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Few-Body Systems

Low-Lying States of Four-Boson Systems with a Repulsive Core and an Attractive Tail in the Interaction

X. G. Li, Bao Cheng-guang

Published Nov 1, 2001• 1 citation
Publisher
DOI
10.1007/s006010170004

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Four identical spinless bosons with purely attractive two-body short-range interactions and repulsive three-body interactions under external spherically symmetric harmonic confinement are considered. The repulsive three-body potential prevents the formation of deeply bound states with molecular character. The low-energy spectrum with vanishing orbital angular momentum and positive parity for infinitely large two-body sss-wave scattering length is analyzed in detail. Using the three-body contact, states are classified as universal, quasiuniversal, or strongly nonuniversal. Connections with the zero-range interaction model are discussed. The energy spectrum is mapped out as a function of the two-body sss-wave scattering length as,as>0{a}_{s}, {a}_{s}>0as​,as​>0. In the weakly to medium-strongly interacting regime, one of the states approaches the energy obtained for a hard-core interaction model. This state is identified as the energetically lowest-lying ``BEC state.'' Structural properties are also presented.
A two-dimensional three-boson system interacting with hard-core repulsion and trapped by parabolic confinement has been investigated. Two density functions associated with breathing motion and deformation, respectively, have been defined. Based on these density functions, the wave functions of low-lying states have been analyzed in detailed. The states are found to have explicit geometric features caused by the hard-core repulsion, these features depend strongly on the constraints imposed by symmetry. Striking similarity exists in the density functions, so that breathing bands can be well defined. A classification scheme is thereby proposed.
In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjo\ifmmode\ddot\else\textasciidieresis\fi{}lander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters F0s{\mathit{F}}_{0}^{\mathit{s}}F0s​ and F0a{\mathit{F}}_{0}^{\mathit{a}}F0a​, the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential.