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 td 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 td=td⁰exp(QkBT) can be invoked is given. Our theory which is essentially parameter-free produces prefactors td⁰ in the whole experimental range of physisorption from 10^-7 to 10^-14 sec.