Exchange terms in the two--nucleon induced non--mesonic weak decay of $\Lambda$--hypernuclei

The contribution of Pauli exchange terms to the two--nucleon induced non--mesonic weak decay of $^{12}_\Lambda$C hypernuclei, $\Lambda NN\to nNN$ ($N=n$ or $p$), is studied within a nuclear matter formalism implemented in a local density approximation. We have adopted a weak transition potential including the exchange of the complete octets of pseudoscalar and vector mesons as well as a residual strong interaction modeled on the Bonn potential. The introduction of exchange terms turns out to reduce the two--nucleon induced non--mesonic rate by 18% and, jointly with an increase in the one--nucleon induced rate by the same magnitude, reveals to be significant for an accurate determination of the full set of hypernuclear non--mesonic decay widths in theoretical and experimental analyses.