On the use of high energy approximations to calculate intensities and angular distributions in atomic or molecular photoelectron spectroscopy

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Abstract
We examine the forms asymptotic in the energy for the differential and integral cross sections for ejection of photoelectrons from atomic or molecular targets. We find the plane wave, length form to be in disagreement with the plane wave, velocity form and the Coulombic, length form at all energies, and the plane wave, velocity form to be in disagreement with the Coulombic, length form at all energies except in the case of photoejection from the 1s orbital. Agreement of the plane wave, velocity form with the Coulombic, length form for initial orbitals of higher angular momentum can be produced by use of the first Born correction to the plane wave due to the presence of the Coulomb potential. It is demonstrated that orthogonalization of the plane wave to other bound orbitals of the system gives a result which will agree with the Coulombic, length and corrected plane wave, velocity forms only for particular values of the screening parameters of these orbitals, demonstrating that orthogonalization of the plane wave cannot lead to correct asymptotic forms except by accident. We discuss the method used to eliminate the divergences in the first Born correction to the electric‐dipole amplitude due to the infinite range of the Coulomb potential by interchange of the order of integration over coordinate space in the amplitude with the integration over momentum space in the Fourier representation of the wavefunction.

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