Magnetic Internal Compton Coefficients in the Born Approximation

Abstract

The absolute and relative probabilities of a nuclear transition in which there is a simultaneous ejection of a $K$ electron and emission of a gamma ray has been calculated quantum-mechanically for the case in which the virtual radiation field is a $2^L$ magnetic multipole. The process will be referred to as an internal Compton effect. The Born approximation has been used and hence the calculations are expected to be valid only if the nuclear charge $Z$ is small and the nuclear energy level separation large. The ratio of the number of continuous energy gamma rays to the number of discrete energy $K$ electrons is independent of the nuclear matrix element and decreases as $Z$ or as $L$ increases. This is true for any energy range and any angular range of the continuous energy gamma rays, where the angles are measured with respect to the coincident continuous energy $K$ electron. The angular distribution is most sensitive to $L$ for comparable electron and gamma-ray energies and for large angular separation. These conclusions are not much affected by inclusion of the $L$ shell. In the limit of small gamma-ray energies, the results reduce to those predicted by semiclassical theory.