Shell model formalism for all hypernuclei types: A guide to solving the nonmesonic weak decay puzzle

C. BARBERO, A. MARIANO, A. SAMANA

physical review C

American Physics Society

Año: 2008 vol. 78 p. 1 - 8

1089-490X

We extend to the case of odd-odd core hypernuclei theshell model (SM) formalism we have developed previously for theevaluation of the hypernuclear weak decay observables,$Gamma_{NM}$, $Gamma_{n/p}$ and $a_Lambda$. Our treatmentreproduce the even-odd and even-even core results as particularcases. Adopting the standard strangeness-changing weak $LambdaN o NN$ transition potential which includes the exchange of thecomplete pseudoscalar and vector meson octets($pi,eta,K, ho,omega,K^*$) we get simple expressions for allobservables. We obtain the numerical values for $^{4}_LambdaHe$, $^{5}_Lambda He$, $^{11}_Lambda B$, $^{12}_Lambda C$,$^{16}_Lambda O$, $^{17}_Lambda O$ and $^{28}_Lambda Si$hypernuclei and compare with experimental data.%We show that the contribution of the $1p_{3/2}$, $1p_{1/2}$, $1d_{5/2}$, $cdots$ single particle states%is proportional to that of the $1s_{1/2}$ one. ThusBecause of actual status of the nonmesonic hypernuclear weakdecay problem, a special attention is paid to the asymmetryparameter. We remark that, in the present form, the SM givesroughly the same value of $a_Lambda$ for all hypernucleus incontradiction with experiments. It is stressed the necessityof including, within the SM framework, the effects of: i)two-nucleon induced decay, ii) $Delta T=3/2$ contribution of vector mesons, and iii) final state interactions, as possible ways to solve the puzzle.