  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).
