Lamb shift inHe+: Resolution of a discrepancy between theory and experiment

An earlier measurement of the $2^2{S}_{1/2}–2^2{P}_{1/2}$ Lamb shift in ${\mathrm{He}}^{+}$ by the anisotropy method is repeated in order to either verify or remove a significant discrepancy between theory and experiment. The principal change from our previous measurement is a redesigned photon detection system to eliminate a residual polarization sensitivity of the photon detectors. The result of the measurement corresponds to a Lamb shift of 14 041.13(17) MHz, in excellent agreement with the theoretical value 14 041.18(13) MHz. The good agreement between theory and experiment provides a clear test of the recently calculated two-loop binding correction of $-1.339\hspace{0.5em}\mathrm{MHz}.$