Line shapes for laser-induced collisions

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 $z=\left|C_3\right|E_0{v}^{-\frac{3}{5}}{\left|C_6\right|}^{-\frac{2}{5}}$ and $d=\delta {\left|C_6\right|}^{\frac{1}{5}}{v}^{-\frac{6}{5}}\mathrm{sgn}\left(C_6\right)$. In terms of a physical description the dimensionless frequency-detuning variable is $d\propto$ (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 $\int {-\infty }^t\frac{C_3{E}_0\mathrm{dt}}{R{\mathrm{}\left(t\right)\mathrm{}}^3}$ evaluated at an impact parameter given by the $b_{\nu }={\left(\frac{C_6}{v}\right)}^{\frac{1}{5}}\propto$ Weisskopf radius = impact parameter where the phase shift due to the Van der Waals potential becomes $\pi$. 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 $\sigma ={\left(\frac{\left|C_6\right|}{v}\right)}^{\frac{2}{5}}H(d,z)\mathrm{}$, where $H(d,z)\mathrm{}$ is tabulated in detail. For large laser fields (i.e., $z>\mathrm{}2\mathrm{}$), the line shape for collisions at a particular relative velocity $v$, laser field amplitude $E_0$, and detuning (from the large-$R$ resonance frequency), $\sigma$ becomes symmetric about $\delta =0\mathrm{}$ with the width decreasing with increasing laser power. The physical reason for the symmetric $H(d,z)\mathrm{}$ 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 $\sigma$ 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 $z\ge 2$, 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 $\delta$ from impact parameters > 15 Å.