The Widths of theL-Series Lines and of the Energy Levels of Au(79)

Abstract

Following a résumé of the Weisskopf-Wigner theory of the shape of spectral lines, and, making certain simplifying assumptions, an expression is derived for the shape of an x-ray absorption discontinuity for the case where absorption is due to the ejection of electrons from inner orbits to the continuum of unoccupied Fermi-Sommerfeld levels. If these levels be assumed equally distributed, the curve ($\mu$ vs. $\lambda$) is a simple arctangent, from which the width of the associated energy level ($K, L\cdots$), corresponding to the full width of half-maximum of a radiated line, may be read directly. A more complicated expression results if the Fermi-Sommerfeld levels be not equally distributed. It is shown that the predicted shape of an absorption limit agrees reasonably well with the observed shape of the $L_{\mathrm{III}}$ limit of Au(79), the width of which was found to be 4.4 volts. Data are presented on the widths of some 23 lines in the $L$-series of Au(79), obtained by a two-crystal spectrometer. These widths, corrected for effect of the crystals, vary from 7.6 to 20.8 volts. Making use of the conclusion of Weisskopf and Wigner, that the width of a line may be interpreted as the sum of the widths of the energy states involved, and starting from the value 4.4 volts for the width of the $L_{\mathrm{III}}$ state, the widths of the several $L$, $M$, $N$ and $O$ states of Au(79) are computed. For a given total quantum number $n$, the width decreases with increasing orbital quantum number $l$. States having the same value of $n$, $l$ have nearly the same width. For any given $l$, the $L$ states are narrowest.