Resonance quantization with persistent effects

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Abstract
Resonance energies and widths are calculated for non-standard situations where the potential matrix does not assume a constant diagonal form for infinite interparticle separation. Two cases are examined. The first (persistent potential effects) is illustrated by the calculation of the Rayleigh scattering amplitude by a diatomic molecule, where a linear open channel potential is coupled to a harmonic closed channel. In the second case (persistent coupling effects) the channel potentials remain coupled at infinity because the channel functions do not describe the separated atoms. In both cases the introduction of complex-energy resonance boundary conditions requires special treatments. Partial widths can be accurately extracted either by explicitly considering the correct asymptotic form of the channel functions or through a suitable asymptotic analysis of the complex-energy probability flux.