The Application of the X-Ray Laws to Optical Spectra of Higher Rank, and the Classification of Ga IV and Ge V

J. E. Mack; Otto Laporte; R. J. Lang

doi:10.1103/PhysRev.31.748

Abstract

Spectra of Ga IV and Ge V.—By application of the Moseley law and the two doublet laws of x-ray spectroscopy, the ( $3 d^{9} 4 s$ ) and ( $3 d^{9} 4 p$ ) levels of Ga IV and Ge V and a tentative ( $3 d^{10}$ ) level for Ga IV, have been found. The levels formerly classified as ${}^{3}D_{1}$ , ${}^{1}P_{1} (3 d^{9} 4 p)$ of Zn III have been interchanged.

Correlation of inverted multiplet levels to series limits.—On the hypothesis that as the nuclear charge increases the levels of an isoelectronic sequence tend to cluster relatively into groups forecasting the next higher ion due to a transition from $ls$ - to $jj$ -coupling, evidence is adduced to show that of the ${}^{3}D$ , ${}^{1}D (d^{9} s)$ , the ${}^{3}D_{2}$ level approaches the limit ${}^{2}D_{3} (d^{9})$ , contrary to the theory of Hund. The case is analogous to that of Ne, in whose empirical series ${}^{3}P_{1} (2 p^{5} 3 s)$ approaches ${}^{2}P_{2} (2 p^{5})$ .

Distinctions between x-ray and optical spectra, in application of the x-ray laws.—(1) Exact representation of isoelectronic optical spectra on a Moseley diagram generally requires knowledge of series limit correlations of individual levels; the problem is close to that of general term-representation. (2) X-ray energy levels are ionization energies of neutral atoms, whereas in isoelectronic spectra the net charge increases with the atomic number $Z$ ; the first order screening number $σ_{1}$ increases with $Z$ in x-ray spectra, but decreases to an asymptote in isoelectronic spectra. The difference might be explained by outer screening.

Shape of the $σ_{1}$ curve for isoelectronic spectra.—If $σ_{1}$ is plotted as a function of $Z$ , the initial slope of the curve depends upon the $n$ - and $l$ -values of the added electron but changes only slowly with the total number of electrons, and substantially not at all with the ion configuration for a given number of electrons; this rule implies that the lines on the Moseley diagram, representing the addition of a given $n_{l}$ electron to different isoelectronic sequences containing nearly the same number of electrons, are parallel, to a second approximation.

The irregular doublet law applied to isoelectronic sequences in the neighborhood of a closed $d$ -shell ( $d^{10}$ ), is valid for ${(p)}^{\frac{1}{2}} - {(s)}^{\frac{1}{2}}$ but not for ${(d)}^{\frac{1}{2}} - {(p)}^{\frac{1}{2}}$ or ${(f)}^{\frac{1}{2}} - {(d)}^{\frac{1}{2}}$ .

Received 1 February 1928

DOI:https://doi.org/10.1103/PhysRev.31.748

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