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Statistical double $Λ$ hypernuclear formation from $Ξ^-$ absorption at rest in light nuclei

We investigate double $Λ$ hyperfragment formation from the statistical decay of double $Λ$ compound nuclei produced in the $Ξ^-$ absorption at rest in light nuclei, $^{12}\mathrm{C}$, $^{14}\mathrm{N}$ and $^{16}\mathrm{O}$. We examine the target and the $ΛΛ$ bond energy dependence of the double $Λ$ hyperfragment formation probabilities, especially of those double hypernuclei observed in experiments. For the $^{12}\mathrm{C}$ ($^{14}\mathrm{N}$) target, the formation probabilities of $^{6}_{ΛΛ}\mathrm{He}$ and $^{10}_{ΛΛ}\mathrm{Be}$ ($^{13}_{ΛΛ}\mathrm{B}$) are found to be reasonably large as they are observed in the KEK-E373 (KEK-E176) experiment. By comparison, for $^{16}\mathrm{O}$ target, the formation probability of $^{11}_{ΛΛ}\mathrm{Be}$ is calculated to be small with $ΔB_{ΛΛ}$ consistent with the Nagara event. We also evaluate the formation probability of ${}^{5}_{ΛΛ}\mathrm{H}$ from a $Ξ^-$-${}^{6}\mathrm{He}$ bound state, ${}^{7}_Ξ\mathrm{H}$.