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 → N N 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 Λ C and 5 Λ He 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 Λ He are confirmed.The free decay of a Λ hyperon occurs almost exclusively through the mesonic mode, Λ → πN , with the nucleon emerging with a momentum of about 100 MeV/c. Inside nuclear matter (p F ≈ 270 MeV/c) this mode is Pauli blocked, and, for all but the lightest Λ hypernuclei (A ≥ 5), the weak decay is dominated by the nonmesonic channel, ΛN → N N , which liberates enough kinetic energy to put the two emitted nucleons above the Fermi surface. In the absence of stable hyperon beams, these nonmesonic decays offer the only way available to investigate the strangeness-changing weak interaction between hadrons. (For reviews on hypernuclear decay, see Refs.[1]- [3].) The simplest model for this process is the exchange of a virtual pion [4], and in fact this can reproduce reasonably well the total (nonmesonic) decay rate, Γ nm = Γ n + Γ p , but fails badly for other observables like the ratio of neutron-induced (Λn → nn) to proton-induced (Λp → np) transitions, Γ n /Γ p , and the asymmetry parameter a Λ . The deficiency of this model is attributed to effects of short range physics, which should be quite important in view of the large momentum transfers involved (∼ 400 MeV/c). Although there have been some attempts to account for this fact by making use of quark models to compute the shortest range part of the transition potential [5]-[9], most of the theoretical work opted for the addition of other, heavier mesons in the exchange process [10]- [23]. None of these models gives fully satisfactory results. Inclusion of correlated two-pion exchange has not been comple...
