On the role of ground state correlations in hypernuclear non-mesonic weak decay

TL;DR

This paper investigates how ground state correlations influence the non-mesonic weak decay of hypernuclei, showing they are crucial for accurate decay width predictions and affect decay ratios.

Contribution

It introduces a comprehensive model including ground state correlations at first order, improving the accuracy of decay width and ratio calculations for hypernuclei.

Findings

GSC contribute 14% to the decay rate in $^{12}_\Lambda$C.

GSC increase the $\Gamma_{n}/\Gamma_{p}$ ratio by 4%.

Predicted decay widths and ratios agree well with experimental data.

Abstract

The contribution of ground state correlations (GSC) to the non--mesonic weak decay of $^{12}_\Lambda$C and other medium to heavy hypernuclei is studied within a nuclear matter formalism implemented in a local density approximation. We adopt a weak transition potential including the exchange of the complete octets of pseudoscalar and vector mesons as well as a residual strong interaction modeled on the Bonn potential. Leading GSC contributions, at first order in the residual strong interaction, are introduced on the same footing for all isospin channels of one-- and two--nucleon induced decays. Together with fermion antisymmetrization, GSC turn out to be important for an accurate determination of the decay widths. Besides opening the two--nucleon stimulated decay channels, for $^{12}_\Lambda$C GSC are responsible for 14% of the rate $\Gamma_1$ while increasing the $\Gamma_{n}/\Gamma_{p}$ ratio by 4%. Our final results for $^{12}_\Lambda$C are: $\Gamma_{\rm NM}=0.98$, $\Gamma_{n}/\Gamma_{p}=0.34$ and $\Gamma_2/\Gamma_{\rm NM}=0.26$. The saturation property of $\Gamma_{\rm NM}$ with increasing hypernuclear mass number is clearly observed. The agreement with data of our predictions for $\Gamma_{\rm NM}$, $\Gamma_n/\Gamma_p$ and $\Gamma_2$ is rather good.