Time-reversal in the impact parameter method

In the impact parameter method the electron hamiltonian depends upon the time through the motion of the nuclei and the consequences of time-reversal invariance are less obvious than they are for time-independent hamiltonians. The authors make use of the hermiticity of the electron hamiltonian and its invariance under time-reversal to derive some useful relations occurring in the impact parameter method. A basis set of either atomic or molecular eigenfunctions which exploit the reflection symmetry in the scattering plane, is adopted, and a quantization axis is chosen which may be fixed or rotating. Systems of arbitrary spin are considered, and require only that nuclei move in a central (but unspecified) potential.