Measuring the antihydrogen Lamb shift with a relativistic antihydrogen beam

Abstract

We propose an experiment to measure the Lamb shift and fine structure (the intervals ${2s}_{1/2}\ensuremath{-}{2p}_{1/2}$ and ${2p}_{1/2}\ensuremath{-}{2p}_{3/2})$ in antihydrogen. A sample of 10 000 antihydrogen atoms at a momentum of 8.85 GeV/$c$ suffices to measure the Lamb shift to 5% and the fine structure to 1%. Atomic collisions excite antihydrogen atoms to states with $n=2$; field ionization in a Lorentz-transformed laboratory magnetic field then prepares a particular $n=2$ state, and is used again to analyze that state after it is allowed to oscillate in a region of zero field. This experiment is feasible at Fermilab.