Nonmesonic weak decay of Lambda-hypernuclei within independent-particle shell-model

TL;DR

This paper investigates the nonmesonic weak decay of Lambda-hypernuclei using independent-particle shell models, analyzing experimental spectra and decay ratios, and finds that phase space kinematics largely explain the observed data with minimal influence from complex interactions.

Contribution

It introduces two versions of the independent-particle shell model to better understand hypernuclear decay spectra and reconcile experimental decay ratios with theoretical predictions.

Findings

Spectra shapes are mainly determined by phase space kinematics.

Good agreement with experimental data achieved using simple models.

The $ ext{π+K}$ exchange potential with soft form factors explains decay ratios.

Abstract

After a short introduction to the nonmesonic weak decay (NMWD) $\Lambda N\go nN$ of $\Lambda$-hypernuclei we discuss the long-standing puzzle on the ratio $\Gamma_n/\Gamma_p$, and some recent experimental evidences that signalized towards its final solution. Two versions of the Independent-Particle-Shell-Model (IPSM) are employed to account for the nuclear structure of the final residual nuclei. They are: (a) IPSM-a, where no correlation, except for the Pauli principle, is taken into account, and (b) IPSM-b, where the highly excited hole states are considered to be quasi-stationary and are described by Breit-Wigner distributions, whose widths are estimated from the experimental data. We evaluate the coincidence spectra in $^{4}_\Lambda$He, $^{5}_\Lambda$He, $^{12}_\Lambda$C, $^{16}_\Lambda$O, and $^{28}_\Lambda$Si, as a function of the sum of kinetic energies $E_{nN}=E_n+E_N$ for $N=n,p$. The recent Brookhaven National Laboratory experiment E788 on $^4_\Lambda$He, is interpreted within the IPSM . We found that the shapes of all the spectra are basically tailored by the kinematics of the corresponding phase space, depending very weakly on the dynamics, which is gauged here by the one-meson-exchange-potential. In spite of the straightforwardness of the approach a good agreement with data is achieved. This might be an indication that the final-state-interactions and the two-nucleon induced processes are not very important in the decay of this hypernucleus. We have also found that the $\pi+K$ exchange potential with soft vertex-form-factor cutoffs $(\Lambda_\pi\approx 0.7$ GeV, $\Lambda_K\approx 0.9$ GeV), is able to account simultaneously for the available experimental data related to $\Gamma_p$ and $\Gamma_n$ for $^4_\Lambda$H, $^4_\Lambda$He, and $^5_\Lambda$He.