Container structure of alpha alpha Lambda clusters in $_Λ^9$Be

Abstract

New concept of clustering is discussed in $Λ$ 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-Röpke (Hyper-THSR) wave function. By using the Hyper-THSR wave function, $2α+ Λ$ cluster structure in ${^{9}_Λ{\rm Be}}$ is investigated. We show that full microscopic solutions in the $2α+ Λ$ cluster system, which are given as $2α+ Λ$ 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 $J^π=0^+$, $2^+$, and $4^+$ states, respectively. We also simulate the structural change by adding the $Λ$ particle, by varying the $ΛN$ interaction artificially. As the increase of the $ΛN$ interaction, the $Λ$ particle gets to move more deeply inside the core and invokes strongly the spatial core shrinkage, and accordingly distinct localized $2α$ clusters appear in the nucleonic intrinsic density, though in ${^{8}{\rm Be}}$ rather gaslike $2α$-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 $2α$ and $Λ$ clusters is essential in understanding the cluster structure in ${^{9}_Λ{\rm Be}}$, in which the very compact spatial localization of clusters is shown in the density distribution.

14 pages, 4 figures, 3 tables, submitted to PTEP