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Journal of Physics B Atomic and Molecular Physics

Two-photon detachment cross section of H-

Steven A. Adelman

Published Oct 1, 1973• 18 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/6/10/014

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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.
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^{1}1Po{\mathit{P}}^{\mathit{o}}Po 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.
Total and differential two-photon ionization cross sections are derived in the framework of perturbation theory, assuming a simple one-electron atomic model. It is shown that for an unpolarized target the angular distribution of the ejected electrons has the general form $\mathrm{a}+b{cos}^{2}\ensuremath{\theta}+c{cos}^{4}\ensuremath{\theta}$, whatever the quantum numbers nnn, lll, of the initial energy level, and the state of polarization (linear or circular) of the incident radiation. The total transition rates for circularly and for linearly polarized light are quite different from each other. For an arbitrary nl\mathrm{nl}nl state, the theoretically allowed maximum value of their ratio is 32\frac{3}{2}23​. Further analytical and numerical results are presented for hydrogen. The Appendix contains several useful summation formulas for spherical harmonics.
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.
The behavior of near-threshold cross sections for dissociation of a target into a pair of particles, as described by Wigner's threshold law, can depend sensitively on the angular momentum of the particles. In this Letter, we investigate the near-threshold nonresonant two-photon detachment process in the negative ion of gold. The expected s-wave threshold behavior is observed with linearly polarized light. Closure of the s-wave channel is realized by using circular polarization, allowing the first observation of a d-wave threshold. Practical applications are discussed, including extensions which could prove valuable for investigations of negative ions with near-threshold structure.
Two-photon ionisation of atomic hydrogen is considered in the non-relativistic dipole approximation at the photoelectric threshold and above it. In this region are obtained convergent analytical expressions for the radial transitions matrix elements, necessary for the calculation of ionisation rates. Partial and total cross sections per unit intensity are calculated for two-photon ionisation of atomic hydrogen in excited states with 2<or=n<or=9 by linearly and circularly polarised light at the photoelectric threshold and above it. At the photoelectric threshold calculations are also carried out for the two-photon ionisation of atomic hydrogen in the ground state.