ABSTRACT
A possibility that we have not considered yet which may occur when the incident particle is an electron, is that the incident electron is captured in the atom and an atomic electron is emitted; or more correctly, we have not taken into account the fact that the electrons are identical. This effect is important at small energies. In the analysis of this effect, we may proceed in a fashion similar to the derivation of the Hartree-Fock theory (see Chapter 4). In order to obtain the potential energy for the incident electron, we form Slater determinant trial functions and minimize the expectation value of the Hamiltonian. We may make the simplifying assumption that the incident electron does not affect the equations for the atomic orbitals. This may be justified by noting that the wave function of the incident electron may be normalized in a large box of volume Ω; then its probability density inside the atom will be proportional to Ω-1 and so will be the potential it exerts on the atomic electrons in the Hartree-Fock approximation. Of course, physically the external electron will affect the atomic ones; this is described by the polarization effect discussed in the last section of the previous chapter, and we can see now that this polarization will be modified by exchange. Obviously, this problem goes beyond the Hartree-Fock approximation and is quite complicated; it is discussed by Goldberger and Watson, 1 p. 855.
