The3S122−3D522interval in atomic hydrogen. I. Two-photon line-shape theory

This paper reports a theoretical treatment of the line shape for two-photon transitions. The time-dependent perturbation-theory treatment is equally appropriate for a fast atomic beam interacting with a microwave field in a waveguide, and for laser excitation of a thermal beam. Two important features of the physical systems are successfully incorporated into the theory. First, the amplitude of the external field to which the atoms are exposed varies in time; the envelope function affects the resonance linewidth and power shift. Second, the theory includes the natural decay of the atomic states; the decay amplitude produces a novel "lifetime shift," which displaces the two-photon resonance from its expected location, even in the limit of weak external fields. This paper gives detailed predictions for shifts and other distortions caused by nonidealities of the experimental apparatus used for the measurement of the $3{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ transition in atomic hydrogen.