  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.
