One- and two-photon detachment of ${\text{O}}^{-}$

Cross sections for one- and two-photon detachment of ${\mathrm{O}}^{-}\left(1s^{2}2s^{2}2p^5{}^2\mathrm{P}^{\mathrm{o}}\right)$ have been determined in a joint experimental and theoretical study. The absolute measurement is based on the animated-crossed-beam technique, which is extended to the case of pulsed lasers, pulsed ion beams, and multiphoton detachment. The ab initio calculations employ $R$-matrix Floquet theory, with simple descriptions of the initial bound state and the residual oxygen atom which reproduce well the electron affinity and ground-state polarizability. For one-photon detachment, the measured and computed cross sections are in good mutual agreement, departing significantly from previous reference experiments and calculations. The generalized two-photon detachment cross section, measured at the Nd:YAG laser wavelength, is in good agreement with the $R$-matrix Floquet calculations. Long-standing discrepancies between theory and experiment are thus resolved.

Figure 1

Experimental setup. ${\mathrm{D}}_1$: circular diaphragm, ${\mathrm{D}}_2$: rectangular diaphragm, RP: rotating glass plate, Q: quadrupolar deflector, MCP: multichannel plates.

Figure 2

Idealized representation of the experiment. The detachment rate, proportional to the square of the photon flux, is integrated along the ion trajectory (dotted lines) to obtain the final detachment probability (thick curve), as in (4). The latter is subsequently convolved with the normalized projection ${\rho }_y$ of the current density onto the $y$ axis (hatched area) to obtain the yield $N$ (shaded area) defined in (5).

Figure 3

Number of neutrals per laser pulse (triangles) as a function of the vertical displacement $Y$ of the laser beam. The data are an average over 31 vertical scans. It has been normalized for the laser pulse energy and the ion beam current, and was subsequently symmetrized. The full line is the result obtained from the basis expansion.

Figure 4

Experimental cross sections for the one-photon detachment of ${\mathrm{O}}^{-}$: open circles, absolute measurement [3]; full circles, relative measurements [4], normalized to the values from [3]; crosses, relative measurement [5] normalized to the ${\mathrm{D}}^{-}$ cross section; full triangles, absolute measurement [6]; full squares, present measurement. The solid line is the present $R$-matrix Floquet calculation. The error bars are the combined statistical and systematic uncertainties.

Figure 5

Theoretical cross sections for the one-photon detachment of ${\mathrm{O}}^{-}$: solid line, present $R$-matrix Floquet calculation; dashed and broken lines, present standard $R$-matrix calculation in, respectively, the length and velocity forms; dashed-dotted and chain lines, B-spline $R$-matrix (BSR) results in length and velocity forms [11]; full triangles, perturbation theory using a one-electron model potential [13]. The full squares are the present experiment.

Figure 6

Asymmetry parameter for the one-photon detachment of ${\mathrm{O}}^{-}\left(1s^{2}2s^{2}2p^5{}^2\mathrm{P}^{\mathrm{o}}\right)$. The solid and dashed lines are the results obtained from the standard $R$-matrix calculation using, respectively, the length and velocity forms of the dipole matrix. The full squares [53], full triangles [51], full circles [52], and the cross [50] are experimental values and the dotted line is the formula from Ref. [52].

Figure 7

Generalized cross section for two-photon detachment of ${\mathrm{O}}^{-}\left(1s^{2}2s^{2}2p^5{}^2\mathrm{P}^{\mathrm{o}}\right)$. The dotted-dashed and broken lines are the present $R$-matrix Floquet results for $M_{\mathcal{L}}=0$ and $M_{\mathcal{L}}=1$, respectively, while the solid line is their statistical average (27). The full triangles are the results from perturbation theory based on a one-electron model potential [13]. The thin solid line is the result obtained from the adiabatic-theory approach [14]. The full circle is the experimental value of [12] while the full square is our absolute experimental result. The error bars are the combined statistical and systematic uncertainties.

Figure 8

(a) Temporal profile of the pulses from the seeded (dashed) and unseeded (full) Nd:YAG laser, and (b) norm of the Fourier transform of the difference between the temporal profile of a single pulse and the mean temporal profile, averaged over 500 pulses. The temporal profile of the seeded laser has been shifted in time for clarity. The vertical dashed lines indicate integer multiples of the free spectral range of the laser cavity.