Rydberg-state mixing in the presence of an external electric field: Comparison of the hydrogen and antihydrogen spectra

We analyze the influence of an external electric field on the $ns$ and $np$ Rydberg states. The impact of an electric field leads to a significant modification of the decay rate. Namely, the additional (linear and quadratic in the field) terms arise in the differential transition probabilities. In contrast to the quadratic term, the linear summand leads to a difference of the hydrogen $\left(\text{H}\right)$ and antihydrogen $\left(\overline{\text{H}}\right)$ spectra. However, this difference vanishes after the integration over photon-emission directions and does not contribute to the total emission probability. The quadratic term results in the significant change of the total decay rate and level width, respectively. The analysis of the linear and quadratic terms depending on the field strength is discussed.