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Physical Review A

Resonant two-color detachment of H− with excitation of H(n=2)

Ning-Yi Du, Anthony F. Starace, N. A. Cherepkov

Published Sep 1, 1993• 12 citations
Publisher

Abstract

The cross sections for resonant two-color, two-photon detachment of ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$ with excitation of the degenerate H(2s) and H(2p) levels are calculated within a semiempirical adiabatic hyperspherical representation. The first photon, with energy ${\mathrm{\ensuremath{\omega}}}_{1}$=0.4017 a.u., is resonant with the well-known Feshback $^{1}$${\mathit{P}}^{\mathit{o}}$ resonance below the H(n=2) threshold. The second photon, with energy ${\mathrm{\ensuremath{\omega}}}_{2}$\ensuremath{\ge}0.126 05 a.u., scans the energy region above the H(n=2) threshold over which long-range dipole-field-induced cross-section oscillations are predicted to occur. Such Gailitis-Damburg oscillations have not yet been observed experimentally. Results for various pairs of light polarization for the two photons are presented. Our resonant two-color, two-photon detachment cross sections are 8--9 orders of magnitude greater than the corresponding nonresonant, single-color, two-photon detachment cross sections obtained by Liu, Du, and Starace [Phys. Rev. A 43, 5891 (1991)]. Unmistakable evidence of long-range dipole-field effects is presented over the 5-meV energy range above the H(n=2) threshold. Furthermore, the differential cross sections for right- and left-circularly polarized, copropagating photons and especially the circular dichroism differential cross sections are shown to have nearly a full cycle of a greatly enhanced dipole-field-induced oscillation extending over the region from threshold to \ensuremath{\approxeq}34 meV above.

DOI
10.1103/physreva.48.2413

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The cross sections for resonant two-color, two-photon detachment of H\ensuremath−{\mathrm{H}}^{\mathrm{\ensuremath{-}}}H\ensuremath− with excitation of the degenerate H(2s) and H(2p) levels are calculated within a semiempirical adiabatic hyperspherical representation. The first photon, with energy \ensuremathω1{\mathrm{\ensuremath{\omega}}}_{1}\ensuremathω1​=0.4017 a.u., is resonant with the well-known Feshback ^{1}$${\mathit{P}}^{\mathit{o}} resonance below the H(n=2) threshold. The second photon, with energy \ensuremathω2{\mathrm{\ensuremath{\omega}}}_{2}\ensuremathω2​\ensuremath{\ge}0.126 05 a.u., scans the energy region above the H(n=2) threshold over which long-range dipole-field-induced cross-section oscillations are predicted to occur. Such Gailitis-Damburg oscillations have not yet been observed experimentally. Results for various pairs of light polarization for the two photons are presented. Our resonant two-color, two-photon detachment cross sections are 8--9 orders of magnitude greater than the corresponding nonresonant, single-color, two-photon detachment cross sections obtained by Liu, Du, and Starace [Phys. Rev. A 43, 5891 (1991)]. Unmistakable evidence of long-range dipole-field effects is presented over the 5-meV energy range above the H(n=2) threshold. Furthermore, the differential cross sections for right- and left-circularly polarized, copropagating photons and especially the circular dichroism differential cross sections are shown to have nearly a full cycle of a greatly enhanced dipole-field-induced oscillation extending over the region from threshold to \ensuremath{\approxeq}34 meV above.
The differential and total cross sections for two-photon detachment of H - are computed analytically within the asymptotic model for both linearly and circularly polarized light. The total cross section for unit flux is of the order 10 -48 cm 2 . The differential cross section for linearly polarized light is nearly isotropic near the two-photon absorption threshold but is sharply peaked along the polarization direction just below the threshold for one-photon detachment. The circular polarization efficiency is very small near the two-quantum threshold but is close to its theoretical maximum near the one-quantum threshold.
Our recent analysis [J. Phys. B 33, R141 (2000)] of the problem of ${\mathrm{H}}^{\ensuremath{-}}$ in both laser and strong static electric fields, which treated effects that are linear in the laser intensity I (e.g., the dynamic polarizability and the single-photon detachment cross section), is extended here to treat effects of higher order $(\ensuremath{\sim}{I}^{2})$ in the laser intensity (e.g., the dynamic hyperpolarizability, the two-photon detachment cross section, the linear in I corrections to the single-photon detachment rate, etc). We introduce the concept of the dynamic hyperpolarizability of an atom in the presence of a strong electric field based on the complex quasienergy approach with properly normalized, quasistationary quasienergy wave functions. Our analysis of the general structure of the dynamic hyperpolarizability tensor of an atom in a nondegenerate (S(S(S-) state is performed for arbitrary field geometries and laser polarizations. The connection of the hyperpolarizability $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ to the complex quasienergy and to atomic ionization rates is established. Analytic results (in terms of Airy functions) are obtained for five irreducible components of a hyperpolarizability tensor (that are independent of the laser polarization and the field geometry) for the case of a weakly bound electron in a three-dimensional, zero-range potential. These results are used for the analysis of the frequency, field geometry, and laser polarization dependence of the two-photon detachment rate as well as of the linear in laser intensity corrections to the single-photon detachment rate. It is shown that the oscillatory behavior of the frequency dependence of both the real and the imaginary parts of $\ensuremath{\gamma}(\mathcal{F};\ensuremath{\omega})$ exists for both the coplanar and orthogonal field geometries, and that this behavior is qualitatively different for frequencies below and above the single-photon detachment threshold. The threshold behavior of the two-photon detachment rate is analyzed in detail and the static electric-field-induced modification of Wigner's threshold law for a short-range potential is discussed.
We report on a study of one-photon single ionization of He(1s21{s}^{2}1s2) accompanied by excitation to He+(2s){}^{+}(2s)+(2s) or He+(2p){}^{+}(2p)+(2p) for photon energies at, and up to a few eV above, the excitation threshold. We find, both numerically and analytically, that as the photon energy approaches threshold from above the photoionization cross section turns sharply at about 200 meV and has a cusp at threshold. The cusp is associated with the adiabatic transfer of population between the 2s2s2s and 2p2p2p bound states of the ion. The photoelectron's electric field induces an energy splitting between the otherwise degenerate 2s2s2s and 2p2p2p states, and consequently the 2s2s2s and 2p2p2p populations oscillate with a period defined by this energy splitting. The number of oscillations is almost independent of the photoelectron's asymptotic speed vvv since over most of its outward journey the photoelectron moves with a speed much larger than vvv. However, on the last leg of its journey, after it has slowed down sufficiently in the Coulomb field of the ion, the photoelectron does move with an almost constant speed vvv. On this last leg the energy splitting is so small that there is insufficient time for 2s2s2s and 2p2p2p populations to undergo a full oscillation; rather, the (equal and opposite) changes in the 2s2s2s and 2p2p2p populations are proportional to vvv (i.e., to the square root of the excess photoelectron energy, which gives rise to a cusp).
A polarization dependence of a two-colour two-photon detachment cross section has been observed and calculated for the first time. In a Penning ion trap, electrons were detached from Cl - by an intense infrared laser beam at 1064 nm and a weak ultraviolet laser beam at 343 nm. Both beams were circularly polarized. The ratio of the two-colour two-photon cross section for photons with the same circular polarization to that for photons with opposite circular polarization was measured to be 1.085 +0.012 -0.007 . Also presented is a simple calculation of the ratio, the result of which is consistent with the observation.
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