Theory of Velocity-Dependent, Collision-Broadened, Doppler-free Line Shapes

Line-shape expressions for two-step resonant excitation in the presence of low-pressure perturbers are derived. These expressions allow for velocity-dependent broadening rates and are well suited for studying the line-shape contributions due to coherent excitation, incoherent excitation (due to dephasing collisions), interference between coherent and incoherent excitation, and velocity-changing collisions. Using the sodium 3S-3P-4D system perturbed by noble-gas atoms as an example and assuming ${C}_{6}$ interaction potentials, line shapes at a variety of laser detunings (Doppler selected atomic velocities) are numerically calculated to study variation in the line shape due to competing excitation paths and speed-dependent collision rates. In order to deal with both the line core and the line wing a composite collision kernel consisting of a Lorentzian kernel for small \ensuremath{\Delta}${v}_{z}$ collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}${v}_{z}$ collisions is used. It is also demonstrated how the inelastic (3${P}_{3/2}$-3${P}_{1/2}$) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.