Refined Impulse Approximation for the Collisional Excitation of the Classical Anharmonic Oscillator

Abstract

A modification of the conventional classical theory of vibrational–translational energy exchange is made which leads to an expression of increased accuracy and which has the proper behavior at high energy. It is pointed out that the refined impulse approximation can be used to calculate the energy transferred to an anharmonic oscillator in configurations where the potential energy curve has positive curvature. The case in which the oscillator potential has negative curvature is analyzed and is shown to lead to energy exchanges which exceed the predictions of the impulse approximation. Expressions are given for the energy transferred in grazing collisions which can be used to estimate total inelastic cross sections.