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

Abstract

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.

Comments: 25 pages, 9 figures, new results, new figures