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

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

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