Line shapes for laser-induced collisions

Abstract

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, $\frac{{C}_{3}{E}_{0}}{{R}^{3}}$ is the coupling parameter at intranuclear separation $R$ and ${E}_{0}$ 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 ${E}_{0}$, 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{}.