Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei

TL;DR

This paper develops a relativistic model for the nonmesonic weak decay of single-lambda hypernuclei, providing results that align well with experimental data and improving upon previous theoretical approaches.

Contribution

It introduces a relativistic formalism within the independent-particle shell model for hypernuclear decay, extending the theoretical framework for future charmed nuclei studies.

Findings

Relativistic results agree with nonrelativistic calculations.

The ratio Γₙ/Γₚ is higher and closer to experimental values.

The model reproduces recent experimental data effectively.

Abstract

Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay of single-$\Lambda$ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the $(\pi,K)$ one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of ${}^{12}_{\Lambda}\textrm{C}$ are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the most noteworthy difference is that the ratio $\Gamma_{n}/\Gamma_{p}$ is appreciably higher and closer to the experimental value in the relativistic calculation. Large discrepancies between ours and previous relativistic calculations are found, for which we do not encounter any fully satisfactory explanation. The most recent experimental data is well reproduced by our results. In summary, we have achieved our purpose to develop a reliable model for the relativistic calculation of the nonmesonic weak decay of $\Lambda$-hypernuclei, which can now be extended to evaluate similar processes in charmed nuclei.