Shell model formalism for the vector proton asymmetry in the nonmesonic weak hypernuclear decay

Abstract

I present an independent-particle shell-model formalism for the calculation of the primary proton asymmetry of nonmesonic weak hypernuclear decay in terms of relative-space transition amplitudes. In previous work the asymmetry has been usually defined in terms of the single-proton angular distribution, having in mind the measurement of this quantity by single-proton detection, as done in the older experiments. More recently one strives for better determinations of this quantity through proton-neutron coincidence measurements, which are expected to suffer less contamination from rescattering inside the nuclear medium. Therefore I start here from a definition of the asymmetry based on the angular distribution of a proton in coincidence with a neutron in back-to-back kinematics. The two calculated quantities are not identical, but should have similar numerical values due to the fact that the opening-angle distribution for the primary nucleons is strongly peaked at this momentum orientation.