Container structure of alpha alpha Lambda clusters in $_\Lambda^9$Be

TL;DR

This paper introduces a new hypernuclear cluster model, Hyper-THSR, to describe $ ext{Lambda}$ cluster structures in ${^{9}_ ext{Lambda} ext{Be}}$, demonstrating high accuracy in reproducing microscopic solutions and revealing the impact of $ ext{Lambda}$ on cluster localization.

Contribution

The paper develops the Hyper-THSR wave function, a novel container-based cluster model, and applies it to accurately describe $ ext{Lambda}$-cluster structures in ${^{9}_ ext{Lambda} ext{Be}}$ with minimal computational complexity.

Findings

Hyper-THSR wave function reproduces microscopic solutions with over 97% overlap.

Adding $ ext{Lambda}$ enhances core localization and induces cluster shrinkage.

Container picture explains the spatial localization of clusters in hypernuclei.

Abstract

New concept of clustering is discussed in $\Lambda$ hypernuclei using a new-type microscopic cluster model wave function, which has a structure that constituent clusters are confined in a container, whose size is a variational parameter and which we refer to as Hyper-Tohsaki-Horiuchi-Schuck-R\"opke (Hyper-THSR) wave function. By using the Hyper-THSR wave function, $2\alpha + \Lambda$ cluster structure in ${^{9}_\Lambda{\rm Be}}$ is investigated. We show that full microscopic solutions in the $2\alpha + \Lambda$ cluster system, which are given as $2\alpha + \Lambda$ Brink-GCM wave functions, are almost perfectly reproduced by the single configurations of the Hyper-THSR wave function. The squared overlaps between the both wave functions are calculated to be $99.5$%, $99.4$%, and $97.7$% for $J^\pi=0^+$, $2^+$, and $4^+$ states, respectively. We also simulate the structural change by adding the $\Lambda$ particle, by varying the $\Lambda N$ interaction artificially. As the increase of the $\Lambda N$ interaction, the $\Lambda$ particle gets to move more deeply inside the core and invokes strongly the spatial core shrinkage, and accordingly distinct localized $2\alpha$ clusters appear in the nucleonic intrinsic density, though in ${^{8}{\rm Be}}$ rather gaslike $2\alpha$-cluster structure is shown. The origin of the localization is associated with the strong effect of Pauli principle. We conclude that the container picture of the $2\alpha$ and $\Lambda$ clusters is essential in understanding the cluster structure in ${^{9}_\Lambda{\rm Be}}$, in which the very compact spatial localization of clusters is shown in the density distribution.