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Physical Review A

Theory of the photodetachment of negative ions in a magnetic field

William A. M. Blumberg, Wayne M. Itano, Daniel J. Larson

Published Jan 1, 1979• 84 citations
Publisher

Abstract

The behavior of the photodetachment cross section of the ${S}^{\ensuremath{-}}$ ion near thresholds in a magnetic field is derived. This cross section is shown to have an oscillatory dependence on photon energy. The calculation is based on first-order time-dependent perturbation theory, and final-state interactions are ignored. The weights of individual transitions between the various Zeeman sublevels for different light polarizations are given in terms of the appropriate angular momentum coupling coefficients. Broadening of the features of the cross section due to the motion of the ions is included in the calculation. The Wigner-law behavior known to be valid for zero magnetic field is shown to result from the magnetic field dependent cross section in the limit of low magnetic field. The theory is shown to be in good agreement with experimental results. The extension of the theory to other atomic negative ions is discussed.

DOI
10.1103/physreva.19.139

Related papers

Photodetachment of atomic negative ions near threshold in a magnetic field

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The effect of final-state interactions on the photodetachment cross section of negative ions in a magnetic field is discussed. Experiments on the location of the $^{2}P_{\frac{3}{2}}$ threshold in ${\mathbf{S}}^{\ensuremath{-}}$ as a function of magnetic field show clearly the effect of the zero-point energy of an electron in a magnetic field. The experiments also give a precise value for the electron affinity and provide information about the interaction between the atom and the detached electron.

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s-wave photodetachment in a static electric field

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Photodetachment from negative ions in a static electric field has been studied using ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$. These experiments were done with greater precision than previous studies and allow a quantitative comparison of data with theory. A 10-keV ion beam was sent through a region with fields of up to 1.5 kV/cm applied parallel to the beam velocity. A pulsed dye-laser beam, perpendicular to the ion beam, photoneutralized the ions. The relative cross sections were measured by detecting the resulting fast neutral atoms. Detachment below threshold and oscillations on the cross section above threshold were observed near the ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ threshold at 16 269.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and near the ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ threshold at 29 138.3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The phase of the oscillations in the data is in good agreement with predictions for s-wave photodetachment in a static electric field, but the amplitude of the oscillations is found to be slightly reduced.

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Trapped Ion Research.

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The trapped ion apparatus has been assembled during the past year and successfully used to study the photodetachment of S(-) ions. A periodic dependence of the photodetachment cross section on the light frequency was observed for the first time in any atom. The oscillatory structure could be attributed to the excitation of the detached electrons to discrete cyclotron levels in the magnetic field. The experiments so far also indicate that state dependent photodetachment should provide an effective means for producing and detecting population differences in trapped ions. (Author)

•Apr 3, 1979•0 citations

Time dependent approach to photodetachment in E, B and parallel E and B fields

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Photodetachment leading to outgoing s‐wave and pz‐wave electrons in dc electric and magnetic fields along the z‐axis, alone and in combination, is treated using a zero order model which neglects the (weak) interaction between the atom and detached electron. Threshold laws and interferences arising in the mixed field case are illustrated, and qualitatively discussed using a time dependent fomulation which gives the total detachment cross section as the fourier transform of the dipole auto‐correlation function. First order time dependent perturbation theory is then used to indicate the insensitivity of the results to inclusion of an atomic final state interaction.

AIP conference proceedings•Jan 1, 1987•0 citations

Zeeman transition strengths in photodetachment from O− and S−

A. K. Langworthy, D. M. Pendergrast, John N. Yukich

We have probed the relative weight of the first Zeeman transition in photodetachment from ${\mathrm{O}}^{\ensuremath{-}}$ and ${\mathrm{S}}^{\ensuremath{-}}$ at the ${}^{2}{\stackrel{\ensuremath{\rightarrow}}{{P}_{3/2}}}^{3}{P}_{2}$ detachment threshold, using laser light polarized perpendicular to a 1T field. For both ion species, we find a nonzero transition strength at the first threshold, a clear discrepancy with previously published theory based on LS coupling in the ion and the atom.

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Threshold behaviour in photodetachment into a final state with large negative polarizability

Johan Rohlén, Anton O. Lindahl, Hannes Hultgren +3 more

In a recent experiment, Lindahl et al. ( Lindahl A. O. et al. , Phys. Rev. Lett. , 108 (2012) 033004) observed a new threshold behavior in the photodetachment of the potassium negative ion when the residual atom is left in the state. Unfortunately the resonance close to threshold made it more difficult to apply the semi-classical model that was developed to describe the threshold behavior. In this paper we present a study of the threshold behavior of the partial cross-section in the photodetachment of the sodium negative ion. The experiment was conducted using a collinear beams apparatus where the detection was performed using a resonance ionization scheme. We observe the same threshold behavior as in the previous experiment, but without any obfuscating resonance. The model derived in the previous paper is found to fit the observed cross-section up to 35 meV above threshold. The present experiment clearly demonstrates the threshold behaviour for the fundamental process of a free electron moving in the field of an atom with a large negative polarizability.

