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

C. BARBERO, A. MARIANO Y A. SAMANA

Physical Review C

American Physical Society

Año: 2008 vol. 78 p. 443241 - 443248

0556-2813

We extend to odd-odd core hypernuclei our independent particle shell model (IPSM) formalism developed previously for the evaluation of the $Gamma_{NM}$, $Gamma_{n/p}$ and a_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 $Lambda N o NN$ transition potential with  exchange of the complete pseudoscalar and vector meson octets ($pi,eta,K, ho,omega,K^*$) we get simple analytical expressions for all observables. Numerical values for $^{4}_Lambda He$, $^{5}_Lambda He$, $^{11}_Lambda B$, $^{12}_Lambda C$, $^{16}_Lambda O$, $^{17}_Lambda O$ and $^{28}_Lambda Si$ 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 $a_Lambda$ for all hypernucleus in contradiction with experiments. We stress the necessity of: i) introduce configuration mixing to go beyond the IPSM and take into account in a more realistic way nuclear structure effects, and/or include more relevant degrees of freedom, still within the IPSM framework, like: ii) modifications of the exchange potential (two-pion, $a_1$ meson, $Delta T=3/2$ terms of vector mesons, etc.), iii) final state interactions accounting for the distortion of the plane waves of emitted nucleons, and iv) two-nucleon induced decay, as possible ways to solve the puzzle.