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

A fully relativistic finite nucleus wave-function approach to the non-mesonic weak decay of the ${_\Lambda^{12} C}$ hypernucleus is presented. The model is based on the calculation of the amplitudes of the tree-level Feynman diagrams for the $\Lambda N\to NN$ 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 $\Lambda N$ 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 $\Gamma_{nm}=\Gamma_n+\Gamma_p$, the $\Gamma_n/\Gamma_p$ ratio, the $a_\Lambda$ intrinsic asymmetry parameter, and the kinetic energy and angular spectra.