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The non-mesonic weak decay of $\Lambda$--hypernuclei is studied within aone-meson-exchange potential supplemented by a chirally motivatedtwo-pion-exchange mechanism. The effects of final state interactions on theoutgoing nucleons are also taken into account. In view of the severediscrepancies between theoretical expectations and experimental data,particular attention is payed to the asymmetry of the protons emitted bypolarized hypernuclei. The one-meson-exchange model describes the non-mesonicrates and the neutron-to-proton ratio satisfactorily but predicts a too largeand negative asymmetry parameter. The uncorrelated and correlated two-pionmechanisms change the rates moderately, thus maintaining the agreement withexperiment. The modification in the strength and sign of some decay amplitudesbecomes crucial and produces asymmetry parameters which lie well within theexperimental observations.

Two-pion-exchange in the non-mesonic weak decay of $\Lambda$-hypernuclei