Effective two-body ΛN → NN weak potentials deduced from three-body ΛNN → NNN interactions and hypernuclear non-mesonic weak decay rates

Abstract

Abstract We intend to study the role of the three-body weak ΛNN → NNN interaction in two-nucleon induced hypernuclear non-mesonic weak decay. The three-body weak interactions are constructed on the basis of the meson-pair exchange (MPE) model and then we derive the effective two-body ΛN → NN weak potentials from the three-body interactions based on the Loiseau–Nogami–Ross approximation. The strong coupling constants of MPE are taken from the Nijmegen ESC and GESC models and the weak ones of MPE are evaluated in the weak Λ–n mixing model by Dalitz and Von Hippel [Phys. Lett. 10, 153 (1964)]. The effective two-body ΛN → NN weak potentials are applied to evaluate hypernuclear non-mesonic decay rates, which should give a certain additional contribution to the two-nucleon induced decay rate Γ2N. Calculations of $\Gamma ^{({\text{eff.2B}})}_{nm}$ are done for $^5_\Lambda {\rm He}$, $^{11}_\Lambda {\rm B}$, and $^{12}_\Lambda {\rm C}$ and the results are compared with experimental data $\Gamma ^\mathrm{exp}_{2N}$. We have demonstrated the possibility of accounting for the two-nucleon induced non-mesonic decays of light and p-shell hypernuclei by introducing the effective two-body potentials deduced from the three-body weak interactions, though the calculated $\Gamma ^{(\text{eff.2B})}_{nm}$ still includes uncertainties. Discussions and limitations of our “effective two-body ΛN → NN model” are given.