Anomalous Threshold Laws in Quantum Sticking
Clougherty, Dennis P.
Original · EN
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 k with k→ 0 where k=√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 k¹⁺α, α> 0 as k→ 0, are shown to arise from a soft gap in the weighted density of states of excitations; α is determined by the behavior of the weighted density of states near the binding energy.
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