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

Abstract

We extend to odd-odd core hypernuclei our independent particle shell model (IPSM) formalism developed previously for the evaluation of the ${\ensuremath{\Gamma}}_{\mathrm{NM}},{\ensuremath{\Gamma}}_{n/p}$, and ${a}_{\ensuremath{\Lambda}}$ hypernuclear weak decay observables. The present procedure reproduces the even-odd and even-even core results as particular cases. Adopting the standard strangeness-changing weak $\ensuremath{\Lambda}N\ensuremath{\rightarrow}\mathit{NN}$ transition potential with exchange of the complete pseudoscalar and vector meson octets ($\ensuremath{\pi},\ensuremath{\eta},K,\ensuremath{\rho},\ensuremath{\omega},{K}^{*}$) we get simple analytical expressions for all observables. Numerical values for ${}_{\ensuremath{\Lambda}}^{4}\mathrm{He},{}_{\ensuremath{\Lambda}}^{5}\mathrm{He},{}_{ \ensuremath{\Lambda}}^{11}\mathrm{B},{}_{ \ensuremath{\Lambda}}^{12}\mathrm{C},{}_{ \ensuremath{\Lambda}}^{16}\mathrm{O},{}_{ \ensuremath{\Lambda}}^{17}\mathrm{O}$, and ${}_{\ensuremath{\Lambda}}^{28}\mathrm{Si}$ hypernuclei are obtained and compared with available experimental data, putting special attention on the asymmetry parameter. We remark that, in the present form, the IPSM gives roughly the same value of ${a}_{\ensuremath{\Lambda}}$ for all hypernuclei in contradiction with experiments. We stress the necessity of introducing configuration mixing to go beyond the IPSM taking into account, in a more realistic way, nuclear structure effects. Moreover, one could to include more relevant degrees of freedom, even within the IPSM framework, like: (i) modifications of the exchange potential (two-pion, ${a}_{1}$ meson, $\ensuremath{\Delta}T=3/2$ terms of vector mesons, etc.), (ii) final state interactions accounting for the distortion of the plane waves of emitted nucleons, and (iii) two-nucleon induced decay, as possible ways to solve the puzzle.