Rapid Calculation of Electron Scattering Factors

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Abstract
The phase amplitude method is used to reduce the radial Schrödinger equation to two separate differential equations, one for the phase and one for the amplitude. These functions are both smooth as opposed to the rapidly oscillating solution of the radial Schrödinger equation for electron energies in the kilovolt range. The partial‐wave phase shifts were obtained rapidly by integrating the differential equations for the phase and amplitude numerically. Hartree—Fock and Thomas—Fermi—Dirac fields were used in the calculation. Results for argon and uranium are given in order to compare with previous results. It was found that the WKBJ approximation to the partial‐wave phase shift is a good approximation for the energies used in electron diffraction. This rapid method of computing electron‐scattering factors will make routine analysis of electron diffraction data more rapid as well as more exact.