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The collisional transfer of kinetic energy from a gas atom to a cold solid is investigated in a simple model. (The solid is one-dimensional; classical mechanics is used throughout; and simplified interactions are assumed.) In two limiting cases the combined equations of motion of the atom and the lattice are solved exactly. The efficiency of energy transfer obtained from these calculations is much higher than that which is predicted from Lennard-Jones' single phonon approximation.
Robert Zwanzig (1960) studied this question.