A precision determination of the Lamb shift in hydrogen

Abstract For over 40 years, optical and microwave spectroscopists, and atomic, nuclear and elementary particle physicists have been engaged in measuring the 22S½-22P½ energy level separation in atomic hydrogen (the Lamb shift) and attempting to predict the splitting theoretically. The discrepancies encountered have influenced the development of theoretical methods of calculation in the areas of atomic structure, quantum electrodynamics and elementary particle physics. In this paper we present the results of a precision microwave determination of the Lamb shift, using a fast atomic beam and a single microwave interaction region. The value obtained is in substantial agreement with the earlier determinations and with the recent calculation by Mohr but is in disagreement with the earlier calculation by Erickson. This disagreement is further accentuated if recent modifications to the size of the proton are included, whereas the agreement with Mohr’s calculation is not affected. The experimental method uses a 21 keV beam of metastable 2 s hydrogen atoms which are obtained by charge exchange of a proton beam extracted from a radio frequency (r.f.) ion source. The experiment is performed in essentially zero magnetic field and uses a precision transmission line interaction region to induce r.f. transitions at the Lamb shift frequency. The result for the 22S½F = 0 to 22P½F = 1 interval in zero field is 909.904 ± 0.020 MHz corresponding to a Lamb shift of 1057.862 ± 0.020 MHz. The paper discusses the method and the host of corrections for systematic effects which need to be applied to the line centre, many of which have not been sufficiently understood or controlled in previous experiments. The paper is introduced with a brief survey of significant landmarks in calculation and measurement of the Lamb shift and concludes with a comparison of the present theoretical and experimental positions.