A relativistic model for the non-mesonic weak decay of the ${}_{\mathrm{\Lambda }}^{12}C$ hypernucleus

A fully relativistic finite nucleus wave-function approach to the non-mesonic weak decay of the ${}_{\mathrm{\Lambda }}^{12}C$ hypernucleus is presented. The model is based on the calculation of the amplitudes of the tree-level Feynman diagrams for the $\mathrm{\Lambda }N\to NN$ process and includes one-pion exchange and one-kaon exchange diagrams. The pseudo-scalar and pseudo-vector choices for the vertex structure are compared. Final-state interactions between each one of the outgoing nucleons and the residual nucleus are accounted for by a complex phenomenological optical potential. Initial $\mathrm{\Lambda }N$ and final $NN$ short-range correlations are included by means of phenomenological correlation functions. Numerical results are presented and discussed for the total non-mesonic decay width ${\mathrm{\Gamma }}_{nm}={\mathrm{\Gamma }}_n+{\mathrm{\Gamma }}_p$, the ${\mathrm{\Gamma }}_n\mathrm{/}{\mathrm{\Gamma }}_p$ ratio, the $a_{\mathrm{\Lambda }}$ intrinsic asymmetry parameter, and the kinetic energy and angular spectra.