Coupled-states approach for elastic and for rotationally and vibrationally inelastic atom–molecule collisions

Abstract

The elastic and inelastic collisions of an atom with a diatomic molecule are treated quantum mechanically in the body−fixed coordinate system. The body−fixed equations of motion are first compared with the usual spaced−fixed ’’close−coupling’’ equations and limiting cases are considered in which the two formalisms become equivalent. The recently developed ’’coupled−states’’ approximation in the body−fixed system is then described in which intermultiplet transitions are neglected and the eigenvalue of the orbital angular momentum operator l̂2 is approximated by h/l (l + 1). Numerically computed cross sections from this approximation are compared to those computed from the standard space−fixed close−coupling equations for the test system He−H2. Agreement to within a few percent is obtained for the integral as well as for the differential cross sections for elastic and for rotationally and vibrationally inelastic scattering in the energy range of 0.9 to 4.2 eV. A coupled−states large basis calculation (j = 0, 2, 4, 6, 8, 10 for n = 0 and j = 0, 2, 4, 6 for n = 1) at 4.2 eV is presented which demonstrates the enormous utility of the method.