  The correlation function is a useful tool to study the interaction between
hadrons. The theoretical description of this observable requires the knowledge
of the scattering wave function, whose asymptotic part is distorted when two or
more particles are charged. For a system of three (or more) particles, with
more than two particles asymptotically free and at least two of them charged,
the asymptotic part of the wave function is not known in a closed form. In the
present study we introduce a screened Coulomb potential and analyze the impact
of the screening radius on the correlation function. As we will show, when a
sufficiently large screening radius is used, the correlation function results
almost unchanged if compared to the case in which the unscreened Coulomb
potential is used. This fact allows the use of free asymptotic matching
conditions in the solution of the scattering equation simplifying noticeably
the calculation of the correlation function. As an illustration we discuss the
$pp$ and $ppp$ correlation functions.
