Nonmesonic Weak Decay of $\Lambda$ Hypernuclei: The Three--Nucleon Induced Mode

The nonmesonic weak decay of $\Lambda$ hypernuclei is studied within a microscopic diagrammatic approach which is extended to include the three--nucleon induced mechanism. We adopt a nuclear matter formalism which, through the local density approximation, allows us to model finite hypernuclei, a one--meson--exchange weak transition potential and a Bonn nucleon--nucleon strong potential. One--, two-- and three--nucleon induced weak decay rates are predicted for $^{12}_\Lambda$C by including ground state correlations up to second order in the nucleon--nucleon potential and the recoil of the residual nucleus. Three--nucleon stimulated decays, $\Lambda NNN\to nNNN$ ($N=n$ or $p$), are considered here for the first time. The obtained decay rates compare well with the latest KEK and FINUDA data. The three--nucleon induced rate turns out to be dominated by $nnp$-- and $npp$--induced decays, it amounts to $\sim$ 7\% of the total nonmesonic rate and it is $\sim 1/2$ of the neutron--induced decay rate. The reduction effect of the nuclear recoil is particularly relevant for the three--nucleon induced rates ($\sim$ 15\%), less important for the two--nucleon induced rates ($\sim$ 4\%) and negligible for the one--nucleon induced rates. Given the non--negligible size of the three--nucleon induced contribution and consequently its importance in the precise determination of the complete set of decay rates, new measurements and/or experimental analysis are encouraged.