Pionic Decay Modes of LightΛHypernuclei

Decay probabilities are calculated for pionic modes of decay of the $\Lambda$ hypernuclei $A<~5$. An effect of the Pauli principle omitted in previous calculations for the two-body ${\pi }^{-}$ and ${\pi }^0$ modes is now included. An estimate for the total decay probability of all ${\pi }^{-}$ (or ${\pi }^0$) modes based on the completeness relation is checked by comparison with calculations based on detailed models of the decay process for two particular systems. As a result, the present data on ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^4{}_{}{}^{}$ decay are now consistent with either (a) spin $J=0\mathrm{}$ for any value $\frac{p}{s}$ less than 1.5, or (b) spin $J=1\mathrm{}$ for any value $\frac{p}{s}$ greater than 1.2, a much weaker conclusion than that reached previously. In either case, if the $\Delta T=\frac{1}{2}$ rule is roughly correct for $\Lambda$ decay, the two-body mode ${\pi }^0+\alpha$ will be prominent among ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^4{}_{}{}^{}$ decay modes. The $\frac{{\pi }^0}{{\pi }^{-}}$ ratio will then be large (∼1.5) for ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^4{}_{}{}^{}$ decay and small ($\sim \frac{1}{6}$) for ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^4{}_{}{}^{}$ decay, compared with the value ∼½ for ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^5{}_{}{}^{}$ and ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ decay.