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. 443241 - 443248

We extend to odd-odd core hypernuclei our independentparticle shell model (IPSM) formalism developed previously for theevaluation of the $Gamma_{NM}$, $Gamma_{n/p}$ and $a_Lambda$hypernuclear weak decay observables. The present procedurereproduces the even-odd and even-even core results as particularcases. Adopting the standard strangeness-changing weak $LambdaN o NN$ transition potential with  exchange of the completepseudoscalar and vector meson octets($pi,eta,K, ho,omega,K^*$) we get simple analytical expressions for allobservables. Numerical values for $^{4}_Lambda He$, $^{5}_LambdaHe$, $^{11}_Lambda B$, $^{12}_Lambda C$, $^{16}_Lambda O$,$^{17}_Lambda O$ and $^{28}_Lambda Si$ hypernuclei are obtainedand compared with available experimental data, putting specialattention on the asymmetry parameter. We remark that, in thepresent form, the IPSM gives roughly the same value of $a_Lambda$for all hypernucleus in contradiction with experiments. We stressthe necessity of: i) introduce configuration mixing to go beyondthe IPSM and take into account in a more realistic way nuclearstructure effects, and/or include more relevant degrees offreedom, 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 stateinteractions accounting for the distortion of the plane waves ofemitted nucleons, and iv) two-nucleon induced decay, as possibleways to solve the puzzle.