Comparison of quantum and classical calculations of thermal-conductivity cross-sections governing the Senftleben-Beenakker effect for HD-He mixtures

The classical approximation to nine cross-sections required for evaluating the mixture thermal conductivity and its magnetic-field dependence is tested by comparison with quantal close-coupling results for the HD-He interaction. Explicit results are given for the relation between the working expressions for the classical and quantal cross-sections as a function of total energy. At the highest total energy considered, 3000 cm-1, the agreement between the quantal and classical results is found to be good for all cross-sections considered, although it deteriorates as the energy is lowered to the j = 1 threshold energy, below which all the quantal results vanish. The cross-sections are thermally averaged for temperatures between 77·3 K and 298 K, and the difference between classical and quantal results is at most 11% at 298 K, with somewhat larger errors at lower temperatures. A hybrid scheme that interpolates between classical results above 3000 cm-1 and quantal results below 516 cm-1 is shown to yield accurate results for thermally averaged cross-sections.