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 εj and χj (x) is given by ∑jχj(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)(kj/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(Eres −εj)]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 Bačić and Simons, and for a Hamiltonian which describes the scattering of HD from a flat Ag surface.