Lamb Shift in Singly Ionized Helium

The energy separation $\mathcal{S}$ between the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $2{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ states of singly ionized helium was measured using a microwave method. Helium atoms in the space between the plates of a spherical-mirror Fabry-Perot resonator are bombarded continuously by electrons of 200-eV energy to produce helium ions in the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ metastable state. The applied modulated rf power induces transitions in the metastable ions to the short-lived $2{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state. The 40.8-eV photons emitted by the decay of the $2{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ ions to the ionic ground state $1{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ are quantum converted to visible photons by a scintillator and are then guided to a photomultiplier. The output of the photomultiplier is detected and amplified synchronously with the rf power. The experiment made use of the Zeeman effect of the fine structure and is performed in an applied homogeneous magnetic field. Three different operating values for the helium pressure are used and the result is extrapolated to a zero-pressure value. A through search was made for all possible systematic errors in the experiment. The value for $\mathcal{S}$ thus obtained is 14 046.2 ± 2.0 MHz. The quoted uncertainty consists of three standard deviations for the statistical error plus estimates of systematic errors. This result agrees with the previous experimental values for $\mathcal{S}$ (within three standard deviations), and with the latest theoretical value of 14 044.5 ± 5.2 MHz.