INTERACTION POTENTIAL MATRIX-ELEMENTS FOR SINGLE-PARTICLE SCATTERING OFF A SIMPLE HARMONIC-OSCILLATOR

The matrix elements of the interaction potential for spinless two-part icle scattering where one of the particles is confined about the origi n by a harmonic-oscillator potential, are explicitly evaluated. This p roblem is important in the quantum-mechanical theory of ultracold part icle sticking to clean surfaces, and is directly relevant to studies o f molecular adsorption/desorption. A new result concerning the Hermite polynomials is obtained, as well as the discovery of a novel family o f polynomials that are intimately connected with the diagonal matrix e lements of the interaction potential. Recursion relations and a genera ting function are obtained for these polynomials. The zeros of these p olynomials are also discussed.