with realistic NN forces

Transcription

1 2νββ decay of deformed nuclei with realistic NN forces Vadim Rodin Amand Faessler, Mohamed Saleh Yousef, Fedor Šimkovic NOW 28, Conca Specchiulla, 9/9/28

2 Introduction Nuclear νββ-decay ( ν=ν) e - Light neutrino exchange mechanism continuum A,Z n n _ ν ν p p A,Z+2 e (A,Z) (A,Z+1) + virtual excitation of states of all multipolarities in (A,Z+1) nucleus (A,Z+2)

3 Introduction Nuclear 2νββ-decay second order weak process within SM n _ ν e - p A,Z n p A,Z+2 _ ν e -

4 Introduction measured T 2ν 1/2 Isotope (compilation of A. Barabash, 25) T 2ν 1/2, in 119 y 48 Ca Ge 15±1 82 Se 9.2±.7 96 Zr 2.±.3 1 Mo.71± Cd 3.± Te (2.5±.3) Te 9±1 136 Xe > 81 (9% CL) 15 Nd.78± U 2±6

5 2νββ νββ Inverse Half-Lives [T 1/2 ( + + )] 1 G 2ν (Q, Z) M 2ν GT 2 m 2 ββ Gν (Q, Z) Mν GT g2 V M g 2 F ν A Eff. neutrino mass m ββ = m j Ue 2 j U e j first raw of the neutrino mixing matrix j 2

6 2νββ νββ Nuclear Matrix Elements M 2ν GT = Mν GT = s f ˆβ s s ˆβ i E s (M i + M f )/2 ˆβ = σ k τ k k f ik P ν (r ik, ω)τ i τ k σ i σ k i Neutrino potential : P ν (r, ω)= 2R πr dq q sin(qr) ω(ω+ ω) R r φ( ωr)

7 Introduction V.R., A. Faessler, F. Simkovic, P. Vogel, PRC 68 (23); NPA 766 (26); NPA 793 (27) g pp fitted to 2νββ-decay half-life stable M ν νββ half-lives T ν 1/2 (in years) assuming m ββ =5 mev. Transition M ν T ν 1/2 76 Ge 76 Se Se 82 Kr Te 13 Xe Nd 15 Sm strongly deformed SM (Nowacki 4): you can forget about it! SNO+ (& SuperNEMO):.1% of nat Nd 56 kg of 15 Nd m ββ.1 ev But: M ν = 1.57 pseudo-su(3) model of Hirsch et al. NPA582 (1995) M ν = 1.61 projected HFB appr. of K. Chaturvedi et al. arxiv: [nucl-th]

8 QRPA in deformed nuclei 2νββ in deformed nuclei; QRPA with schematic separable forces F. Šimkovic, L. Pacearescu, A. Faessler, NPA 733 (24) R. Alvarez-Rodriguez et al., PRC 7 (24) QRPA with realistic forces in deformed nuclei (νββ of 15 Nd) applied first to 2νββ (PhD thesis of M. Saleh Yousef) M. Saleh Yousef, V.R., A. Faessler, F. Šimkovic arxiv: [nucl-th] νββ (PhD thesis of D. Fang, work in progress)

9 QRPA in deformed nuclei Basic relationships 1M(K), m = 1M(K), m = 3 16π 2[D1 MK (φ,θ,ψ)q m,k + ( 1)1+K D 1 M K (φ,θ,ψ)q m, K ] + g.s. (K=±1), 3 8π 2D1 MK (φ,θ,ψ)q m,k + g.s. (K= ) M 2ν GT = K=,±1 m i m f + f β K K+, m f K +, m f K +, m i K +, m i β K + i ω K,mi m f case I (shifted QRPA spectrum) ω K,mi m f = (ω K,m f ω K,1 f +ω K,mi ω K,1i )/2+ ω 1 + 1,exp case II (unshifted QRPA spectrum) ω K,mi m f = (ω m f K +ωm i K )/2

10 QRPA in deformed nuclei Deformed Woods-Saxon s.p. wave functions τω τ decomposed over the spherical harmonic oscillator ones ηω τω τ = η B τ η ηω τ ηω = Σ C jω lω Σ 1/2Σ NlΛ=Ω τ Σ Σ is the spherical harmonic oscillator wave function in the j-coupled scheme

11 QRPA in deformed nuclei Two-body deformed wave function p n = Fpη JK p nη n η p η n, JK η p η n,j η p η n, JK = C JK j p Ω p j n Ω n η p Ω p η n Ω n and F JK pη p nη n = B p η p B n η n ( 1) j n Ω n C JK j p Ω p j n Ω n Two-body residual interaction m.e. V p n, p n = 2 Fpη JK p nη n Fp JK η p n η n G(η p η n η p η n, J) V pn, p n = 2 J K pn =Ω p +Ω n =Ω p +Ω n J η p η n η p η n η p η n η p η n F JK pn pη p n η n F JK pn p η p nη n G(η p η n η p η n, J)

12 Results GT strength functions (g ph = 1.15;χ=3.73/A.7 MeV) S(GT - ) Realistic Separable 76 β 76 Ge 2 =. Ge =.1 exp S(GT + ) Se =. 76 Se = E ex [MeV] E ex [MeV]

13 Results Realistic 76 Ge 76 Se Separable M 2ν GT [MeV-1 ] A B A B I M 2ν GT [MeV-1 ] A sph. def. B A B II g pp κ[mev] def.= exp. defor.: ( 76 Ge)=.1, ( 76 Se)=.16 (P. Raghavan, At. Data Nucl. Data Tabl. 42 (1989))

14 Results GT strength functions Realistic Separable S(GT - ) Nd 15 Nd =. =.37 = S(GT + ) Sm 15 Sm =. =.23 = E ex [MeV] E ex [MeV]

15 Realistic Results 15 Nd 15 Sm Separable M 2ν GT [MeV-1 ] M 2ν GT [MeV-1 ] A B C sph. def. (1) def. (2) A B C g pp A B A B C C κ[mev] 1 I II def. (1) exp. defor.: ( 15 Nd)=.37±.9, ( 15 Sm)=.23±.3 (P. Raghavan, At. Data Nucl. Data Tabl. 42 (1989)) def. (2) calc. defor.: ( 15 Nd)=.24, ( 15 Sm)=.21 (P. Moeller et al., At. Data Nucl. Data Tabl. 59 (1995))

16 Conclusions Realistic (G-matrix based) NN interaction is implemented in the QRPA equations for deformed nuclei GT strength functions and 2νββ decay matrix element are calculated for 76 Ge and 15 Nd. Prospect for QRPA calculation of M ν for 15 Nd is opened Supported by: DFG TR27 Neutrinos and beyond and EC