Effects of Coulomb interaction in relativistic $N/D$ equations with allowance for inelasticity

The quasipotential approach is used to investigate the analytic properties of the partial-wave $S$ matrix in the relativistic Coulomb-nuclear scattering problem of particles having charges of the same kind. A procedure for separating the Coulomb singularities of the partial-wave amplitudes is considered, and it is shown that in the complex plane of the square of the relative momentum $\nu$ of the particles the matrix $\hat\tau_{CH}(\nu)$ of the partial-wave amplitudes renormalized in a certain manner has on the physical sheet an analytic structure analogous to that of the matrix of partial-wave amplitudes when the Coulomb interaction is switched off. In the multichannel case, a system of modified $N/D$ equations is formulated with allowance for inelasticity and the Coulomb effects.