The Compton scattering by particles possessing charge and dipole moment

Abstract

The simplest exact classical theory, of a particle possessing charge and dipole moment proportional to the spin leads to a wave equation with an explicit spin interaction with the field. This wave equation is used in this paper to calculate the scattering probability coefficient in the Compton effect by two methods. The first method uses the unquantized radiation field; the second uses Dirac's scheme of field quantization. The scattering probability coefficient is given in the general case in terms of the charge e, the constant of proportionality in the dipole moment C, and the quantities k, l specifying the spin. Some special results are considered for particles of spin ½ and 1. Formulae are given for the scattered intensity as a function of the angle of scattering, and the total scattering cross-section as a function of the energy of the unpolarized incident radiation. Graphs are given for these formulae when the magnetic part of the dipole moment takes the empirical values in the case of the electron, proton and neutron. In the case of the meson, normal and abnormal values of the dipole moment are used.