Examples of the Zeeman effect at intermediate strengths of magnetic field

Abstract

In a recent paper called “The Zeeman Effect and Spherical Harmonics,” Prof. Darwin gives a set of formulæ from which can be determined the frequencies and intensities of the lines in the standard Zeeman Effect. Except for s — p doublets these quantities could previously only be calculated for strong or weak magnetic fields, and the interest of the new formulæ lies in the fact that from them we can also calculate the frequency and intensity at any intermediate field. Approximate algebraic solutions are available for strong or weak fields, but the new method makes numerical solutions for all strengths easily practicable. The present work gives the application of the new formulæ to three cases which involve simple but lengthy calculation. These are the s — p and p — d doublets and the s — p triplets, but we describe first the case of the s — p triplets as this illustrates most fully the method under consideration. As these cases involve respectively 10, 34 and 19 lines, it will be readily seen that the discussion of any more complicated systems would lead to a large amount of work. The simplest case of all, that of the s — p doublets, is already known from the work of Voigt (by entirely different methods). As, however, so much of the material for working out the s — p doublets by the new method is the same as we require for the p — d doublets, we have included in a brief form the results for the simpler case. The theory and procedure is, of course, similar for all the three examples considered, so we now give an outline of the calculations and results before entering into the detail for the several cases separately. Referring to 5 of the previous paper, we find the following rules for forming the “chains of equations” on which the whole calculation is based.