  In paper I (physics/0010068) entitled "The No-sticking Effect in Ultra-cold
Collisions", we showed that under very general circumstances, atoms approaching
a surface will not stick as its incoming energy approaches zero. This is true
of either warm or cold surfaces. Here we explore the transition region from non
sticking to sticking as energy is increased. The key to understanding the
transition region is the WKB approximation and the nature of its breakdown.
Simple rules for understanding the rollover to higher energy, post-threshold
behavior, including analytical formulae for some asymptotic forms of the
attractive potential are presented. We discuss a practical example of
atom-surface pair in various substrate geometries. We also discuss the case of
low energy scattering from clusters.
