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

The non–mesonic weak decay of double–$\mathrm{\Lambda }$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon–induced mechanism, $\mathrm{\Lambda }N\to nN$, widely studied in single–$\mathrm{\Lambda }$ hypernuclei, additional hyperon–induced mechanisms, $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }n$, $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{0}n$ and $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{-}p$, are accessible in double–$\mathrm{\Lambda }$ hypernuclei and are investigated here. As in previous works on single–$\mathrm{\Lambda }$ 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 ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{10}$Be and ${}_{\mathrm{\Lambda }\mathrm{\Lambda }}^{13}$B. Our predictions are compared with a few previous evaluations. The rate for the $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }n$ decay is dominated by $K$–, $K^{\ast }$– and $\eta$–exchange and turns out to be about 2.5% of the free $\mathrm{\Lambda }$ decay rate, ${\mathrm{\Gamma }}_{\mathrm{\Lambda }}^{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}$, while the total rate for the $\Lambda \Lambda\to \Sigma^0 n$and$\Lambda \Lambda\to \Sigma^- p$decays,dominatedby$\pi$--exchange,amountstoabout0.25\mathrm{\%}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.