Fine Structure of the Hydrogen Atom. VI

Measurements of improved accuracy of transition frequencies from the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}(m=+\frac{1}{2})$ state to several of the $2{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ magnetic sub-states in deuterium are presented and analyzed. The shape of the observed resonance curves is discussed and compared with theory.

The experimental result is given for the $2{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ separation, $\Delta E_{\mathrm{D}}-{\mathcal{S}}_{\mathrm{D}}=9912.59\mathrm{}\pm 0.10$ Mc/sec, for deuterium. This is combined with the result for ${\mathcal{S}}_{\mathrm{D}}$ from the preceding article to obtain the $2{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ separation, $\Delta E_{\mathrm{D}}=10,971.59\mathrm{}\pm 0.20$ Mc/sec for deuterium. From $\Delta E_{\mathrm{D}}$ and the auxiliary constants $R_{\mathrm{D}}$ and $c$ a new value is computed for the fine structure constant $\alpha =\frac{1}{(137.0365\mathrm{}\pm 0.0012)}$. The uncertainty stated is considered to be a limit of error for our experimental procedure without allowance for the uncertainty of the auxiliary constants.