Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Comment on “Photodetachment in combined static and dynamic electric fields”

I. I. Fabrikant, M. V. Frolov, Nikolai L. Manakov, Anthony F. Starace

Published Aug 8, 2001• 8 citations
Publisher

Abstract

The theoretical analysis of C. Rangan and A. R. P. Rau [Phys. Rev. A 61, 033405 (2000)] on the process of photodetachment of ${\mathrm{H}}^{\ensuremath{-}}$ in a strong static electric field, which calls into question the predictions of B. Gao and A. F. Starace [Phys. Rev. A 42, 5580 (1990)] and also of M. Q. Bao et al. [Phys. Rev. A 58, 411 (1998)], is shown in this Comment to be incorrect. First, we point out that a number of assumptions of Rangan and Rau's analysis rest on tenuous theoretical grounds. Second, we adduce two completely independent and different analyses of the problem which precisely confirm the results of Gao and Starace. These independent analyses also provide the interpretation that Gao and Starace's predicted strong-field effects are due to the exact account of the influence of the static electric field, not only on the final state of the detached electron, but also on the initial bound-electron state.

DOI
10.1103/physreva.64.037401

Related papers

Dynamic hyperpolarizability and two-photon detachment in the presence of a strong static electric field: Application to H^{-}

M. V. Frolov, Nikolai L. Manakov, Anthony F. Starace

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 $(S$-) 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.

Physical Review A•Jul 1, 2001•7 citations

s-wave photodetachment in a static electric field

N. D. Gibson, B. J. Davies, Daniel J. Larson

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.

Physical Review A•Mar 1, 1993•40 citations

Final-state-interaction effects on one- and two-photon detachment of H− in the presence of a static electric field

Min-Qi Bao, I. I. Fabrikant, Anthony F. Starace

We present a detailed theoretical formulation of the problem of an electron moving in a static electric field, a laser field, and an atomic potential. Our formulation treats the electron-atom interaction in the zero-range potential approximation and employs both the quasienergy approach and an analytic expression for the Green's function describing electron propagation in a combination of static and laser electric fields. Our formulation is applied to one- and two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$ in a strong static electric field and takes into account all final-state interactions of the detached electron with the static and laser fields and with the atomic core. Our results show that rescattering effects are small in the case of one-photon detachment, where our results are close to those obtained previously by Gao and Starace [Phys. Rev. A 42, 5580 (1990)], who ignored rescattering effects but who found a strong-field treatment of the laser field to be important, even in the limit of weak laser fields, owing to interference terms involving both the laser and static electric fields. Our results for two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$, on the other hand, show that rescattering effects are very significant. In the presence of a strong static electric field, moreover, the two-photon detachment cross section is found to be very sensitive to the magnitude of the static field.

Physical Review A•Jul 1, 1998•11 citations

Negative-ion photodetachment in an electric field

Hin-Yiu Wong, A. R. P. Rau, Chris H. Greene

A multichannel study of the photodetachment of a negative ion such as ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ in the presence of a constant electric field is presented. The analysis is carried out as a series of frame transformations for the outgoing photoelectron. An earlier analysis in the absence of the external field is now augmented by the further transformations from spherical to cylindrical symmetry that are required. The interplay between the various thresholds due to fine structure in the negative ion and residual atom and the effects of the external field are analytically treated. The net effect is to eliminate the thresholds, to induce modulations in the detachment cross section, and to introduce field-assisted-tunneling contributions to the photodetachment. Numerical illustrations are provided. Our treatment closely parallels similar treatments of photoionization of neutral atoms in an electric field and of photodetachment in a magnetic field.

Physical Review A•Apr 1, 1988•59 citations

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

William P. Reinhardt

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

Comment on “Weakly bound states of the He-He-Ca triatomic system”

David López‐Durán, Tomás González‐Lezana, Gerardo Delgado-Barrio +2 more

We discuss the computational results on the energetics and features of the bound states of one and two He atoms attached to a Ca atom, which have been presented by Gou and Li in a recently published paper in Phys. Rev. A 85, 012510 (2012). We show that, given their choice for the interaction potential-energy surface, the energy they found for the three-particle complex's ground state must be incorrect. We also point out that a large number of their excited states for the same system do not really exist since they are located above either of the two-atom components' bound-state energies.

Physical Review A•Jul 25, 2012•3 citations
The theoretical analysis of C. Rangan and A. R. P. Rau [Phys. Rev. A 61, 033405 (2000)] on the process of photodetachment of H\ensuremath−{\mathrm{H}}^{\ensuremath{-}}H\ensuremath− in a strong static electric field, which calls into question the predictions of B. Gao and A. F. Starace [Phys. Rev. A 42, 5580 (1990)] and also of M. Q. Bao et al. [Phys. Rev. A 58, 411 (1998)], is shown in this Comment to be incorrect. First, we point out that a number of assumptions of Rangan and Rau's analysis rest on tenuous theoretical grounds. Second, we adduce two completely independent and different analyses of the problem which precisely confirm the results of Gao and Starace. These independent analyses also provide the interpretation that Gao and Starace's predicted strong-field effects are due to the exact account of the influence of the static electric field, not only on the final state of the detached electron, but also on the initial bound-electron state.
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.
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.
We present a detailed theoretical formulation of the problem of an electron moving in a static electric field, a laser field, and an atomic potential. Our formulation treats the electron-atom interaction in the zero-range potential approximation and employs both the quasienergy approach and an analytic expression for the Green's function describing electron propagation in a combination of static and laser electric fields. Our formulation is applied to one- and two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$ in a strong static electric field and takes into account all final-state interactions of the detached electron with the static and laser fields and with the atomic core. Our results show that rescattering effects are small in the case of one-photon detachment, where our results are close to those obtained previously by Gao and Starace [Phys. Rev. A 42, 5580 (1990)], who ignored rescattering effects but who found a strong-field treatment of the laser field to be important, even in the limit of weak laser fields, owing to interference terms involving both the laser and static electric fields. Our results for two-photon detachment of ${\mathrm{H}}^{\ensuremath{-}}$, on the other hand, show that rescattering effects are very significant. In the presence of a strong static electric field, moreover, the two-photon detachment cross section is found to be very sensitive to the magnitude of the static field.
A multichannel study of the photodetachment of a negative ion such as ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ in the presence of a constant electric field is presented. The analysis is carried out as a series of frame transformations for the outgoing photoelectron. An earlier analysis in the absence of the external field is now augmented by the further transformations from spherical to cylindrical symmetry that are required. The interplay between the various thresholds due to fine structure in the negative ion and residual atom and the effects of the external field are analytically treated. The net effect is to eliminate the thresholds, to induce modulations in the detachment cross section, and to introduce field-assisted-tunneling contributions to the photodetachment. Numerical illustrations are provided. Our treatment closely parallels similar treatments of photoionization of neutral atoms in an electric field and of photodetachment in a magnetic field.
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 discuss the computational results on the energetics and features of the bound states of one and two He atoms attached to a Ca atom, which have been presented by Gou and Li in a recently published paper in Phys. Rev. A 85, 012510 (2012). We show that, given their choice for the interaction potential-energy surface, the energy they found for the three-particle complex's ground state must be incorrect. We also point out that a large number of their excited states for the same system do not really exist since they are located above either of the two-atom components' bound-state energies.