Quantum Theory of the Unmodified Spectrum Line in the Compton Effect

The theory is based on the following assumptions: (a) The energy of the primary quantum plus the kinetic energy of the electron in its Bohr orbit (supposed circular) is equal to the energy of the scattered quantum plus the kinetic energy of the recoil electron after removal from the Bohr orbit and before it has escaped from the electrostatic field of the atom; (b) the vector sum of the momenta of the primary quantum and the electron in its orbit is equal to the sum of the momenta of the scattered quantum and the recoil electron just after removal from its orbit; (c) in order for the scattering to take place according to (a) and (b) the difference between the energies of the primary and scattered quanta must at least equal the binding energy of the electron in its Bohr orbit. From these assumptions it is found that there are certain positions of the electron in its orbit from which the electron cannot be ejected by the primary quantum. In these positions the mass of the whole atom is added to that of the electron, and the change of wave-length is negligible. For $\mathrm{MoK}\alpha$ rays scattered by the K electrons of C, the theory indicates that there are no unmodified rays scattered at angles less than 23°, and that the change of wave-length of the modified rays scattered at 90°, lies between.01 and.06 A. These conclusions are in general agreement with experimental results of A. H. Compton and of Clark, Duane and Stifler.