Patterns of term structure in simple spectra.

Abstract

view Abstract Citations (3) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Patterns of term structure in simple spectra. Layzer, David Abstract Theoretically, a pure configuration of electrons outside closed subshells has a definite, calculable pattern of term structure. For example, the two intervals between the three terms of (closed sub- shells) (p1) have the theoretical ratio 1.5. The observed patterns, however, often vary widely from atom to atom. For example, the above-mentioned ratio for (Is ) ( p1) is about -5 in Bei and 8 in BIl. Discrepancies of this kind are generally, and in my opinion correctly, ascribed to the mixing of configurations. Two obstacles have stood in the way of a successful quantitative theoretical description of configuration mixing: the lack of reliable criteria for recognizing the important components in a configuration mixture; and the lack of workable mathematical machinery for calculating the degree of mixing of given configurations. In this paper I try to overcome both these obstacles. My first point is that the data can be grouped so as to exhibit useful regularities in the structure of configuration-sequences. A configuration-sequence is defined as a set of identical configurations in an iso-electronic sequence, e.g., (Is2) ( p2) in Bei, BIl, CIII If 1(Z) is the interval between two terms of a configuration in such a sequence, Z denoting the atomic number, then the interval-difference I (Z I) - 1(Z) becomes sensibly constant for moderately large Z. The set of all independent interval-differences for a given sequence characterizes the sequence as a whole. A simple theoretical argument now shows that the structure of this set is influenced only by a very special kind of configuration mixing, which I call stable mixing. Only a small number of configurations can participate in a stable mixture, and these may be readily enumerated in every instance. I have found a method of predicting the structure of the set of interval-differences characterizing a configuration-sequence, and have successfully applied it to the sequence (is ) ( p2). This method, moreover, may be used to predict patterns of term structure in individual atoms. The crux of the method lies in the construction of analytic one-electron wave functions of a very general form. The 15, 25, and 2p wave functions are as accurate as the corresponding numerical wave functions of Hartree and Fock. The variational wave functions are used as the basis for a perturbation treatment, which can be carried out to any desired degree of accuracy. The Observatory, University of Michigan, Ann Arbor, Mich. Publication: The Astronomical Journal Pub Date: April 1951 DOI: 10.1086/106496 Bibcode: 1951AJ.....56...43L full text sources ADS |