A fully relativistic treatment of the radiation accompanying nuclear capture of orbital electrons is presented. All effects of the electrostatic field surrounding the nucleus are taken into account. As a preliminary step, convenient representations for the electron Green's function and initial state wave function in a Coulomb field are derived. These forms, involving Dirac operators applied to scalar functions and free-particle angular eigenfunctions, are developed from the second-order Dirac equation. They are particularly useful for calculations since the procedures which make use of the properties of traces can be employed with them.

With the aid of these representations the photon energy spectrum and polarization associated with allowed radiative $K$ capture are computed. Relativistic Coulomb corrections are shown to decrease the expected photon intensity significantly at all energies. Since their effect is not sensitively dependent on energy, the predicted shape of the spectrum is not greatly altered. The Coulomb field also influences the degree of polarization of the photons emitted, but has an appreciable effect only near the lower end of the spectrum.

The influence of atomic screening on the capture from the $K$ and $L$ shells is also taken into account approximately. It is shown that screening considerably decreases the likelihood of radiative capture of all but the innermost electrons.

Finally, the existing experimental evidence is reviewed and shown to agree with the theory presented. Some additional experimental tests are proposed.

• Received 28 June 1957

DOI:https://doi.org/10.1103/PhysRev.109.1307