Fine-Structure Measurement of Singly Ionized Helium,n=4

Abstract

Precision measurements of the energy differences ${\mathcal{S}}_{4}(4^{2}S_{\frac{1}{2}}\ensuremath{-}4^{2}P_{\frac{1}{2}})$ and $\ensuremath{\Delta}{E}_{4}\ensuremath{-}{\mathcal{S}}_{4}(4^{2}P_{\frac{3}{2}}\ensuremath{-}4^{2}S_{\frac{1}{2}})$ in ${({\mathrm{He}}^{4})}^{+}$ are reported. The experimental results, ${\mathcal{S}}_{4}=1768\ifmmode\pm\else\textpm\fi{}5$ MHz and $\ensuremath{\Delta}{E}_{4}\ensuremath{-}{\mathcal{S}}_{4}=20179.7\ifmmode\pm\else\textpm\fi{}1.2$ MHz, agree with the values predicted by quantum electrodynamic theory, ${\mathcal{S}}_{4}=1768.34\ifmmode\pm\else\textpm\fi{}0.51$ MHz and $\ensuremath{\Delta}{E}_{4}\ensuremath{-}{\mathcal{S}}_{4}=20180.78\ifmmode\pm\else\textpm\fi{}0.56$ MHz. An electron gun excites the states of interest in a section of waveguide containing helium gas. A magnetic field applied perpendicular to the waveguide axis is used to scan a microwave resonance between suitable Zeeman levels for a fixed frequency of oscillating electric field in the waveguide. Any induced electric dipole transitions $4^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}4^{2}P_{\frac{1}{2}}$ or $4^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}4^{2}P_{\frac{3}{2}}$ reduce the intensity of 1215-\AA{} radiation which is emitted in the natural decay of $4S$ to $2P$. This light is directed onto an ultraviolet-detecting phototube whose output is measured by a lock-in detector for which the synchronous signal is provided by square-wave amplitude modulation of the microwave field. The resonances obtained by varying the magnetic field are fitted to a theoretical line-shape formula by a computerized least-squares program. The resulting best-fit parameters include either ${\mathcal{S}}_{4}$ or $\ensuremath{\Delta}{E}_{4}\ensuremath{-}{\mathcal{S}}_{4}$, depending on the transition studied. Consideration is given to the dependence of the resonance center on the gun current, helium pressure, and microwave power level.