Separable expansions for realistic multichannel scattering problems

A new approach to the multichannel scattering problem with realistic local or nonlocal interactions is developed. By employing the negative-energy solutions of uncoupled Sturmian eigenvalue problems referring to simple auxiliary potentials, the coupling interactions appearing in the original multichannel problem are approximated by finite-rank potentials. By resorting to integral-equation techniques the coupled-channel equations are then reduced to linear algebraic equations which can be straightforwardly solved. Compact algebraic expressions for the relevant scattering matrix elements are thus obtained. The convergence of the method is tested in the single-channel case with realistic optical potentials. Excellent agreement is obtained with a few terms in the separable expansion for both real and absorptive interactions.