Quasipotential Coulomb scattering of scalar particles

A study is made of the quasipotential modeling of scattering of strongly interacting scalar particles of equal masses $m$ when the quasipotential in the coordinate representation has the Coulomb form $V(r)=-gr^{-1}$ ($g>m$). In this case, the integral quasipotential equation for the partial-wave amplitudes reduces to a Sturm–Liouville problem in the momentum space with two turning points. To calculate the partial-wave amplitudes, the reference equation method is used in a form that is suitable when the original equation contains two (or more) turning points. In conclusion, there is a discussion of the asymptotic properties of the effective coupling constant which arises in the model.