Interference in the Zeeman Effect of Forbidden Lines

Abstract

The Zeeman effect of forbidden lines involving simultaneous electric quadrupole and magnetic dipole radiation will exhibit interference between these two different modes of radiation. The predicted intensity of any Zeeman component includes, in general, a term dependent on the fact that both modes of radiation are possible, as well as the usual transition probabilities for independent electric quadrupole and magnetic dipole radiation. Such additional interference terms appear only in the Zeeman effect and not in total line intensities. Proofs of these assertions and formulas for the Zeeman intensities are developed. The latter are compared with observations of the Zeeman effect of the forbidden lines of the $6p^2$ configuration of Pb I, by Jenkins and Mrozowski. Good agreement with experiment is obtained only if interference is taken into account. Their observations on the Zeeman effect correspond to a somewhat smaller value of the quadrupole moment of the transition electron in Pb I than is computed from comparison of total line intensities. Both these values of the quadrupole moment of the transition electron are 100 percent or more smaller than that given by a rough estimate from screening constant data using hydrogenic wave functions and the known positions of the levels to evaluate the effective nuclear charge. In the absence of Hartree wave functions for Pb I, no better estimate seems possible. A brief discussion of the hyperfine structure of forbidden lines is included, in which it is shown that the rules for determining the relative intensities of electric dipole hyperfine multiplets also give the intensity ratios in the hyperfine structure of magnetic dipole lines.