Preprint USM-TH-66

CERN announced in January 1996 the detection of the rst eleven atoms of antimatter ever produced. The experiment w as based on a method proposed earlier by S. Brodsky, C. Munger and I. Schmidt, and which furthermore predicted exactly the number of atoms that were detected for the particular conditions of the experiment. The study of antihydrogen aords science the opportunity to continue research on the symmetry between matter and antimatter. In this talk the importance of antihydrogen as a basic physical system is discussed. Dierent production methods that have been tried in the past are brie BLOCKINy presented, and the method that was used in the CERN experiment is analyzed in detail. It consists in producing anti-hydrogen by circulating a beam of an antiproton ring through an internal gas target. In the Coulomb eld of a nucleus, an electron-positron pair is created, and antihydrogen will form when the positron is created in a bound rather that a continuum state about the antiproton. The theoretical calculation of the production cross section is presented in detail. A discussion of the detection systems used both in the CERN experiment and in another similar experiment that is right n o w underway a t F ermilab are also given. Finally I present and discuss possible future experiments using antihydrogen, including the measurement of the antihydrogen Lamb shift.