On the effect of the Delta(1232) in hypernuclear non-mesonic weak decay: a microscopic approach

The non-mesonic weak decay of $\Lambda$-hypernuclei is studied within a microscopic diagrammatic approach which includes, for the first time, the effect or the $\Delta$-baryon resonance. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation, a one-meson exchange weak transition potential, a Bonn nucleon-nucleon strong potential and a $\Delta N\to NN$ strong potential based on the Landau-Migdal theory. Ground state correlations and final state interactions (FSI), at second order in the baryon-baryon strong interaction, are introduced on the same footing for all the isospin channels of one- and two-nucleon induced decays. Weak decay rates and single and double-coincidence nucleon spectra are predicted for $^{12}_\Lambda$C and compared with recent KEK and FINUDA data. The $\Delta(1232)$ introduces new FSI-induced decay mechanisms which lead to an improvement when comparing the obtained nucleon spectra with data, while it turns out to have a negligible effect on the decay rates. Discrepancies with experiment remain only for emission spectra involving protons, but are mostly restricted to double-nucleon correlations in the non-back-to-back kinematics.