Three-body calculation of Be double-Λ hypernuclei

Abstract

Energy levels and Λ Λ bond energy of the double- Λ hypernucleus are calculated by considering two- and three-cluster interactions. Interactions between constituent particles are contact interactions for reproducing the low binding energy of nuclei. The effective action is constructed to involve three-body forces. In this paper, we also compare the obtained binding energy result with experimental and other cluster and shell models. The results of all schemes agree very well showing the high accuracy of our method to calculate the other many-body hyperonic nuclei using three-cluster interactions. The experimental values of $B_{\Lambda {\Lambda }}(^{10}_{\Lambda {\Lambda }}$ Be) = (11.90 ± 0.13) MeV, $B_{\Lambda {\Lambda }}(^{11}_{\Lambda {\Lambda }}$ Be) = (20.49 ± 1.15) MeV and $B_{\Lambda {\Lambda }}(^{12}_{\Lambda {\Lambda }}$ Be) = (22.23 ± 1.15) MeV seem to be more compatible with our calculated value of $B_{\Lambda {\Lambda }}(^{10}_{\Lambda {\Lambda }}$ Be) = 14.04 MeV, $B_{\Lambda {\Lambda }}(^{11}_{\Lambda {\Lambda }}$ Be) = 19.31 MeV and $B_{\Lambda {\Lambda }}(^{12}_{\Lambda {\Lambda }}$ Be) = 21.45 MeV in comparison with the other calculated results by Hiyama et al, Gal et al and Guleria et al.