Transformation theory and translation factors in inelastic atomic collisions

Abstract

It is shown through the use of transformation theory that unique semiclassical atomic scattering states which obey the asymptotic conditions of formal scattering theory can be derived by transforming "nontraveling" atomic states, i.e., states whose coordinate variables are referred to a stationary origin, to frames at rest with respect to the incoming or outgoing particles. An overview of the problem of properly defining such scattering states is presented. The operator which carries out the necessary transformation from inertial to noninertial frames is derived and its properties are discussed. The relation of this transformation operator to the "translation factor" discussed in the literature is presented. The application of this operator to transform the time-dependent Schr\"odinger equation from an inertial to a noninertial frame is presented and shown to introduce new terms in the resulting equation. The implications of these new terms to scattering problems are discussed.