Evaluation of coincidence number of pairs and asymmetry parameter in nonmesonic hypernuclear decay

TL;DR

This paper develops a theoretical framework to evaluate coincidence numbers and asymmetry parameters in nonmesonic hypernuclear decay, incorporating nuclear medium effects and final state interactions, and compares well with experimental data.

Contribution

The authors introduce a new theoretical approach that includes secondary configurations and nuclear medium effects using an optical potential, improving the modeling of hypernuclear decay observables.

Findings

Good agreement with experimental data for $^{5}_ ext{Lambda}He$ and $^{12}_ ext{Lambda}C$ decays.

The treatment of final state interactions (FSI) within a simplified subspace is effective.

The framework can be extended to include more complex configurations and two-nucleon induced decay contributions.

Abstract

We develop a theoretical framework for the evaluation of the coincidence number of pairs, $N_{nN}$, and the asymmetry parameter, $a_\Lambda$, in nonmesonic hypernuclear decay $\Lambda N\rightarrow nN$. The primary nomesonic weak hyperon-nucleon decay process is described through the independent particle shell model. When the effect of the strong interactions experimented by the two nucleons leaving the residual nucleus is included, we have in addition to the $2p1h$ primary configuration $2p'1h'$, $3p2h$, $4p3h$, $\cdots$, etc secondary ones. We work within the $2p'1h'$ subspace of final states assuming a simple approach for finite nuclei based on the eikonal approximation. An optical potential including the nucleon-nucleus isoscalar and isovector interaction is introduced to take into account the minimum nuclear medium effects and to describe the nucleon-nucleus dispersion process along the outgoing path. We applied the proposed description to the calculation of the observables in $^{5}_\Lambda He$ and $^{12}_\Lambda C$ nonmesonic decays. The calculated results show that our treatment of FSI even considered as restricted to a subspace of states gives a good agreement with experimental data, similar to that ones presented by more elaborated evaluations. This indicates that the developed theoretical scheme seems to be appropriated to include more complex configurations. We also discuss the ground state normalization effects at the moment of including the two-nucleon induced decay ($\Lambda NN \rightarrow nNN$) contribution.