Desorption by phonon cascades for gas-solid systems with many physisorbed surface bound states

We give the extension of our quantum-statistical theory of desorption for systems with many physisorbed bound states in the surface potential. Rate equations are set up and the desorption time $t_d$ is properly identified as the smallest eigenvalue of the matrix of transition probabilities. The latter are calculated exactly in second-order perturbation theory for a surface Morse potential. We show that desorption in weakly coupled systems with many bound states proceeds predominantly through one-phonon cascades. Two-phonon contributions are shown to be small. Desorption times are calculated for the He-LiF, He-NaF, He-graphite, H-NaCl, He-Ar, and Xe-W systems. The temperature regime over which a Frenkel-Arrhenius parametrization $t_d=t_d^0\exp \left(\frac{Q}{k_{B}T}\right)$ can be invoked is given. Our theory which is essentially parameter-free produces prefactors $t_d^0$ in the whole experimental range of physisorption from ${10}^{-7\mathrm{}}$ to ${10}^{-14\mathrm{}}$ sec.