Production of relativistic antihydrogen atoms by pair production with positron capture and measurement of the Lamb shift

A beam of relativistic antihydrogen atoms — the bound state ( e⁺) — can be created by circulating the beam of an antiproton storage ring through an internal gas target. An antiproton which passes through the Coulomb field of a nucleus will create e⁺e⁻ pairs, and antihydrogen will form when a positron is created in a bound instead of continuum state about the antiproton. The cross section for this process is roughly 3Z ² pb for antiproton momenta about 6 GeV/c. A sample of 600 antihydrogen atoms in a low-emittance, neutral beam will be made in 1995 as an accidental byproduct of Fermilab experiment E760. We describe a simple experiment, Fermilab Proposal P862, which can detect this beam, and outline how a sample of a few-10⁴ atoms can be used to measure the antihydrogen Lamb shift to 1 %. Work supported in part by Department of Energy contract DE-AC03-76SF00515 (SLAC). Work supported by Fondo Nacional de Investigación Científica y Tecnológica, Chile.