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The contribution of Pauli exchange terms to the two--nucleon inducednon--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 alocal density approximation. We have adopted a weak transition potentialincluding the exchange of the complete octets of pseudoscalar and vector mesonsas well as a residual strong interaction modeled on the Bonn potential. Theintroduction of exchange terms turns out to reduce the two--nucleon inducednon--mesonic rate by 18% and, jointly with an increase in the one--nucleoninduced rate by the same magnitude, reveals to be significant for an accuratedetermination of the full set of hypernuclear non--mesonic decay widths intheoretical and experimental analyses.

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