Electron–Atom Collisions

This book deals with collisions of electrons with atoms. Both the nonrelativistic and the relativistic theories are presented here. Since we are interested in applications, the first part of the book is devoted to the basic concepts of computational physics, describing the main numerical tools necessary for solving problems concerning the scattering of charged particles by central fields. We also briefly describe the main special functions of mathematical physics and provide methods to numerically calculate them. The second part of the book is dedicated to the nonrelativistic approach to the study of electron–atom scattering and to an introduction to Pauli matrices and spin. The Thomas Fermi and Hartree–Fock methods for describing many-electron atoms and, in particular, for calculating the so-called screening function are described in the second part of the book. The screening function is crucial for the calculation of phase shifts, and its analytical approximation is also presented to make easier the calculation of the electrostatic atomic potential. In the third part of the volume, after an introduction to the quantum relativistic equations (Klein–Gordon equation and Dirac equation), the Mott theory is described. It represents the quantum-relativistic theory of elastic scattering of electrons by central fields, the so-called relativistic partial wave expansion method. The last part of the book presents several applications. It contains exercises devoted to the calculation of the special functions of mathematical physics (notably, Legendre polynomials and spherical Bessel functions, both regular and irregular) and to their use for computing phase shifts, scattering amplitudes, differential elastic scattering cross-sections, and spin-polarization parameters. The exercises are provided with an increasing degree of difficulty. With the aid of these exercises, the reader can use all the information described in the first three parts of the book to write her/his own computer codes for the computation of all the quantities relevant to the scattering processes.