The internal conversion coefficient for radium C

Abstract

It is well known that the γ-rays emitted from a radio­active nucleus are often partially absorbed by the atomic system, giving rise to secondary β-rays. From observations of the resultant γ-ray intensity, and that of the β-rays, it is possible to infer the proportion of γ-rays reabsorbed in the atomic system. This factor is called the “internal conversion co­efficient.” Its theoretical value has been discussed by Miss Swirles and R. H. Fowler. Miss Swirles treats the nucleus as an oscillating Hertzian doublet, radiating classically, and considers the radiation field as producing photoelectric transitions in the planetary electrons, according to the Schrodinger theory. The rate of emission of γ-rays from the nucleus is taken to be the classical rate of radiation of energy by the dipole, divided by hv . The values obtained in this way were about 10 times too small, except for the γ-ray of energy 14.26 x 10 5 e. v., which has an internal conversion coefficient several hundred times that given by the theory. This special case has been discussed by Fowler ( loc . cit .), and we shall not consider it here. An obvious defect in the theory is the use of Schrödinger’s equation, which may not be expected to hold so near the nucleus, or for electrons of such high energy. It therefore seemed possible that the more correct, relativistic equation of Dirac might give results in accordance with experiment in the majority of cases, and the calculation has been carried out by Casimir. The same model is used, and, for purposes of calculation, the interaction of the other electrons is neglected, so that we have a single electron in the field of a charged nucleus. For the β-rays emitted from the K-shell, we may take the actual nuclear charge in carrying out the calculation. In the case of extremely hard γ-rays, whose energies may be considered large compared with mc 2 , it is legitimate to use the asymptotic expansion for the wave function repre­senting the β-ray. If we apply this theory to the range covered by experiment, we obtain results (Casimir, loc. cit. ) which are still much too small, so that we were tempted to attribute the bulk of the conversion to some special type of interaction with the nucleus. It seems fairly certain that this must be the case for the γ-ray with hv = 14.26 x 10 5 e. v., which has an abnormally high internal conversion coefficient.