2 { K T ( q, ω )[ < J f T J J i > + < J f T J J i > ] m K TI ( q, ω ) mag el,5 * 2Re[ < J f T J J i >< J f T J J i > ]} el,5 2 1 < J f T J J i > ig A < J f σ j0 ( qr) J i > 3 4π < J f T J mag q IV 2 1 J i > g < J f σ j0 ( qr) J i > 2M 3 4π < J σ j ( qr) J > < J σ J > j ( qr) f 0 i f i 0 1 cf. B ( GT ) = < J f σ J i > 2 J + 1 i q ω 2 θ θ q ω 2 θ K T ( q, ω ) = + tan, K (, ) tan tan 2 TI q ω = + 2 2q 2 2 2q 2 2

24 56 Fe( ν, e ) 56 Co e GXPF1 B(GT) cf. KB3 Caurier et al. Honma et al. GT (mb/sr MeV) B(GT)=9.47 B(GT) exp = B(GT) KB3 =8.85

25 DAR GXFP1 cf. KB3 Kolb, Langanke, Martinez-Pinedo σ σ = exp cm ( GT ) = 2.56 ± 1.08± 0.43cm B( GT) = σ = cm ( GT ) B( GT ) = 8.85

26 56 (, ) 56 e Feν e Co B(GT) GXPF1 Honma et al. T=8 MeV 56 Fe

27 Fe, Ni Isotopes q=(0.74) 2 for GT (Honma) Woosley, Kolb-Langanke: GT + 0 -,1 -,2 -,0 +,2 + GXPF1(Honma et al.): GT only

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29 B(GT)=2.9 GXPF1 2.7 KB EXP cf σ = fm ( total; GT +...) (Kolb, Langanke)

30 B(GT) for 58Ni

31 T= 6 MeV

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40 1. P-shell SFO BGT ( ) σν (, e) ( νν, ' n) Summary 2. fp-shell GXPF1 BGT ( ), more fragmented, σν (, e) e-capture and -decay rates steller core collapse and supernovae explosion mechanism Remaning issues: Inclusion of spin-dipole contributions Study of effects of n from ( ν, en) (n, ) in r-process in stars