The Quadratic Zeeman Effect

Abstract

The Zeeman effects of the principal series lines of sodium and potassium in the range $n=10 \mathrm{to} 35$ are observed in absorption, using the new 60-inch cyclotron magnet. With a field of 27,000 gauss, the lines having $n$ in the neighborhood of ten show a normal triplet representing the complete Paschen-Back effect of the narrow $^{2}P$ doublet. From about $n=12 \mathrm{to} 20$ all components show an increasing displacement toward short wave-lengths proportional to ${({n}^{*}),}^{4}$ the shift of the $\ensuremath{\pi}$ components being half that of the center of the two $\ensuremath{\sigma}$ components. This is the quadratic Zeeman effect, varying as ${H}^{2}$, and is here measured and compared quantitatively with theory for the first time. The agreement with the simple theory is excellent as far as $n=20$. Beyond this the lines show an additional displacement in the same direction, increasing as a higher power of $n$. At the same time the lines are broadened toward the red, with indications of an unresolved component whose intensity increases rapidly with $n$. The displacement is interpreted as a perturbation by the $F$ states, whose separation from the $P$ states in this region becomes comparable with the magnetic energy. The additional lines causing the broadening represent forbidden transitions $^{2}S\ensuremath{\rightarrow}^{2}F$. Beyond $n=28$ the broadening increases suddenly and becomes symmetrical, until the lines are no longer distinguishable at $n=35$. All of these perturbation effects are compared with the theoretical results given in the accompanying paper by Schiff and Snyder. Some features are accounted for quantitatively, while the others are satisfactorily explained qualitatively.