The photoelectric effect for γ-rays

Abstract

1. Introduction .—A discussion of the photoelectric effect for hydrogen­ like atoms has been given by many authors. In the simplest case it is assumed that the wave-length of the incident radiation is large compared with the “ radius of the atom.” If z be a co-ordinate measured from the centre of the atom, the axes may be chosen so that the perturbing vector potential involves the factor exp. (±2π i z /λ), where λ is the wave-length of the radiation. For very large wave-lengths we put this equal to unity, or we may use the first two terms of the expansion. For very short wave-lengths, however, the expansion is illusory, and we must use some other method. For γ-ravs the “radius of the atom” is large compared with the wave-length of the rays. A knowledge of the wave-function near the nucleus is therefore necessary. Further, the photo-electrons emitted have velocities comparable to that of light. In view of these two circumstances it is necessary to use a relativistic theory of the atom, and in the following we shall endeavour to apply the theory of the Dirac electron. In 2 we develop a normalised solution of the equations for the hydrogen­like atom, when the total energy, E, is greater than mc 2 , the rest energy of an electron. Next we consider the perturbation theory, which gives the total number of electrons emitted and their resultant forward momentum, in terms of the matrix elements representing transitions from the ground state to states where the electron is free. The chief difficulty is the evaluation of these matrix elements, which is only carried through when the atomic number Z is small, and the wave-length of the incident light is such that the energy of one quantum is comparable to mc 2 , corresponding to wave-lengths of the order 10 -10 cm. The first restriction is very unsatisfactory, since the photoelectric effect is best observed in heavy atoms. The results obtained are, however, in qualita­tive agreement with the experimental results for heavy atoms, if we exclude the variation with atomic number.