Finite range scattering wave function method for scattering and resonance lifetimes

A generic expression for the scattering wave function in terms of the full discrete spectral Green’s function on a finite range is used to obtain the “finite range scattering wave function (FRSW)” which is accurate over a finite range of the scattering coordinate. We show that the representation of the FRSW in a finite basis set can be used to compute the scattering matrix and related quantities when the interaction potential is also restricted to this range. Comparisons of numerical results for several model problems with those of other methods and with analytical results indicate that the FRSW method is very accurate when converged and requires comparable or less computation than other methods. The main difference between the present method and other variational scattering methods is that the real Green’s function is used and that the scattering wave function itself is calculated nonvariationally. Thus the FRSW can be used to solve quantum mechanical problems involving scattering wave functions over a finite range such as scattering theory, resonance studies, and photodissociation. Results of two implementations are presented. Both require only one representation of the real Green’s function in a finite basis. One requires energy dependent matrix elements, while the other does not.