Lamb-shift measurement in hydrogenic phosphorus

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