The two-state model of laser-induced collisions introduced by Gudzenko and Yakovlenko is shown to lead to cross sections with a universal behavior in terms of the variables $z=|{C}_{3}|{E}_{0}{v}^{\ensuremath{-}\frac{3}{5}}{|{C}_{6}|}^{\ensuremath{-}\frac{2}{5}}$ and $d=\ensuremath{\delta}{|{C}_{6}|}^{\frac{1}{5}}{v}^{\ensuremath{-}\frac{6}{5}}\mathrm{sgn}({C}_{6})$. In terms of a physical description the dimensionless frequency-detuning variable is $d\ensuremath{\propto}$ (detuning of the laser from the large-
R resonance) (time of collision at the Weisskopf radius). The dimensionless variable
z is independent of laser frequency and measures the power dependence of the cross section. It is in fact proportional to $\ensuremath{\int}{\ensuremath{-}\ensuremath{\infty}}^{t}\frac{{C}_{3}{E}_{0}\mathrm{dt}}{R{(t)}^{3}}$ evaluated at an impact parameter given by the ${b}_{\ensuremath{\nu}}={(\frac{{C}_{6}}{v})}^{\frac{1}{5}}\ensuremath{\propto}$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\ensuremath{\pi}$. Above,
R3C3E0 is the coupling parameter at intranuclear separation
R and
E0 is the laser field amplitude. The cross section is of the form $\ensuremath{\sigma}={(\frac{|{C}_{6}|}{v})}^{\frac{2}{5}}H(d,z)$, where
H(d,z) is tabulated in detail. For large laser fields (i.e.,
z>2), the line shape for collisions at a particular relative velocity
v, laser field amplitude
E0, and detuning (from the large-
R resonance frequency), $\ensuremath{\sigma}$ becomes symmetric about $\ensuremath{\delta}=0$ with the width decreasing with increasing laser power. The physical reason for the symmetric
H(d,z) at large
z is shown to be the decreased importance of curve-crossing effects for large positive
d corresponding to the onset of adiabatic behavior and the increased importance of contributions to $\ensuremath{\sigma}$ from such large impact parameters that the Van der Waals shifts can be neglected. Correspondingly, at large
z the linewidth is due entirely to time-of-collision effects. When $z\ensuremath{\ge}2$, both the long-range version of the atom-atom interaction and the assumption of straight-line orbits are excellent because of the dominant contribution to $\ensuremath{\delta}$ from impact parameters > 15 \AA{}.
The behavior of the quasistatic wing of the light-induced collisional-energy-transfer (LICET) line shape is analyzed. The reaction can be written as
A∗+B+\ensuremath{\Elzxh}\ensuremath{\Omega}\ensuremath{\rightarrow}A+
B∗∗. The two-level model is found to be inadequate to describe the falloff of the spectral line shape in the quasistatic wing. The three-level model, on the other hand, leads to the prediction of a cross section that depends on the detuning in various ways, according to the strength of the collisional coupling and the influence of the van der Waals shifts on the levels under consideration. Good agreement with existing experimental results is found. To check the approximations made in the derivation of these results, numerical evaluation of the transition probability has been performed for several cases. A Monte Carlo simulation of the full LICET spectrum is also presented.
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
C6 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}
vz collisions and a Keilson-Storer kernel for large \ensuremath{\Delta}
vz collisions is used. It is also demonstrated how the inelastic (3
P3/2-3
P1/2) velocity-changing collision kernel may be obtained from experimental data at low pressures. Theoretical line shapes and broadening rates are compared with experiment.
The shape of an isolated spectral transition is analyzed in terms of an approximation to the Waldmann–Snider kinetic equation. This equation is written in the form of a drift and collision operator acting on a density matrix. With the use of the spherical approximation, the collision operator is subdivided into an elastic Boltzmann-like collision term, an inelastic loss term, and a dephasing term. The Boltzmann-like term is responsible for Dicke narrowing of spectral lines, the inelastic loss term leads to line broadening and the dephasing term may contribute both to line broadening and shifting. Simple approximations to these terms are powerful enough to account for some of the details of experimental line shapes such as asymmetrical deviations from a Lorentzian line shape. Model numerical calculations are carried out assuming classical scattering potentials of the form 1/rn in the Boltzmann-like term and single complex frequencies for the other two. It was found that as long as the density was scaled to give the same diffusion constant, the exact form of the scattering cross section had little effect on the final line shape.
The close-coupled theory of collisions in a radiation field is used to calculate the absorption profile for the Sr $^{1}\ensuremath{\leftarrow}^{1}$S resonance line broadened by collisions with Ar. The calculations predict the polarization ratios of Sr
1P fluorescence following line wing excitation by either linear or circular polarized light. Ab initio calculations were used to obtain the ground and excited SrAr molecular-potential curves, which were adjusted to give improved agreement with experiment. The radiative-scattering theory gives a unified description of the absorption coefficient and polarization redistribution from the small detuning impact limit region to the far spectral wings. The cross sections for elastic and inelastic depolarizing collisions of Sr
1P1+Ar were also calculated. The calculated absorption coefficient, impact-broadening rate, linear- and circular-polarization ratios, and depolarization rate coefficients are for the most part in good agreement with experiment.
The quantum-mechanical Baranger-Kolb-Griem theory of pressure broadening is reexamined in order to include both the effects due to overlapping lines and finite duration of collision. A general line-shape formula is derived which for near wings can be presented as a linear combination of the Lorentzian and dispersion profiles. The asymmetry parameter is expressed by means of evolution operators for the initial and final states. It is shown that in the weak-coupling case only the resultant asymmetry parameter can be approximately given as the sum of parameters describing the asymmetry due to line mixing and finite collision time.