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 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 $ΛN\to NN$ 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 $Γ^0(Γ_{NM}^{\rm th}\cong Γ^0)$ 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 ($Γ_{n/p}^{\rm th}\lsim 0.42; Γ_p^{\rm th}\gsim 0.60 Γ^0$). It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.