A Multichannel “Potential Curves Hopping” Model for Inelastic Collisions

We introduce a multichannel “potential curves hopping” model and obtain the exact quantum mechanical S-matrix by solving the associated set of coupled second-order ordinary differential equations that describes the inelastic collisions between atomic particles. The only assumption is that the interaction matrix element between each pair of channels (say, γ and β) is of the form Uγβ(r) = Uβγ(r) =: Uγβ δ( r - rγβ), where δ (c) is the Dirac deltafunction, and rγβ and Uγβ are parameters which can be chosen freely.Semiclassical techniques can be incorporated directly in the theory if the Schrödinger equations for the uncoupled channels allow this treatment. The formulation is particularized to the two-channel problem and illustrated with a semiclassical example the He+ + Ne problem at 70.9 eV.