Coupled-channel method for nuclear scattering of Dirac particles: High-energy electrons on calcium

We obtain a solution of the Dirac equation in the presence of the electromagnetic field of a complex nucleus by means of coupled-channel partial wave analysis using a new method in which the asymptotic solutions of the coupled radial wave equations include all electromagnetic couplings. A compu er program employing this method is used to determine the importance of dispersion effects in the scattering of 250 MeV electrons from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$. We find the dispersion effects to be less than 1% for angles below 90° (i.e., considerably less than experimental error over the range investigated experimentally), thus supporting the view that the difference in the differential cross sections from ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}$ arises primarily from a difference in the ground state charge distributions of the two isotopes.