Theory of the line shape of the 1S–2S transition for magnetically trapped antihydrogen

Abstract

Abstract The physics that determines the line shape of the 1S–2S transition in magnetically trapped H ¯ is explored. Besides obtaining an understanding of the line shape, one goal is to replace the dependence on large scale simulations of H ¯ with a simpler integration over well defined functions. For limiting cases, analytic formulas are obtained. Example calculations are performed to illustrate the limits of simplifying assumptions. We also describe a χ 2 method for choosing experimental parameters that can lead to the most accurate determination of the transition frequency.