L 2 R -matrix studies of molecular collision processes-energy dependence of σ vj → v'j' for 4 He + H 2

Abstract

In this paper the Wigner-Eisenbud R -matrix theory is formulated to describe inelastic encounters between an atom A and a diatomic molecule BC. The formulation incorporates two particular aspects, (i) Intermolecular potentials V possess long-range ‘tails’ which vary asymptotically as R -n and consequently the R -matrix boundary is placed at a point R m beyond which V is slowly varying and weak. The scattered wave is propagated from R m to the asymptotic region, first by an adaption of the d. w. B. approximation, and secondly by an R -matrix propagation technique. (ii) The basis functions for the determination of the R -matrix in the strong interaction region ( O ≤ R ≤ R m ) are determined as eigen­functions of a suitable zero-order Hamiltonian H 0 the radial part of which includes a centrifugal contribution of the form ћ 2 J ( J + 1)/2 μ R 2 . Calculations are presented for the 4 He + H 2 system, and the results compared with those from a conventional coupled-channel calculation. Essentially exact agreement is found over a wide range of collision energies (0.55-0.9 eV). The R -matrix is determined at a single energy only, and reassembled at all other required energies. It is argued that the combina­tion of the full Wigner-Eisenbud technique in the strong interaction region, with a propagation method in the region where V is slowly varying and weak, ensures that the two techniques are used to their best advan­tage.