The Lamb-shift experiment in Muonic helium

We propose to measure several transition frequencies between the 2S and the 2P states (Lamb shift) in muonic helium ions (mu He-4(+) and mu He-3(+)) by means of laser spectroscopy, in order to determine the alpha-particle and helion root-mean-square (rms) charge radius. In addition, the fine and hyperfine structure components will be revealed, and the magnetic moment distribution radius will be determined. The contribution of the finite size effect to the Lamb shift (2S - 2P energy difference) in mu He+ is as high as 20 %. Therefore a measurement of the transition frequencies with a moderate (for laser spectroscopy) precision of 50 ppm (corresponding to 1/20 of the linewidth) will lead to a determination of the nuclear rms charge radii with a relative accuracy of 3 x 10(-4) (equivalent to 0.0005 fm). The limiting factor for the extraction of the radii from the Lamb shift measurements is given by the uncertainty of the nuclear polarizability contribution. Combined with an ongoing experiment at MPQ aiming to measure the 1S - 2S transition frequency in the helium ion, the Lamb shift measurement in mu He+ will lead to a sensitive test of problematic and challenging bound-state QED terms. This measurement will also help to clarify the discrepancy found in our previous mu p experiment. Additionally, a precise knowledge of the absolute nuclear radii of the He isotopes and the hyperfine splitting of mu He-3(+) provide a relevant test of few-nucleon theories.