Relationships between nonmesonic-weak-decays in different hypernuclei

Using as a tool the s-wave approximation (sWA), this work demonstrates that the nonmesonic weak decay transition rates $Γ_{n}$ and $Γ_{p}$ can be expressed in all hypernuclei up to $^{29}_Λ$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. $^5_Λ$He, $^7_Λ$Li, $^9_Λ$Be, $^{11}_Λ$B, $^{13}_Λ$C, $^{17}_Λ$O, $^{29}_Λ$Si, etc should roughly have the same ratio $Γ_{n}/Γ_{p}$, 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).

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