Cluster-breaking and reconfiguration effects in ${}_{\hat{I}}{›}^{12}\mathrm{B}$ hypernucleus

Abstract

We investigate the cluster-breaking effect and spatial distribution of negative-parity states in the ${}_{\hat{I}}{›}^{12}\mathrm{B}$ hypernucleus using the Hyper-Brink model with cluster-breaking(CB-Hyper-Brink) optimized via Control Neural Network (Ctrl.NN). The results demonstrate that the inclusion of cluster-breaking is essential for accurately reproducing the observed low-lying energy levels and for making reliable predictions of the Hoyle-analog state 1-4 in ${}_{\hat{I}}{›}^{12}\mathrm{B}$. Cluster-breaking manifests as strong spin-orbit correlations and the dissolution of ideal cluster configurations, as revealed by the analysis of one-body spin-orbit operator expectation values and the spatial overlap with projected cluster bases. The interplay between short-range repulsion and intermediate-range attraction in the Lambda N interaction induces the cluster reconfiguration effect, which is characterized by the coexistence of Lambda-alpha and Lambda-triton correlations; this reconfiguration effect leads to a modest stabilization and shrinkage of cluster structures. The variation in electric quadrupole transition strengths, B(E2), between the ground and Hoyle-analog states serves as a sensitive probe for the degree of cluster-breaking, providing direct evidence for its physical relevance. These findings highlight the crucial role of cluster-breaking in characterizing the hypernuclear structure and offer a comprehensive framework for understanding the interplay between clustering and shell-model dynamics in hypernuclei.