5. Connections to momentum space approaches

A discussion of the high energy limit of photoabsorption (and related processes), similar to that presented here in coordinate space, can be given in momentum space. The matrix element is an integral over initial and final wave functions and the photon-electron operator, now all represented in momentum space. Such an approach is illustrated by work in the SO region [6] and the QF region [7,9]. Using the standard form of the electron-photon interaction in Coulomb gauge (corresponding to V-form in coordinate space) the matrix element, in these regions, can be written in terms of the initial (bound) state wave function in momentum space, evaluated for large momenta appropriate to the region ( ${\bf p}_{1}$ in the SO region or relative momentum ${\bf p}$ in the QF region). Using the Schrödinger equation in momentum space, we may evaluate the matrix element in an iterative procedure, obtaining the leading powers in inverse momenta from the interaction potential energy evaluated at these large momenta. For the SO region the relevant part of the interaction is the e-N interaction, while for the QF region the relevant portion is the e-e interaction. In this way the leading term in the power expansion in 1/p is obtained directly from the interaction potential energy, as it is in the coordinate representation when A-form is used. The final result is the same as the coordinate space result. The SO result of [6], obtained in momentum space, and the result of [5], obtained in coordinate space using A-form, are both expressed in terms of the value of the wave function at the coalescence.