Magnus expansion and eikonal approximation in potential scattering

An expansion procedure due to Magnus is applied to the case of potential scattering. This technique, which is superior to the usual Born-Dyson expansion in that it preserves unitarity at each state, leads in first approximation to an expression for the scattering amplitude which contains as special cases the eikonal approximation and also the second Born approximation. In particular the first Magnus approximation provides a basis for the ad hoc addition of the real part of the second Born contribution to the eikonal scattering amplitude as was considered by Byron et al.     

Kinetic theory of vibrational relaxation in a radiation field: The optic-acoustic effect

A microscopic derivation is presented of the rate equations governing vibrational relaxation occurring in the optic-acoustic effect. Detailed expressions applicable to the spectrophone experiment are given both for an excitation source consisting of a broadband radiation field and for laserdriven systems. It is clear from the present treatment that no real advantage accrues from the use of laser excitation sources in the standard spectrophone experiment, due to the resultant strong dependence of the driving force itself on the mechanical chopper frequency. For broadband radiation field the dependence on the chopper frequency is removed and the standard result containing the Einstein coefficient of induced absorption is recovered. The spectrophone response for the simplest case of a two-level system is given explicitly and its similarity to phenomenologically derived expressions is pointed out.The work of F.R.M. was supported in part by a grant from the National Research Council of Canada. The work of A.T. was supported by the Foundation for Fundamental Research on Matter, which is sponsored by the Netherlands Organization for the Advancement of Pure Research.     

On the energy distribution of sputtered dimers

A theoretical expression is obtained for the energy distribution of sputtered dimers from crystal surfaces. The derivation is based on a model where the atoms which constitute a dimer, are sputtered independently from the crystal according to their respective single particle energy distribution functions. Two neighbouring atoms are then supposed to form a dimer if the sum of their initial relative kinetic energy and potential energy is less than zero. A comparison with experimental results for K₂ and KI sputtered from polycrystalline K and KI surfaces respectively, shows a good agreement.