Container structure of alpha-alpha-Lambda clusters in 9-Lambda-Beryrium

Abstract

A new concept of clustering is discussed in |$\Lambda$| hypernuclei using a new-type microscopic cluster model wave function, which has a structure in which constituent clusters are confined in a container, whose size is a variational parameter and which we refer to as a hyper-Tohsaki–Horiuchi–Schuck–Röpke (hyper-THSR) wave function. By using the hyper-THSR wave function, the |$2\alpha + \Lambda$|-cluster structure in |${{^9_\Lambda}\hbox{Be}}$| is investigated. We show that full microscopic solutions in the |$2\alpha + \Lambda$|-cluster system, which are given as |$2\alpha + \Lambda$| Brink-GCM (generator coordinate method) wave functions, are almost perfectly reproduced by the single configurations of the hyper-THSR wave function. The squared overlaps between 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$| interaction artificially. With the increase of the |$\Lambda N$| interaction, the |$\Lambda$| particle gets to move more deeply inside the core and strongly invokes the spatial core shrinkage. Accordingly, distinct localized |$2\alpha$| clusters appear in the nucleonic intrinsic density, though, in the |${^8{\rm Be}}$| nucleus, a gaslike |$2\alpha$|-cluster structure is shown. The origin of the localization is associated with the strong effect of the 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.