Multiphonon processes in a quantum-statistical theory of desorption

A complete fourth-order quantum-statistical calculation of the isothermal desorption time td in a gas-solid system is presented showing localized physisorption including all one-phonon and two-phonon processes in fourth order. The multiphonon interaction terms arising from higher-order derivatives of the surface potential turn out to contribute significantly to the desorption rate. Extensive numerical work confirms that the relaxation time approach to desorption phenomena is acceptable for weakly coupled systems for which h|E₀|td where E₀ is the energy of the bound state. Second-order calculations are sufficient as long as |E₀|kBTωD, where ωD is the Debye energy of the solid. Fourth-order contributions become important for |E₀|<ωD and kBTωD. Moreover, for ωD≤|E₀|≤2ωD fourth-order terms are essential because second-order contributions are zero in this region of bound-state energies.