Cyclotron trap

The cyclotron trap was developed at SIN/PSI to increase the stopping density of negatively charged particle beams for the formation of exotic atoms in low pressure gases. A weak focusing magnetic field, produced by superconducting solenoids, is used. Particles are injected radially through the fringe field to a moderator, which decelerates them into orbits bound by the field. Further deceleration by moderators and/or low-pressure gases leads the particles to the centre of the device, where they can be stopped or eventually extracted. Experiments became feasible with this technique, such as those dealing with pionic hydrogen/deuterium at SIN/PSI. Muonic hydrogen laser experiments also became possible with the extraction of muons from the cyclotron trap. The formation of antiprotonic hydrogen in low pressure targets led to successful experiments at LEAR/CERN.

Laser spectroscopy of light muonic atoms and the nuclear charge radii

The energy levels of hydrogen-like atomic systems are shifted slightly by the complex structure of the nucleus, in particular by the finite size of the nucleus. These energy shifts are vastly magnified in muonic atoms and ions, i.e. the hydrogen-like systems formed by a negative muon and a nucleus. By measuring the 2S-2P energy splitting in muonic hydrogen, muonic deuterium and muonic helium, we have been able to deduce the p, d, ^33He and ^44He nuclear charge radii to an unprecedented accuracy. These radii provide benchmarks for hadron and nuclear theories, lead to precision tests of bound-state QED in regular atoms and to a better determination of the Rydberg constant.

Chemical effect on muonic atom formation through muon transfer reaction in benzene and cyclohexane samples

To investigate the chemical effect on the muon capture process through a muon transfer reaction from a muonic hydrogen atom, the formation rate of muonic carbon atoms is measured for benzene and cyclohexane molecules in liquid samples. The muon transfer rate to carbon atoms of the benzene molecule is higher than that to the carbon atoms of the cyclohexane molecule. Such a deviation has never been observed among those molecules for gas samples. This may be because the transfers occur from the excited states of muonic hydrogen atoms in the liquid system, whereas in the gas system, all the transfers occur from the 1s (ground) state of muon hydrogen atoms. The muonic hydrogen atoms in the excited states have a larger radius than those in the 1s state and are therefore considered to be affected by the steric hindrance of the molecular structure. This indicates that the excited states of muonic hydrogen atoms contribute significantly to the chemical effects on the muon transfer reaction.

Hadronic vacuum-polarization contribution to various QED observables

Due to precision tests of quantum electrodynamics (QED), determination of accurate values of fundamental constants, and constraints on new physics, it is important in a consistent way to evaluate a number of QED observables such as the Lamb shift in hydrogen-like atomic systems. Even in a pure leptonic case, those QED variables are in fact not pure QED ones since hadronic effects are involved through intermediate states while accounting for higher-order effects. One of them is hadronic vacuum polarization (hVP). Complex evaluations often involve a number of QED quantities, for which treatment of hVP is not consistent. The highest accuracy for a calculation of the hVP term is required for the anomalous magnetic moment of a muon. However, a standard data-driven treatment of hVP, based on a dispersion integration of experimental data on electron-positron annihilation to hadrons and some other phenomena, leads to a contradiction with the experimental value of $$a_\mu $$ a μ . This experimental value can be considered as an indirect determination of the hVP contribution to $$a_\mu $$ a μ and the scatter of theory and experiment allows one to obtain a conservative estimation of the related hVP contribution. In this paper, we derive exact and approximate relations between the leading-order (LO) hVP contributions to various observables. Using those relations, we obtain for them a consistent set of the results, based on the scatter of $$a_\mu $$ a μ values. While calculating the LO hVP term, we have to remember that next-to-LO (NLO) hVP corrections are often comparable with the uncertainty of the LO term. Special attention is payed to hVP contribution to simple atoms. In particular, we discuss the NLO contribution to the Lamb shift in ordinary and muonic hydrogen and other two-body atoms for $$Z\le 10$$ Z ≤ 10 . We also consider the NLO contribution of the muonic vacuum polarization to the Lamb shift in hydrogen-like atoms. With the $$a_\mu $$ a μ puzzle unresolved, one may still require present-days values of the hVP contributions to various observable for comparison to experiment etc. the presence of contradicting values and a lack of consistency means an additional uncertainty for $$a_\mu $$ a μ and for key contributions to it, including the LO hVP one. We present here an estimation of such a propagated uncertainty in hVP contributions to different QED observables and recommend a consistent set of the related LO hVP contributions. Graphic Abstract