The internal conversion of γ-rays with the production of electrons and positrons

Abstract

A γ-ray emitted from the nucleus of a radioactive atom may be absorbed by one of the outer electrons, with the production of a β-ray. This process has already been treated at length and fairly satisfactory results have been obtained. If the energy of the γ-ray is greater than 2 mc 2 it is possible for the γ-ray to be absorbed by one of the electrons in a state of negative energy. This electron is then emitted eith an energy hν 0 - | E' |, where hν 0 is the energy of the γ-ray and E' the energy of the electron in the negative energy state. We are thus left with an electron of energy hν 0 - | E' |, and a hole, or positron, of energy | E' |. The problem has been treated by Oppenheimer and Plesset, who gave an approximate answer in the form I ~ α 3 Z 2 , where I is the Internal Conversion Coefficient, that is, the number of pairs created for each γ-ray emitted from the nucleus, α is the fine structure constant and Z the atomic number of the nucleus. The approximations used were very rough, and as the problem could be treated rigorously it was decided that an accurate computation would be worth attempting. While these calculations were in progress, Oppenheimer and Nedelski gave another calculation of I, in which they found that for high energies it was almost independent of the atomic number of the nucleus emitting the γ-ray. They therefore neglected completely the electrostatic field of the nucleus. According to these authors the method should be valid when Z c /137 ν ≪ 1