Lamb-shift measurement in hydrogenic phosphorus

The final result of a 2s ${}_{}{}^2{}_{}{}^{}$ ${\mathit{S}}_{1/2–}$2p ${}_{}{}^2{}_{}{}^{}$ ${\mathit{P}}_{1/2}$ Lamb-shift measurement by the laser resonance method in hydrogenic phosphorus is reported. Metastable 2s ${}_{}{}^2{}_{}{}^{}$ ${\mathit{S}}_{1/2}$ ions were prepared using a β≊0.08 velocity beam of ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}_{}^{14+}{}_{}{}^{}$ ions obtained from the MP tandem accelerator at the Centre de Recherches Nucléaires in Strasbourg. From the metastable state the transition to the 2p ${}_{}{}^2{}_{}{}^{}$ ${\mathit{P}}_{3/2}$ state was induced with a high-power dye laser leading to a measured transition energy of ΔE=2.231 33(12) eV. Subtracting the well-known fine-structure splitting Δ${\mathit{E}}_{\mathrm{FS}}$=2.314 82(2) eV, the Lamb shift is deduced to be ${\mathit{E}}_{\mathrm{expt}}$(LS)=20 188(29) GHz. This result is compared with the theoretical value ${\mathit{E}}_{\mathrm{theor}}$(LS)=20 254(10) GHz and with other experimental results for the Lamb shift in the region Z≤18. Finally, the utility of the Lamb-shift measurements in testing the G(Zα) function of the self-energy, which includes only terms in (Zα${)}^{\mathit{n}}$, n≥6, is discussed.