Pseudostate description of diatomic-molecule scattering from a hard-wall potential

Abstract

A collinear scattering of a structured particle from a hard wall is studied with consideration of vibrational transitions initiated by the collision. It is shown that this problem can be solved analytically in the framework of the source-function method. With the use of the continuum discretization technique we are able to take into account both discrete and continuum states. No approximations of the interatomic potential is required. We illustrate our approach for the case of a hydrogen molecule bound by the realistic Morse potential. simple systems. The results by Sato and Kayanuma (13) indicate that the initial molecule ground state cannot survive after the collision when the energy difference between this state and the first-excited state goes to zero. Contrarily, Kavka et al. (9) show that an arbitrarily weakly bound molecule scattering from an arbitrarily high step potential remains in the ground state with probability equal to unity. Moreover, the molecule center of mass cannot get closer to the hard wall than ξ0 ln(V0/Ein) where ξ0 is a constant of order of the mean distance between the atoms, V0 is the potential barrier heights and Ein is the molecule impact energy. The case where the hard wall is infinitely high is particularly interesting because the molecule reflects from the surface at an infinitely large distance from the surface. In the next section we present the general analytical solution to the problem of interest for case where V0 is infinite. Our approach requires no approximations on the form of the interparticle interaction. To illustrate our theory we give a numerical example in Sec. III. In the conclusion we present the summary of the results.