Electric Field Dependence of the Atomic-Hydrogen Hyperfine Separation

The Stark shift of the atomic-hydrogen hyperfine separation has been measured in a hydrogen maser, designed to study in particular the dependence of the shift on the angle $\theta$ between the external electric and magnetic fields. A method of designing shielded solenoids to produce arbitrary magnetic fields is presented. The result of the experiment is $\delta {\nu }_{\mathrm{stark}}=(-7.1\mathrm{}\pm 1.1)\times {10}^{-5\mathrm{}}{E}^2 (\theta =0)$ using electrostatic units for the electric field $E$, and $\frac{\delta {\nu }_{\mathrm{stark}}(\theta =0)-\delta {\nu }_{\mathrm{stark}}(\theta =\frac{\pi }{2})}{\delta {\nu }_{\mathrm{stark}}(\theta =0)}=-1\%\pm 10\%.$