Surface resonances and sticking in the Hutchison model

It is shown that using the Hutchison prescription to account for inelastic effects on surface resonances can be partially justified when sticking is taken into account. The prescription is to multiply each elastic matrix element for collision with the repulsive potential by the appropriate `square root of the Debye-Waller factor'. It is shown that, under certain assumptions, it is correct to do so for the collisions entering and exiting the resonant surface state.