The adiabatic-diabatic approach to vibrational inelastic scattering: Theory and study of a simple collinear model

Abstract

The quantum mechanical problem of the vibrational excitation of a harmonic oscillator in one dimension is treated with an adiabatic basis set. The Smith transformation [Phys. Rev. 179, 111 (1969)] is used to eliminate the dynamical coupling terms and leads to a new diabatic representation. The rate of convergence of calculated transition probabilities in the new diabatic representation is compared with calculations based on the usual asymptotic representation for a variety of different mass combinations and collision energies. These calculations revealed that: (i) the new diabatic potential matrix converges to the usual asymptotic one as the size of the adiabatic basis set becomes large enough; (ii) the transition probabilities converge much faster than the potential matrix elements and faster than those calculated by the usual method. Typically only about two states more than the upper state considered are required whereas in the usual representation many more states are needed, several of which are frequently closed.