Ground state normalization in the nonmesonic weak decay of $^{12}_{\Lambda}C$ hypernucleus within a nuclear matter formalism

TL;DR

This paper evaluates the nonmesonic weak decay width of the $^{12}_{\Lambda}C$ hypernucleus using a nuclear matter formalism, accounting for ground state correlations and two-body induced decay, achieving results consistent with experimental data.

Contribution

It introduces a ground state normalization procedure in the nuclear matter formalism to accurately evaluate decay widths, including two-body induced decay effects.

Findings

The two-body induced decay adds approximately 38% spurious intensity to the decay width.

The calculated decay width (0.956) aligns well with recent experimental data.

Ground state normalization significantly impacts the decay width calculation.

Abstract

The nonmesonic weak decay width of $^{12}_{\Lambda}C$ hypernucleus has been evaluated within a nuclear matter formalism, using the local density approximation. In addition to the one-body induced decay $(\Lambda N \to n N)$, it has been also considered the two-body induced decay $(\Lambda NN \to n N N)$. This second decay is originated from ground state correlations, where a renormalization procedure to ensure a ground state normalized to one has been implemented. Our results show that the plain addition of the two-body induced decay implies a lost in the ground state-norm, which adds $\sim 38%$ of spurious intensity to the nonmesonic weak decay width. By an adequate selection of the $\Lambda N$-transition potential, our result for the nonmesonic weak decay width of $^{12}_{\Lambda}C$ is 0.956, in good agreement with the most recent data.