Numerical Version of the Complex-Scaling Green’s Operator Method

A new treatment of scattering problems is formulated by improving the complex-scaling Green’s operator (CSGO) method, which can calculate the transition or scattering matrix from the spectral representation of the complex-scaled Green’s function and the asymptotic solution expressed in terms of the analytic function. In the present formulation, the CSGO method is extended to handle the general scattering problem in charged-particle systems by employing the Coulomb wave function numerically calculated under the complex-scaled asymptotic Hamiltonian. We call the new method the CSGO-numerical (CSGON) method, and it is applied to the scattering problem of the $^4$He + proton system to check its validity. The continuum level density (CLD) method, which is another method to solve the scattering problem, is also applied to the same system. The numerical precision and the applicability of the CSGON method is discussed by comparing it with the CLD and CSGO methods.