Quantum rearrangement scattering calculations using the invariant imbedding method

We derive an algorithm to calculate quantum transmission and reflection amplitudes (S-matrix elements) for rearrangement reactions using the invariant imbedding method. Our approach can incorporate closed channels, treat complex potentials (to simulate decay), and can be used within an adiabatic representation (in which derivative coupling terms are present) or within a diabatic representation. The method can also be used to determine bound-state energies when only closed channels are present. The method is demonstrated on a rearrangement problem with two coupled potential surfaces (four channels) as a function of energy in the energy region from the lowest channel threshold through the highest channel threshold.