Nonmesonic weak decay of double-Λ hypernuclei: A microscopic approach

The nonmesonic weak decay of double-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei is studied within a microscopic diagrammatic approach. In addition to the nucleon-induced mechanism, $\mathrm{\ensuremath{\Lambda}}N\ensuremath{\rightarrow}nN$ and $\mathrm{\ensuremath{\Lambda}}NN\ensuremath{\rightarrow}nNN$, widely studied in single-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei, additional hyperon-induced mechanisms, $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}n$, $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}n$, and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}p$, are accessible in double-$\mathrm{\ensuremath{\Lambda}}$ hypernuclei and are investigated here. As in previous works on single-$\mathrm{\ensuremath{\Lambda}}$ 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 ${}_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{10}\mathrm{Be}$ and ${}_{\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{B}$. Our predictions are compared with a few previous evaluations. The rate for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}n$ decay is dominated by $K$-, ${K}^{*}$-, and $\ensuremath{\eta}$-exchange and turns out to be about 2.5% of the free $\mathrm{\ensuremath{\Lambda}}$ decay rate, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{free}}$, while the total rate for the $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{0}n$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}p$ decays, dominated by $\ensuremath{\pi}$-exchange, amounts to about 0.25% of ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{\ensuremath{\Lambda}}}^{\mathrm{free}}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the nonmesonic decay of strangeness $\ensuremath{-}2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$ dibaryon.