Close-coupling approach to gas-solid energy transfer

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Abstract
The inelastic scattering of a gas molecule from a solid surface is treated quantum mechanically and in three dimensions using the close‐coupling formalism. Energy transfer processes involving internal states of the molecule and one‐phonon states of the solid are included as well as arbitrary diffractions. The phonon quantum number is replaced by a continuous variable. The dependence of the unknown wavefunction on this continuous variable is expressed as an expansion in a complete set of known functions having this continuous quantum number as argument. This substitution results in the continuously infinite set of coupled differential equations being replaced by an infinite set of discrete coupled equations. Truncating this set after a finite number of terms leads to finite sets of coupled equations which are solved by standard techniques. In applying this procedure to a simple example (which, nevertheless, provides a stringent test of the method) reasonably accurate results are obtained with a basis set of only 25 functions describing the continuous quantum number. On the basis of this test, it is suggested that this method appears to be practical for computing accurate gas‐solid one‐phonon energy transfer probabilities and should be most useful when many one‐phonon states are involved in the collisions (thereby complimenting ``near‐specular'' energy transfer theories).