Fractional gauge transformations of the first kind: Optimization of crosshyphen;section calculations

摘要

A theory of matterhyphen;radiation interactions is presented that incorporates a fractional gauge transformation. The transformation is achieved with the Gouml;pperthyphen;Mayer generator multiplied by a continuously variablegaugeparameter. The derived Hamiltonian contains a mixture ofAsdot;pandEsdot;xinteraction terms: The field and matter variables within the full gaugehyphen;invariant, matterhyphen;radiation Hamiltonian are intermixed. Practical implications for calculating accurate transition cross sections using convenient, but inexact, matter eigenstates are developed by interpreting gaugehyphen;generalized perturbation theory as a gaugehyphen;variational theory. By minimizing the matter/field/interaction ground state energy with respect to gauge variations, the optimum matterhyphen;radiation basis for the chosen set of inexact matter states is obtained. The gauge optimization technique is demonstrated quantitatively for the 2psgr;undash;1ssgr;gelectronic transition of H+2using the simple LCAOhyphen;MO basis.