Behavior of Electron Wave Functions near the Atomic Nucleus and Normalization Screening Theory in the Atomic Photoeffect

The behavior of electron wave functions near but outside the atomic nucleus is discussed. It is shown that point-Coulomb shapes persist to quite large distances ($r\ensuremath{\cong}5{\ensuremath{\lambda}}_{e}$, where ${\ensuremath{\lambda}}_{e}$ is the Compton electronic wavelength) for bound states and also for energy-shifted continuum states. The screening effects on continuum-state normalizations cancel the screening effects on the kinematic factor $\mathrm{pE}$ in cross sections. These results are used to examine the normalization screening theory in atomic photoeffect, which is characterized by distances both small on an atomic scale and large compared to the size of the nucleus. It is argued that this theory, which describes screening effects simply as a change in normalization, can be good to 1% for photon energies more than 10 keV above the $K$-shell threshold in Al, 30 keV in Cu, 60 keV in Sn, 150 keV in Pb, and 200 keV in U. This agrees well in order of magnitude with exact numerical calculations.

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