Close coupled equations for inelastic scattering in the quasiclassical approximation. The equations for normalized amplitudes

For the description of inelastic scattering a new form of close coupled equations is proposed. The coupled equations considered in our previous study are normalized. The solutions for the normalized amplitudes do not contain exponentially large terms. The normalization removes the last problem in the numerical solution of the Delos-Thorson equations. Under quasiclassical conditions our coupled system involves the analytical wavefunctions of elastic scattering in the quasiclassical approximation of Wentzel, Kramers, Brillouin (WKB) which are simple and universal. The system obtained is as convenient for numerical realization as that of a semiclassical method, but in contrast to the latter it is accurate when the collisional energy and energy of transition are of the same order of magnitude.