Fine Structure of Short-Lived States of Hydrogen by a Microwave-Optical Method. II

This article describes improvements in the apparatus used in Part I by Lamb and Sanders to determine fine-structure separations in excited states $n=3\mathrm{} \mathrm{and} 4$ of deuterium. Experimental and theoretical studies are made of the effects of environmental electric fields on the relative intensities of various resonances in order to obtain information about possible Stark shifts of the fine-structure levels. The density matrix method, used in Part I for two levels, is extended to $N$ levels and is worked out more explicitly for the case of three levels. The splitting $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ is found to be 315.30±0.80 Mc/sec compared with a calculated value of 315.34 Mc/sec. Less precise measurements are made for other separations which are also in good agreement with theory.