QUANTUM-THEORY OF STICKING

We present an exact solution of a one-dimensional (1D) model: a particle of incident energy E colliding with a target which is a 1D harmonic "solid slab" with N atoms in its ground state; the Hilbert space of the target is restricted to the (N + 1) states with zero or one phonon present. For the case of a short-range interaction V(z) between the particle and the surface atom supporting a bound state, an explicit nonperturbative solution of the collision problem is obtained. For finite and large N, there is no true sticking but only so-called Feshbach resonances. A finite sticking coefficient s (E) is obtained by introducing a small phonon decay rate eta and letting N --> infinity. Our main interest is in the behavior of s (E) as E --> 0. For a short-range V(z), we find s(E) approximately E1/2, regardless of the strength of the particle-phonon coupling. However, if V(z) has a Coulomb z-1 tail, we find s(E) --> alpha, where 0 < alpha < 1. [A fully classical calculation gives s (E) --> 1 in both cases.] We conclude that the same threshold laws apply to 3D systems of neutral and charged particles, respectively. In an appendix we elucidate the nature of sticking by the behavior of a wave packet incident on a finite N target.