PARTIAL WIDTHS BY ASYMPTOTIC ANALYSIS OF THE COMPLEX SCALED RESONANCE WAVE-FUNCTION

The complex scaled square-integrable resonance wave function describing the scattering of a particle at a distance r from a target with internal state energies and wave functions denoted ∈j and χj (x) is given by Σjχj(x)φj(r), where the φj(r)'s are the channel functions. The partial widths Γj (i.e., the decay rates into the channels open for dissociation) are obtained by calculating |φj(r)(k j/m)1/2 exp[ -ikjr exp(iθ)]|2 as r → ∞, where exp(iθ) is the complex scaling factor, m is the reduced mass of the two scattered entities, and kj = [2m(E res - ∈j)]1/2. Eres is the complex resonance eigenvalues of the complex scaled Hamiltonian H(x,r exp(iθ)). The wave function is determined either from a propagation plus matching technique or using a basis of particle-in-a-box functions. The former procedure is applicable even in the limit of zero rotation angle. Illustrative examples are given for a two-channel model Hamiltonian studied previously by Noro and Taylor, and by Bacic and Simons, and for a Hamiltonian which describes the scattering of HD from a flat Ag surface. © 1990 American Institute of Physics.