Anomalous threshold laws in quantum sticking.
It has been stated that for a short-ranged surface interaction, the probability of a low-energy particle sticking to a surface always vanishes as s approximately k with k-->0 where k=sqrt[E]. Deviations from this so-called universal threshold law are derived using a linear model of particle-surface scattering. The Fredholm theory of integral equations is used to find the global conditions necessary for a convergent solution. The exceptional case of a zero-energy resonance is considered in detail. Anomalous threshold laws, where s approximately k(1+alpha),alpha>0 as k-->0, are shown to arise from a soft gap in the weighted density of states of excitations; alpha is determined by the behavior of the weighted density of states near the binding energy.
Clougherty
Dennis P
DP
Department of Physics, University of Vermont, Burlington, VT 05405-0125, USA.