Atomic Energy Relations. I

A simple method for the calculation of approximate energies of atomic levels is presented in this paper. It is based on the derivation of linear relations which express the unknown energy in terms of observed energy values of the atom and its ions. It is shown that the degree of approximation increases with the amount of experimental data available for use in the calculation and also how the best formulas can be obtained for each case. Several tables are given containing formulas for configurations involving s and p electrons. They are applied to the spectra of carbon, nitrogen and oxygen and the energy values so determined are compared with those known from observations. In an appendix the method of approximation is compared with the quantum mechanical perturbation method

Separations in Hyperfine Structure

The quantum mechanics conception of a spinning electron in an s state makes it probable that its interaction energy with a nuclear moment i is simply proportional to the average of is cos (is). Expressions for this average cosine have been obtained and applied to different examples. In more complicated cases it can only be said that the interaction energy is proportional to ij cos (ij), which makes the interval rule hold for hyperfine structure

Correction to the Moliere's formula for multiple scattering

The quasiclassical correction to the Moliere's formula for multiple scattering is derived. The consideration is based on the scattering amplitude, obtained with the first quasiclassical correction taken into account for arbitrary localized but not spherically symmetric potential. Unlike the leading term, the correction to the Moliere's formula contains the target density $n$ and thickness $L$ not only in the combination $nL$ (areal density). Therefore, this correction can be reffered to as the bulk density correction. It turns out that the bulk density correction is small even for high density. This result explains the wide region of applicability of the Moliere's formula.Comment: 6 pages, RevTe

On unification and admissible rules in Gabbay-de Jongh logics

In this paper we study the admissible rules of intermediate logics with the disjunction property. We establish some general results on extension of models and sets of formulas, and eventually specialize to provide a a basis for the admissible rules of the Gabbay-de Jongh logics and to show that that logic has finitary unification type

The Paschen-Back Effect of Hyperfine Structure

The study of the Paschen-Back effect in hyperfine structure is of particular interest as it is the only possibility to verify the complete theory of the gradual change of the Zeeman effect from weak to strong fields, as there are no suitable multiplets available for this purpose. The theory of the Zeeman effect for any field strength has been studied by Heisenberg and Jordan [Zeits. f. Physik. 37, 263 (1926)] and by Darwin [Proc. Roy. Soc. A115, 1 (1927)] for the case of ordinary multiplets. There may be shown to be a very close analogy between ordinary multiplets and the hyperfine structure separations, the former being due to the interaction between the total extranuclear moment and the nuclear moment

Multiple Conclusion Rules in Logics with the Disjunction Property

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics