Threshold effects in strong-field detachment of ${\mathrm{H}}^{-}$ and ${\mathrm{F}}^{-}$: Plateau enhancements and angular distribution variations

Above-threshold detachment (ATD) rates for ${\mathrm{H}}^{-}$ and ${\mathrm{F}}^{-}$ ions in the high-energy plateau region are calculated as functions of photon number and laser intensity by solving the time-dependent Schrödinger equation within the Sturmian-Floquet approach. Pronounced enhancements of the ATD rates are found (up to an order of magnitude) as the laser-field intensity passes across ponderomotive-potential-induced channel closings. We confirm the zero-range potential model results of Borca et al. [Phys. Rev. Lett. 88, 193001 (2002)] for negative ions whose initial states have $s$ symmetry, and we investigate here the case of initial states having $p$ symmetry. Depending on the symmetry of the initial state, the enhancement is found to be most pronounced for even- or odd-channel closures, which is consistent with threshold laws applicable at the closing of particular multiphoton channels. Variations of ATD electron angular distributions as functions of laser intensity near channel closings are also investigated and found to be sensitive to initial-state symmetry.

Figure 1

Partial rates ${\Gamma }^{\left(n\right)}$ (in atomic units) for $n$-photon above-threshold detachment of ${\mathrm{H}}^{-}$ by a linearly polarized $\mathrm{C}{\mathrm{O}}_2$ laser field. The present renormalized results (open circles) are compared to the available published results of Telnov and Chu [45] (asterisks) for two laser intensities and to the available published (and renormalized) results of Gribakin and Kuchiev [46] (open triangles) for one laser intensity, as indicated in the figure. See text for details of the renormalization procedure.

Figure 2

Intensity dependence of the partial rates ${\Gamma }^{\left(n\right)}\left(I\right)$ for detachment of the ${\mathrm{H}}^{-}$ ion by a laser field operating at frequency $\omega =0.0043\mathrm{a.u.}$, in the region where the ponderomotive shift causes the $n=8$, 9, 10, and 11 channel closures (at intensities 1.76, 2.87, 3.99, and $5.12\times {10}^{10}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$, respectively). These results compare well with results of a ZRP model calculation [17].

Figure 3

The same as Fig. 2 but for the ${\mathrm{F}}^{-}$ ion irradiated by a laser field of frequency $\omega =0.0253\mathrm{a.u.}$, in the region of intensities over which the $n=7$, 8, 9, and 10 channels become closed (at intensities of the laser field equal to 4.69, 6.97, 9.30, and $11.72\times {10}^{12}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$, respectively). The results for the partial rates have been averaged over the projections of the initial angular momentum, $l=1$.

Figure 4

Angular distributions (ADs) for ${\mathrm{F}}^{-}$ detachment by eight photons (averaged over the projections of the initial angular momentum, $l=1$) for a linearly polarized laser field of frequency $\omega =0.0253\mathrm{a.u.}$ when the laser-field intensity is varied in the vicinity of the closing of the eight-photon channel, i.e., $I=6.94$, 6.95, 6.954, 6.96, 6.964, and $6.97\times {10}^{12}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$ (in order from top left to bottom right panels). The ADs for each intensity are peaked along the direction of the laser polarization $\widehat{\mathit{\epsilon }}$, which is marked by the solid horizontal line in each panel; no electrons are observed to be ejected perpendicularly to $\widehat{\mathit{\epsilon }}$.

Figure 5

The same as in Fig. 4 for the nine-photon channel near the closing of the nine-photon channel for six laser-field intensities, $I=8.90$, 9.10, 9.21, 9.26, 9.29, and 9.30 $\times {10}^{12}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$ (from top left to bottom right panels, respectively). The ADs, initially peaked along the laser-field polarization $\widehat{\mathit{\epsilon }}$, for higher intensities become strongly peaked in the perpendicular direction (for $I=9.21\times {10}^{12}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$ the probability for electron detachment in the direction of $\widehat{\mathit{\epsilon }}$ is zero), whereas at intensities close to the threshold they become isotropic.

Figure 6

The ADs for the nine-photon detachment channel of ${\mathrm{F}}^{-}$ by a laser field of frequency $\omega =0.0253\mathrm{a.u.}$ and linear polarization along the horizontal axis, for an intensity $I=9.21\times {10}^{12}\frac{\mathrm{W}}{{\mathrm{cm}}^2}$. The left panel corresponds to detachment of an initial state with $(l,m)=(1,0)$, whereas the right panel corresponds to initial states $(l,m)=(1,1)$ or $(1,-1)$. The average of these ADs over the initial-state angular momentum projections is presented in Fig. 5c.

Figure 7

Comparison of the radial electron wave functions for three different model potentials [34, 56, 57], as noted in the figure, describing ${\mathrm{H}}^{-}$ within the SAE approximation.