MomentT-matrix approach toe+-H scattering. I. Angular distribution and total cross section for energies below the pickup threshold

A formalism is developed for calculation of electron and positron scattering from atoms at low and intermediate energies in terms of appropriate matrix elements of the off-shell $T$ operator. The technique is based on an $L^2$ discretization of the full electronic Hamiltonian, initially avoiding all specification of channels and asymptotic boundary conditions. Scattering information relating to specific initial and final channels is obtained by taking appropriate off-shell matrix elements, followed by construction of the total real axis discontinuity of the off-shell elements via moment techniques. The formalism is applied to the problem of purely elastic $e^{+}$-H scattering, resulting in converged total cross sections and angular distributions below the pickup threshold.