The R-matrix formalism for two-particle scattering problems

•The R-matrix method is extended to two-particle scattering events.•The scattering wavefunctions are antisymmetrized in the entire system.•The continuity relations are imposed for the wavefunctions and particle fluxes.•A consistent system of equations is obtained for the expansion coefficients.•The antisymmetrized wavefunctions are essential for entangled asymptotic states.