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

The non--mesonic weak decay of double--$\Lambda$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon--induced mechanism, $\Lambda N\to nN$, widely studied in single--$\Lambda$ hypernuclei, additional hyperon--induced mechanisms, $\Lambda \Lambda\to \Lambda n$, $\Lambda \Lambda\to \Sigma^0 n$ and $\Lambda \Lambda\to \Sigma^-p$, are accessible in double--$\Lambda$ hypernuclei and are investigated here. As in previous works on single--$\Lambda$ 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 $^{10}_{\Lambda\Lambda}$Be and $^{13}_{\Lambda\Lambda}$B. Our predictions are compared with a few previous evaluations. The rate for the $\Lambda \Lambda\to \Lambda n$ decay is dominated by $K$--, $K^*$-- and $\eta$--exchange and turns out to be about 2.5\% of the free $\Lambda$ decay rate, $\Gamma_{\Lambda}^{\rm free}$, while the total rate for the $\Lambda \Lambda\to \Sigma^0 n$ and $\Lambda \Lambda\to \Sigma^- p$ decays, dominated by $\pi$--exchange, amounts to about 0.25\% of $\Gamma_{\Lambda}^{\rm free}$. 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.