Kinematical and nonlocality effects on the nonmesonic weak hypernuclear decay

Abstract

We make a careful study about the nonrelativistic reduction of one-meson-exchange models for the nonmesonic weak hypernuclear decay. Starting from a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*), the strangeness-changing weak ΛN → NN transition potential is derived, including two effects that have been systematically omitted in the literature, or, at best, only partly considered. These are the kinematical effects due to the difference between the lambda and nucleon masses, and the first-order nonlocality corrections, i.e., those involving up to first-order differential operators. Our analysis clearly shows that the main kinematical effect on the local contributions is the reduction of the effective pion mass. The kinematical effect on the nonlocal contributions is more complicated, since it activates several new terms that would otherwise remain dormant. Numerical results for ¹²_ΛC and ⁵_ΛHe are presented and they show that the combined kinematical plus nonlocal corrections have an appreciable influence on the partial decay rates. However, this is somewhat diminished in the main decay observables: the total nonmesonic rate, Γ_nm, the neutron-to-proton branching ratio, Γ_n/ Γ_p, and the asymmetry parameter, a_Λ. The latter two still cannot be reconciled with the available experimental data. The existing theoretical predictions for the sign of a_Λ in ⁵_ΛHe are confirmed.