Three-body correlations in exotic-atom-like three- and four-bosons

An exotic atom is defined as a Coulomb bound system that includes particles other than nucleons or electrons, e.g., an atomic system including mesons. In particular, exotic atoms with anti-$K$-meson ($\bar{K}$) have been focused on from interest in understanding the interaction between an $\bar{K}$ and a nucleon ($\bar{K}N$ interaction). The $\bar{K}N$ interaction is known to be short-range and strongly attractive, which predicts nuclear deeply bound states consisting of $\bar{K}$ and nucleons. However, the existence of those states is still under discussion and we need further investigation on such systems. The present study discusses the relationship between the nuclear and atomic bound states in the exotic-atom-like systems with respect to the strength of the two-body interaction. For simplicity we first consider a simple model consisting of identical bosons whose interaction has long-range and short-range attraction parts. We investigate changes of the binding energy of the three-body system with varying the strength of the short-range attraction, and quantify the evaluation of the three-body correlations in the three- and four-body systems.