  Three-body correlations in three-body exotic atoms are studied with simple
models that consist of three bosons interacting through a superposition of
long- and short-range potentials. We discuss the correlations among particles
by comparing the energy shifts given by precise three-body calculations and by
the Deser-Trueman formula, in which the long- and short-range contributions are
factorized. By varying the coupling of the short-range potential, we evaluate
the ranges of the strength where the two-body correlations dominate and where
the three-body correlations cannot be neglected.
