Inelastic atom-surface scattering: A comparison of classical and quantum treatments

Abstract

The validity of the classical approximation is investigated for the calculation of the energy transferΔε and sticking coefficient of particles scattered by harmonic solids. If in zeroth order the static approximation for the force between particle and solid is valid, the energy transfer can be calculated classically, if the WKB approximation for the matrix element of the force holds. This is the case except at low impact energies. The characteristic energy below which quantum effects become important depends strongly on the long range behavior of the force.

For the sticking coefficient one has to distinguish quantum effects of particle and solid. Quantum effects for the particle can again be neglected if the WKB approximation for the matrix elements is valid. The solid, however, can be treated classically only, if the number of excited phonons is large compared to unity. This requires energy transfersΔε large compared to the Debye energy of the solid.