Cluster-breaking and reconfiguration effects in $_Λ^{12}\rm{B}$ hypernucleus

TL;DR

This work develops a CB-Hyper-Brink framework, optimized by a Control Neural Network, to study cluster-breaking and shell-model dynamics in the negative-parity spectrum of $^{12}_{\Lambda}$B. By introducing imaginary generator coordinates, the model captures cluster dissolution and, with $K$-projection and Hill-Wheeler superposition, resolves the interplay between clustering and shell-like components, predicting a Hoyle-analog state and detailing how the $\Lambda$ hyperon induces shrinkage and a cluster-reconfiguration mechanism via $\Lambda$-$α$ and $\Lambda$-t correlations. The analysis of one-body spin-orbit operators and $B(E2)$ transitions shows that cluster-breaking is essential for the accurate description of hypernuclear structure and provides a sensitive observable to gauge its strength, with results stable across different $\Lambda N$ interactions. Overall, the study illuminates how strangeness alters clustering and shell-model dynamics in hypernuclei, offering a comprehensive framework for cluster-shell competition in $\Lambda$ hypernuclei.

Abstract

We investigate the cluster-breaking effect and spatial distribution of negative-parity states in the $_Λ^{12}\rm{B}$ 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 $_Λ^{12}\rm{B}$. 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.

Figures (5)

• Figure 1: The spectrum of $^{11}\rm{B}$ and $_\Lambda^{12}\rm{B}$ together with the calculations of GCM-Brink zhou_2_2018 and AMD suhara_cluster_2012. "Cal. ($^{11}\rm{B}$)" and "Cal. ($_\Lambda^{12}\rm{B}$)" are our results obtained with CB-Brink model and CB-Hyper-Brink model, respectively. The dashed lines in present calculations are obtained without cluster breaking (CB) effect. "Exp. ($^{11}\rm{B}$)" and "Exp. ($_\Lambda^{12}\rm{B}$)" are the experimental energy levels of $^{11}\rm{B}$Kelley2012 and $_\Lambda^{12}\rm{B}$tang_experiments_2014, respectively. An energy level of $^{11}\rm{B}$ with uncertain identification is shown in dashed line. The star indicates that the "Cluster interaction" was employed in the GCM-Brink zhou_2_2018 and Hyper-Brink calculations.
• Figure 2: The scatter plots showing the overlap between each basis state and the $3/2_1^-$ ($3/2_3^-$) state of $^{11}\rm{B}$ are presented in the upper (lower) panel. The color, size, and transparency collectively represent the value of the overlap. The horizontal and vertical axes represent the expectation value of the one-body spin-orbit operator $\mathcal{\hat{O}}^{ls}$ and the squared radii $\hat{R^2}$ for each basis state in units of fm$^2$, respectively.
• Figure 3: The scatter plots showing the overlap between each basis state and the $1_1^-$ and $1_4^-$ states of $_\Lambda^{12}\rm{B}$ are presented, similarly to Fig. \ref{['R-LS']}.
• Figure 4: The contour plots of the squared overlap $U(R_{\alpha\alpha}, \boldsymbol{R}^t, \boldsymbol{R}^\Lambda)$, as defined in Eq. (\ref{['eq:overlap-brink']}), for $^{11}\rm{B}$($3/2^-_1$) and $_\Lambda^{12}\rm{B}$($1^-_1$) are presented as functions of $\boldsymbol{R}^t$. The horizontal and vertical axes represent the $z$ and $x$ components of $\boldsymbol{R}^t$, respectively. The distance between the two $\alpha$ clusters is fixed at an optimal value to maximize the squared overlap.
• Figure 5: The contour plots of the squared overlap $U(R_{\alpha\alpha}, \boldsymbol{R}^t, \boldsymbol{R}^\Lambda)$ are presented for $^{11}\rm{B}$($3/2^-_3$) and $_\Lambda^{12}\rm{B}$($1^-_4$) as functions of $\boldsymbol{R}^t$, similarly to Fig \ref{['overlap-ground']}. For $_\Lambda^{12}\rm{B}$($1^-_4$), the two configurations $\alpha+ {_\Lambda^{5}\rm{He}}+ {^{3}\rm{H}}$ and $\alpha+ \alpha+ {_\Lambda^{4}\rm{H}}$ are considered.