The problem of the interaction of two particles has been treated by Møller, using a correspondence method, and the same formula for the interaction has been found by Bethe and Fermi and by Fock, using the methods of Quantum Electrodynamics. In these derivations only free particles have been considered, and the object of this paper is to consider bound particles, taking into account the possibility of one of the particles having a finite life-time in its initial state. An example of this kind appears in the theory of the internal conversion of γ-rays, where we have to consider the interaction of a nuclear particle in an excited state with an electron in the K-shell. On the non-relativistic theory, the interaction of two particles is given simply by the Coulomb force, whereas according to Quantum Electrodynamics any interaction must take place via the field, if we suppose this to include longitudinal waves as well as transverse ones. It has been shown, however, that the longitudinal waves are equivalent to the Coulomb interaction, and in practice it is easier to replace this part of the field by Coulomb forces. Let us suppose that we have a system of two particles which makes a radiationless transition from a state Ψ
i
to a state Ψ
f
. The Coulomb interaction has non-zero matrix elements for this transition, which may be written down, but to find the effect of the transverse waves in the field (light quanta) we must proceed as follows. We assume the system to interact with the field, and pass over first into a state Ψ
q
, where, if we performed an experiment, there would be a definite probability of finding light quanta present. From this state it passes over to the final state with no quanta present. This is the procedure we shall adopt to calculate the matrix elements of the interaction, and we shall show that for bound electrons also it gives the same result as Møller’s theory.
Isospin Mixing in Light Nuclei