Elastic Scattering of Electrons by the Coulomb Field of Nuclei Using Born Approximations

Abstract

Calculations including the second Born cross section for the elastic scattering of electrons by nuclei are performed taking a model for which the matrix elements are particularly simple. The potential corresponding to this model is a mixture of an attractive Coulomb and a repulsive Yukawa potential of range $\frac{1}{B}$ and relative strength $C$. The density is given by $\rho =-(C-1\mathrm{})\mathrm{}{\delta }^3\left(\mathrm{r}\right)+\frac{C{B}^2}{4\pi }\frac{e^{-Br}}{r}.$ Since the scattering is fairly insensitive to the details of the nuclear model, one can use the calculations made here to find scattering cross sections on different models by suitably choosing $B$ and $C$. This is done here for the uniform density model and the results are compared with the phase-shift calculations of Acheson for 15- to 35-Mev electrons. A fairly close agreement with his results is obtained up to medium elements ($Z\lesssim 50$).