{sigma} exchange in the nonmesonic decays of light hypernuclei and violation of the {delta}I=1/2 rule

Nonmesonic weak decays of s-shell hypernuclei are analyzed in microscopic models for the $\ensuremath{\Lambda}N\ensuremath{\rightarrow}NN$ weak interaction. A scalar-isoscalar meson \ensuremath{\sigma} is introduced, and its importance in accounting for the decay rates, $n/p$ ratios, and proton asymmetry is demonstrated. Possible violation of the $\ensuremath{\Delta}I=1/2$ rule in the nonmesonic weak decay of the \ensuremath{\Lambda} is discussed in a phenomenological analysis, and several useful constraints are presented. The microscopic calculation shows that the current experimental data indicate a large violation of the $\ensuremath{\Delta}I=1/2$ rule, although no definite conclusion can be derived because of the large ambiguity of the decay rate of ${}_{\ensuremath{\Lambda}}^{4}H$.