Microscopic approach to the proton asymmetry in the nonmesonic weak decay of Λ hypernuclei

Abstract

The non--mesonic weak decay of polarized $\Lambda$--hypernuclei is studied with amicroscopic diagrammatic formalism in which one-- and two--nucleon induced decay mechanisms,$\vec{\Lambda} N \to NN$ and $\vec{\Lambda} NN \to NNN$, are considered togetherwith (and on the same ground of) nucleon final state interactions.We adopt a nuclear matter formalism extended to finite nuclei via the local densityapproximation. Our approach adopts different one--meson--exchange weaktransition potentials, while the strong interaction effects are accountedfor by a Bonn nucleon--nucleon interaction. We alsoconsider the two--pion--exchange effect in the weak transition potential.Both the two-nucleon induced decay mechanism and the final state interactionsreduce the magnitude of the asymmetry.The quantum interference terms considered in the present microscopic approachgive rise to an opposite behavior of the asymmetry with increasing energy cutsto that observed in models describing the nucleon final state interactionssemi-classically via the intranuclear cascade code.Our results for the asymmetry parameter in$^{12}_{\Lambda}$C obtained with different potential models are consistent withthe asymmetry measured at KEK.