Extension of Λ <i>NN</i> → <i>NNN</i> Weak Interactions and the Two-Nucleon Induced Hypernuclear Nonmesonic Decays: Roles of Strange-Meson and Δ 33-Induced (ρρ)-Pair Exchanges

Abstract In the preceding paper we introduced three-body $\Lambda NN \rightarrow NNN$ weak interactions and proposed a framework to deduce the effective two-body $\Lambda N \rightarrow NN$ potentials to be used for estimates of nonmesonic decay rates of hypernuclei. In order to complete the framework, here we extend the treatment to include new diagrams arising from strange-meson exchanges and the $\Delta _{33}$-isobar induced $(\rho \rho )$-pair exchange. Thus we present new forms of the $V^{(\text {eff.2B})}_{(K \pi )\kappa }$, $V^{(\text {eff.2B)}}_{(K \pi )K^{*}}$, and $V^{(\text {eff.2B})}_{D33(\rho \rho )}$ potentials. By adding these potentials to the previous ones, we investigate in full the roles of various types of effective $\Lambda N \rightarrow NN$ potentials in the estimates of two-nucleon induced nonmesonic decays. It is shown that the destructive interference of the tensor forces between the strange-meson-exchange potentials and the non-strange-meson-exchange ones is particularly important in reducing the theoretical two-nucleon induced nonmesonic decay rates. The potential $V^{(\text {eff.2B})}_{D33(\rho \rho )}$ is weak in comparison with $V^{(\text {eff.2B})}_{\rm FM(\pi \pi )}$. The full terms of the potentials have features of strong central, moderately strong, or weak tensors, and weak parity-violating vector forces. Erroneous overestimates of the decay rates reported in the previous paper are corrected, and new numbers calculated with the full terms are presented for the two-nucleon induced decay rates of the $^5_\Lambda {\rm He}$, $^{11}_\Lambda {\rm B}$, and $^{12}_\Lambda {\rm C}$ hypernuclei, which are comparable to the experimental data.