Fractional gauge transformations of the first kind: Optimization of cross-section calculations

Abstract

A theory of matter-radiation interactions is presented that incorporates a fractional gauge transformation. The transformation is achieved with the Göppert-Mayer generator multiplied by a continuously variable gauge parameter. The derived Hamiltonian contains a mixture of A⋅p and E⋅x interaction terms: The field and matter variables within the full gauge-invariant, matter-radiation Hamiltonian are intermixed. Practical implications for calculating accurate transition cross sections using convenient, but inexact, matter eigenstates are developed by interpreting gauge-generalized perturbation theory as a gauge-variational theory. By minimizing the matter/field/interaction ground state energy with respect to gauge variations, the optimum matter-radiation basis for the chosen set of inexact matter states is obtained. The gauge optimization technique is demonstrated quantitatively for the 2pσu –1sσg electronic transition of H+2 using the simple LCAO-MO basis.