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The Non-Mesonic Weak Decay of Double-Lambda Hypernuclei: A Microscopic Approach

The non--mesonic weak decay of double--$Λ$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon--induced mechanism, $ΛN\to nN$, widely studied in single--$Λ$ hypernuclei, additional hyperon--induced mechanisms, $ΛΛ\to Λn$, $ΛΛ\to Σ^0 n$ and $ΛΛ\to Σ^-p$, are accessible in double--$Λ$ hypernuclei and are investigated here. As in previous works on single--$Λ$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one--meson exchange weak transition potential (including the ground state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two--pion--exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei $^{10}_{ΛΛ}$Be and $^{13}_{ΛΛ}$B. Our predictions are compared with a few previous evaluations. The rate for the $ΛΛ\to Λn$ decay is dominated by $K$--, $K^*$-- and $η$--exchange and turns out to be about 2.5\% of the free $Λ$ decay rate, $Γ_Λ^{\rm free}$, while the total rate for the $ΛΛ\to Σ^0 n$ and $ΛΛ\to Σ^- p$ decays, dominated by $π$--exchange, amounts to about 0.25\% of $Γ_Λ^{\rm free}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the non--mesonic decay of strangeness $-2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$--dibaryon.