  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
$s\sim k$ with $k\to 0$ 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 $s\sim k^{1+\alpha}, \alpha > 0$ as $k\to 0$, 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.
