Nonmesonic weak decay of double-$\mathrm{\Lambda }$ hypernuclei: A microscopic approach

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

Figure 1

Goldstone diagrams for the evaluation of the $\mathrm{\Lambda }N\to nN$, $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }n$, $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{0}n$, and $\mathrm{\Lambda }\mathrm{\Lambda }\to {\mathrm{\Sigma }}^{-}p$ decay rates in infinite nuclear matter.

Figure 2

Direct and exchange Goldstone diagrams for the $\mathrm{\Lambda }\mathrm{\Lambda }\to \mathrm{\Lambda }n$ decay.