The internal conversion of γ-rays

Ellis and Wooster have discussed in two recent papers the experimental evidence for the absorption of γ-rays in the X-ray levels of the atom in which they are emitted. In the present paper this absorption will be investigated on the lines of quantum mechanics. The problem is that of the perturbation of a heavy atom by a Hertzian doublet placed at its centre. It will be assumed that the characteristic functions corresponding to the orbits considered are those of a hydrogen-like atom. The normalised expressions for all these functions are given by Oppenheimer. If A be the perturbing term in the potential energy it may be shown by an extension of an argument given by Dirac, that the increase in the number of systems in a given stater (or in the case of positive energies in an interval of length 2πh ) from time —T to T, where T is large compared with the periods of the atom, is ΔN (r ) = 1/h 2 (Σs + ∫) (N (s ) - N (r ) | ∫T -T A (rs )dt |2 , (1) where N(s ) and N(r ) are the numbers of systems initially in the statesr ands , andh is here (Planck’s constant)/2π. Of these the number of transitions from the states to an interval of positive energy (Er , Er -d Er ) is, supposing N (r ) = 0.