Interpretation of hyperfine structure.—Discussion of H. F. S. in Tl II. Relative g (I) factors of Tl, Bi and Pb (207), and nuclear structure

As the theory of hyperfine structure separations is employed in section II in discussing the hyperfine structure of Tl lI, and again in section III in comparing the Landég (I) factors of Tl, Pb and Bi, its status is briefly considered in this introduction. The theory of the interaction of a single valence electron of thes type with a magnetic nucleus is somewhat indefinite, insomuch as it can not be directly verified. The expression for the interaction W =a ns I. s cos (Is) (1) is undoubtedly correctly formulated, as it has been experimentally verified. The relative hyperfine separations of states of the 6snd and the 6snf configurations of Tl II, treated in this paper, and of certain configurations in other spectra. in which the interactions with the magnetic nucleus of all the valence electrons except the deeply penetratings electron are negligible, are in good agreement with the predictions based on this equation. The theoretical expression for the interaction constant, ans , which governs the magnitude of the separations, can only be determined by a quantum mechanical treatment of the state of the atom under consideration; and always involves the factorg (I), which as yet has never been determined by other independent methods. Consequently, the validity of the expression for ans cannot be checked directly. There is, however, the possibility of checking somewhat inexactly the expression for ans by comparing the value ofg (I) calculated from the experimental data by the use of the theoretical expression with that expected from our conception of the nucleus. Such comparisons show thatg (I) is of the order expected for a spinning proton; but beyond this are, as yet, of little value in checking the formula for ans since our theory of the nucleus is very uncertain, especially in view of the conclusion expressed in section III.