Hypernuclear weak decay puzzle

Abstract

A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak Λ-core coupling formalism. The extreme particle-hole model and the quasiparticle Tamm-Dancoff approximation are explicitly worked out. It is shown that the nuclear structure manifests itself basically through the Pauli principle, and a very simple expression is derived for the neutron- and proton-induced decays rates Γ_n and Γ_p, which does not involve the spectroscopic factors. We use the standard strangeness-changing weak ΛN→NN transition potential which comprises the exchange of the complete pseudoscalar and vector meson octets (π,η,K,ρ,ω,K*), taking into account some important parity-violating transition operators that are systematically omitted in the literature. The interplay between different mesons in the decay of ¹²_ΛC is carefully analyzed. With the commonly used parametrization in the one-meson-exchange model (OMEM), the calculated rate Γ_NM = Γ_n + Γ_p is of the order of the free Λ decay rate Γ⁰(Γ^th_NM ≅ Γ⁰) and is consistent with experiments. Yet the measurements of Γ_n/p = Γ_n / Γ_p and of Γ_p are not well accounted for by the theory (Γ^th_n/p ≲ 0.42,Γ^th_p ≳ 0.60Γ⁰). It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.