Coherence Effects in Resonance Fluorescence

The crossed-level method of atomic spectroscopy is discussed and the angular distribution formula for both the incoherent and coherent resonance scattering is derived. The form of this distribution function, as given here, explicity displays the geometric factors depending on radiation propagation vectors. With the application to hydrogen in mind, the distribution function is expressed explicitly for single electron transitions with external fields possessing axial symmetry. The properties of the distribution function are discussed with emphasis on the case of unpolarized radiation. For the case of hydrogen there are two possible applications of major interest. The first concerns the possibility of a precision measurement of the $2p$ fine structure splitting and, hence, a determination of the fine structure constant. Explicit results for the shape and other properties of the resonance line with a uniform magnetic field obtained. The other application is concerned with the possibility of measuring the $2s-2p$ Lamb splitting. This requires an electric field parallel to the magnetic field. Unfortunately, the level crossings which are sensitive to the Lamb splitting cannot radiate sufficiently rapidly while those which do radiate appreciably occur at field strengths which are extremely insensitive to the Lamb splitting.