The effect of a nucleus spin on the optical spectra.—II

Abstract

In a recent paper the author has considered the effect of a nuclear spin of half a quantum on the optical spectra of an atom with a central field. The investigation had special reference to cæsium, the hyperfine structure of which has been examined by Jackson, but the results obtained were not in very good agreement with the experimental observations. In the former paper it was stated that the method could be extended to the case of an atom with a nuclear spin of i n quanta (where 2 i n is an integer), but that the investigation of such a case would be difficult when i n > ½, owing to the large number of wave-functions required by the method used to describe any state of the atom. It has been found, however, that the work is not so arduous as was anticipated, and in the present paper a general method of solving the problem is developed, and applied to the cases i n = 1, 1½, 4½. The first two cases are, as yet, of little practical interest, but are sufficiently simple to make a general solution possible. On the other hand, the case of i n = 4½ has practical application to bismuth, the hyperfine structure of which has been investigated in two papers by Back and Goudsmidt. In the second of these, which deals with the Zeeman effect, it is shown conclusively that the hyperfine structure is due to a spin of 4½ quanta. It has been found too difficult in the present work to obtain a general solution of the multiplet levels of bismuth, but it has been possible to calculate the intensities of the components of the lines p λ/3 → s ½ , and p ½ → s ½ , the former of which has been examined by Back and Goudsmidt, and the results obtained are in fair agreement with theirs. There is, of course, the usual lacuna regarding the S levels, and we have to make special assumptions to obtain these. In addition the P → S transitions for i n = 1 and i n = 1½ are calculated. In all cases we treat the problem as that of one electron in a central field.