Europhysics Letters (EPL)•May 30, 2014•5 citations
The behavior of the photodetachment cross section of the S\ensuremath−{S}^{\ensuremath{-}}S\ensuremath− ion near thresholds in a magnetic field is derived. This cross section is shown to have an oscillatory dependence on photon energy. The calculation is based on first-order time-dependent perturbation theory, and final-state interactions are ignored. The weights of individual transitions between the various Zeeman sublevels for different light polarizations are given in terms of the appropriate angular momentum coupling coefficients. Broadening of the features of the cross section due to the motion of the ions is included in the calculation. The Wigner-law behavior known to be valid for zero magnetic field is shown to result from the magnetic field dependent cross section in the limit of low magnetic field. The theory is shown to be in good agreement with experimental results. The extension of the theory to other atomic negative ions is discussed.
The effect of final-state interactions on the photodetachment cross section of negative ions in a magnetic field is discussed. Experiments on the location of the 2P32^{2}P_{\frac{3}{2}}2P23​​ threshold in ${\mathbf{S}}^{\ensuremath{-}}$ as a function of magnetic field show clearly the effect of the zero-point energy of an electron in a magnetic field. The experiments also give a precise value for the electron affinity and provide information about the interaction between the atom and the detached electron.
Photodetachment from negative ions in a static electric field has been studied using ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$. These experiments were done with greater precision than previous studies and allow a quantitative comparison of data with theory. A 10-keV ion beam was sent through a region with fields of up to 1.5 kV/cm applied parallel to the beam velocity. A pulsed dye-laser beam, perpendicular to the ion beam, photoneutralized the ions. The relative cross sections were measured by detecting the resulting fast neutral atoms. Detachment below threshold and oscillations on the cross section above threshold were observed near the ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ threshold at 16 269.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and near the ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ threshold at 29 138.3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The phase of the oscillations in the data is in good agreement with predictions for s-wave photodetachment in a static electric field, but the amplitude of the oscillations is found to be slightly reduced.
The trapped ion apparatus has been assembled during the past year and successfully used to study the photodetachment of S(-) ions. A periodic dependence of the photodetachment cross section on the light frequency was observed for the first time in any atom. The oscillatory structure could be attributed to the excitation of the detached electrons to discrete cyclotron levels in the magnetic field. The experiments so far also indicate that state dependent photodetachment should provide an effective means for producing and detecting population differences in trapped ions. (Author)
Photodetachment leading to outgoing s‐wave and pz‐wave electrons in dc electric and magnetic fields along the z‐axis, alone and in combination, is treated using a zero order model which neglects the (weak) interaction between the atom and detached electron. Threshold laws and interferences arising in the mixed field case are illustrated, and qualitatively discussed using a time dependent fomulation which gives the total detachment cross section as the fourier transform of the dipole auto‐correlation function. First order time dependent perturbation theory is then used to indicate the insensitivity of the results to inclusion of an atomic final state interaction.
We have probed the relative weight of the first Zeeman transition in photodetachment from ${\mathrm{O}}^{\ensuremath{-}}$ and ${\mathrm{S}}^{\ensuremath{-}}$ at the ${}^{2}{\stackrel{\ensuremath{\rightarrow}}{{P}_{3/2}}}^{3}{P}_{2}$ detachment threshold, using laser light polarized perpendicular to a 1T field. For both ion species, we find a nonzero transition strength at the first threshold, a clear discrepancy with previously published theory based on LS coupling in the ion and the atom.
In a recent experiment, Lindahl et al. ( Lindahl A. O. et al. , Phys. Rev. Lett. , 108 (2012) 033004) observed a new threshold behavior in the photodetachment of the potassium negative ion when the residual atom is left in the state. Unfortunately the resonance close to threshold made it more difficult to apply the semi-classical model that was developed to describe the threshold behavior. In this paper we present a study of the threshold behavior of the partial cross-section in the photodetachment of the sodium negative ion. The experiment was conducted using a collinear beams apparatus where the detection was performed using a resonance ionization scheme. We observe the same threshold behavior as in the previous experiment, but without any obfuscating resonance. The model derived in the previous paper is found to fit the observed cross-section up to 35 meV above threshold. The present experiment clearly demonstrates the threshold behaviour for the fundamental process of a free electron moving in the field of an atom with a large negative polarizability.