Relationships between nonmesonic-weak-decays in different hypernuclei

TL;DR

This work uses the s-wave approximation to relate nonmesonic weak decay rates across various hypernuclei, predicting consistent decay rate ratios for stable nuclei and variations near neutron or proton drip-lines.

Contribution

It demonstrates that decay rates in hypernuclei up to silicon can be expressed using a simple linear combination, enabling analytic predictions of decay ratios across different nuclei.

Findings

Decay rates can be expressed as a linear combination of three elementary rates.

Hypernuclei on the stability line have similar decay rate ratios.

Ratios vary significantly near neutron and proton drip-lines.

Abstract

Using as a tool the s-wave approximation (sWA), this work demonstrates that the nonmesonic weak decay transition rates $\Gamma_{n}$ and $\Gamma_{p}$ can be expressed in all hypernuclei up to $^{29}_\Lambda $Si (and very likely in heavier ones too) in the same way as in the s-shell hypernuclei, i.e. as a linear combination of only three elementary transition rates. This finding leads to the analytic prediction that, independently of the transition mechanism, all hypernuclei that are on the stability line (N = Z), i.e. $^5_\Lambda $He, $^7_\Lambda $Li, $^9_\Lambda $Be, $^{11}_\Lambda$B, $^{13}_\Lambda $C, $^{17}_\Lambda $O, $^{29}_\Lambda $Si, etc should roughly have the same ratio $\Gamma_{n}/\Gamma_{p}$, the magnitude of which rapidly increases when one approaches the neutron drip-line (N >> Z), and opposite happens when one goes toward the proton drip-line (N << Z).