Statistical double $Lambda$ hypernuclear formation from $Xi^-$ absorption at rest in light nuclei

We investigate double $Lambda$ hyperfragment formation from the statistical decay of double $Lambda$ compound nuclei produced in the $Xi^-$ absorption at rest in light nuclei, $^{12}mathrm{C}$, $^{14}mathrm{N}$ and $^{16}mathrm{O}$. We examine the target and the $LambdaLambda$ bond energy dependence of the double $Lambda$ hyperfragment formation probabilities, especially of those double hypernuclei observed in experiments. For the $^{12}mathrm{C}$ ($^{14}mathrm{N}$) target, the formation probabilities of $^{6}_{LambdaLambda}mathrm{He}$ and $^{10}_{LambdaLambda}mathrm{Be}$ ($^{13}_{LambdaLambda}mathrm{B}$) 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 $^{11}_{LambdaLambda}mathrm{Be}$ is calculated to be small with $Delta B_{LambdaLambda}$ consistent with the Nagara event. We also evaluate the formation probability of ${}^{5}_{LambdaLambda}mathrm{H}$ from a $Xi^-$-${}^{6}mathrm{He}$ bound state, ${}^{7}_{Xi}mathrm{H}$.