The R-matrix formalism for two-particle scattering problems

Abstract

The R-matrix formalism is extended to include two-particle scattering events. The system is the same as in the case of one-particle R-matrix formalism and consists of a number (≥2) of leads connected to a scattering region. When the particles are identical fermions, our approach conserves the anti-symmetry of the wavefunction in the entire system, which opens the possibility to account for asymptotic entangled states. The particles have a mutual interaction when they are both in the scattering region. Using a proper Ansatz for the two-particle wavefunctions, we obtain a consistent system of equations which gives the coefficients for the two-particle scattering functions expanded in terms of anti-symmetrized products of one-particle scattering functions, when at least one particle is in the leads, or of the two-particle eigenstates of the Hamiltonian, when both particles are in the scattering region. Our formalism applies also to bosons.