Relativistic Theory of the Photoelectric Effect. Part I. Theory of the $K$-Absorption of X-rays. Part II. Photoelectric Absorption of Ultragamma Radiation

Part I: A strict theory of the absorption of x-rays is developed on the basis of relativistic quantum electrodynamics. The theory is applied to the absorption of x-rays by a Dirac electron in the field of a nucleus. Corrections to the non-relativistic theory are appreciable only for heavy elements, where the present calculations give a $K$-discontinuity twenty percent smaller than the earlier ones. The agreement with experiment is not improved.

Part II: The theory is applied to the calculation of the absorption of quanta whose energy is larger than the proper energy $m{c}^2$ of the electron. The cross section for absorption is here given approximately by $\sigma \sim 2\times {10}^{-22\mathrm{}}{Z}^5\lambda .$ This result is applied to account for the excess absorption over that predicted by the Klein-Nishina formula found experimentally for the gamma-rays of ThC″ by Chao and Tarrant. The theory is in fairly good agreement with experiment for Cu, but disagrees violently with it for Pb. An examination of the approximations made in deriving and applying the theoretical result shows that they cannot have introduced this discrepancy. There is thus a definite conflict between electrodynamical theory and experiment.