Theory of a one-photon nonlinear resonance under transit conditions

The field dependence of the susceptibility of a gas interacting with a standing wave is calculated near the center of a line for a field of arbitrary profile. An allowance is made for the effects of spatial modulation of the gas. Numerical calculations are reported for a field with a Gaussian profile allowing for degeneracy. These calculations can be checked directly against experimental results for a transition corresponding to a line at λ = 3.39 μ in CH₄, which should make it possible to determine accurately the dipole moment of the transition. The amplitude and half-width of a Lamb dip are calculated for a field of arbitrary profile on the basis of perturbation theory. The problem of approximation of a real Gaussian field with a model field characterized by an amplitude constant over a circular cross section is considered. The precision of model calculations is determined for weak and strong fields. Resonances in atomic beams are discussed under transit conditions. It is shown that in this case there is a slow atom effect, which is responsible for lines with a characteristic width that is a linear function of the homogeneous width of a transition when excited particles are detected on the basis of their fluorescence.