Recently (e.g., Rich, 1981; Mills, 1983) it has been realized that the effect of the annihilation width on microwave absorption line shape for the Zeeman transitions between the hf levels of the Ps atom in its ground state has to be accounted for at a better level of approximation than it has been in the past. In the traditional Breit-Rabi representation the subtle effects of the annihilation widths show up as an extra off-diagonal coupling between the off-resonant and one of the near-resonant states. In this paper we derive an analytical line-shape formula by solving the rotating-wave amplitude equations within the BR representation, where the off-resonant off-diagonal coupling is treated by the adiabatic-elimination procedure. The resulting line shape is found to be slightly asymmetric in form—a conclusion which has been first reached by Mills (1983). It is seen explicitly that due to the off-diagonal coupling an effective decay constant is dependent on the microwave frequency ($\omega$). It is also shown that only if, as a zeroth approximation, this $\omega$ dependence is neglected, then a formula for the hyperfine interval $\Delta W$, recently given by Rich (1981) on the basis of heuristic arguments, may be obtained. Explicit illustrations of the present slightly asymmetric line-shape function, and the $\omega$ dependence of the said effective decay constant [${\Lambda }_{1,0}\left(\omega \right)$] are also presented. We have taken this opportunity to point out certain apparent discrepancies noted among some of the previous line-shape formulas.

• Received 17 September 1982

DOI:https://doi.org/10.1103/PhysRevA.30.2316