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

Near-threshold photodetachment of heavy alkali-metal anions

Cristian Bahrim, Uwe Thumm, A.A. Khuskivadze, I. I. Fabrikant

Published Nov 20, 2002• 11 citations
Publisher

Abstract

We calculate near-threshold photodetachment cross sections for ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ using the Pauli equation method with a model potential describing the effective electron-atom interaction. Parameters of the model potential are fitted to reproduce ab initio scattering phase shifts obtained from Dirac R-matrix calculations. Special care is taken to formulate the boundary conditions near the atomic nucleus for solving the Pauli equation, based on the analytic solution of the Dirac equation for a Coulomb potential. We find a ${}^{3}{P}_{1}^{o}$ resonance contribution to the photodetachment cross section of ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ ions. Our calculated total photodetachment cross sections for Cs agree with experiments after tuning the resonance position by 2.4 meV. For ${\mathrm{Rb}}^{\ensuremath{-}}$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ the resonance contribution is much smaller than for Cs. We therefore also provide angle-differential cross sections and asymmetry parameters which are much more sensitive to the resonant contribution than total cross sections.

DOI
10.1103/physreva.66.052712

Related papers

Boundary Conditions for the Pauli Equation: Application to Photodetachment of Cs −

Cristian Bahrim, I. I. Fabrikant, Uwe Thumm

We formulate the boundary conditions near the atomic nucleus for solving the Pauli equation, based on the analytic solution of the Dirac equation for a Coulomb potential. We then integrate the Pauli equation using an effective potential that is adjusted to reproduce Dirac R-matrix scattering phase shifts, and find the (3)P(o)(1) resonance contribution to the photodetachment cross section of Cs-. Our photodetachment cross sections agree with recent experiments by Scheer et al. [Phys. Rev. Lett. 80, 684 (1998)] after tuning the resonance position by 2.4 meV. We also provide angle-differential photodetachment cross sections and the corresponding asymmetry parameter beta near the Cs(6s) threshold.

Physical Review Letters•Aug 31, 2001•8 citations

Low-lying 3Po and 3Se states of Rb−,Cs− , and Fr−

Cristian Bahrim, Uwe Thumm

Our Dirac R-matrix calculations suggest that none of the heavy alkali-metal negative ions, Rb, Cs, and Fr, has an excited bound state. Their lowest excited state appears to be a multiplet of ${}^{3}{P}_{J}^{o}$-shape resonances, the $J=1$ component of which was recently observed in photodetachment experiments on ${\mathrm{Cs}}^{\ensuremath{-}}.$ We analyze these ${}^{3}{P}_{J}^{o}$ and the ${}^{3}{S}^{e}$ excited negative ion states in partial and converged total scattering cross sections for slow electrons with incident kinetic energies below 120 meV. Our results are in excellent agreement with available experimental data. We also propose a new value for the electron affinity of Fr, provide the scattering length for electronic collisions with Rb, Cs, and Fr, and discuss the nuclear charge dependence of relativistic effects in the resonance profiles.

Physical Review A•Jan 18, 2000•72 citations

Negative-ion resonances in cross sections for slow-electron–heavy-alkali-metal-atom scattering

Cristian Bahrim, Uwe Thumm, I. I. Fabrikant

We analyze negative-ion resonances in elastic and inelastic total scattering cross sections for slow electron collisions with the heavy-alkali-metal atoms Rb, Cs, and Fr. Our calculations are based on the Dirac $R$-matrix method [Thumm and Norcross, Phys. Rev. A 45, 6349 (1992)]. For incident electrons of up to 2.8 eV kinetic energy, we compare a ${}^{3}{P}^{o}$ shape resonance and ${}^{3}{P}^{e},$ ${}^{1}{P}_{1}^{o},$ and ${}^{1}{D}_{2}^{o}$ Feshbach resonances, located below the first excitation threshold of the atomic target in the low-lying spectra of the ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ negative ions, with available experimental data and other calculations. We provide the resonance parameters, partial and converged total elastic and inelastic scattering cross sections, and discuss the relative importance of relativistic effects for the three heavy-alkali-metal targets.

Physical Review A•Mar 19, 2001•36 citations

Effect of polarization on photodetachment thresholds

J. Sandström, G. Haeffler, Igor Yu. Kiyan +5 more

We have measured the near-threshold cross sections for the photodetachment of ${\mathrm{Li}}^{\ensuremath{-}}$ into the ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(2{p}_{1∕2})$, ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(3p)$, ${e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(3s)$, and ${e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(4s)$ continuum channels and the photodetachment of ${\mathrm{K}}^{\ensuremath{-}}$ into the ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{K}(4{p}_{3∕2})$ continuum channel. The data was analyzed using both a top-of-barrier model and a modified effective range theory. Both approaches explicitly take into account the significant polarization potential in the final continuum channels. The study involving both experiment and theory enabled us to investigate the effect of the polarization on near-threshold photodetachment. Furthermore, since photodetachment and electron scattering are related in the half-collision concept, we were able to determine low-energy electron scattering quantities such as phase shifts, elastic cross sections, and $s$ wave scattering lengths for electron scattering on excited Li and K atoms. The results allowed us to predict a virtual state in the ${e}^{\ensuremath{-}}(ks)\text{\ensuremath{-}}\mathrm{Li}(3p)$ system.

Physical Review A•Nov 16, 2004•12 citations

Observation of thresholds and overlapping resonances below the 10 2P1/2 and 2P3/2 thresholds in the photodetachment of Cs −

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

A collinear beam apparatus has been used to study photodetachment of Cs${}^{\ensuremath{-}}$. Partial cross sections were measured using state-selective detection based on a resonance ionization scheme. Several resonances were observed in the Cs($10{\phantom{\rule{0.16em}{0ex}}}^{2}S$), Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}F$), Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}G$), and Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) final-state channels below the Cs($10{\phantom{\rule{0.16em}{0ex}}}^{2}P$${}_{3/2}$) channel opening. A model was developed to account for the interference between overlapping resonances. This model is essentially a generalization of the Fano [U. Fano, Phys. Rev. 124, 1866 (1961)] and Shore [B. W. Shore, Phys. Rev. 171, 43 (1968)] parametrizations for single resonances. Resonance parameters were extracted by fitting the model to the data sets. The openings of the Cs($10{\phantom{\rule{0.16em}{0ex}}}^{2}S$) and Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}F$) channels, where the polarizabilities of the atomic states are large and positive, showed rapid onsets. In the case of the Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}G$) and Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) channels, on the other hand, the photodetachment cross sections increased slowly with energy. For the Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) channel this is the expected behavior, since it is the result of a large and negative polarizability of the $6{\phantom{\rule{0.16em}{0ex}}}^{2}H$ state. In addition, the excitation of the Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) state with respect to the Cs ground state was found to be 28 356.3(2) ${\mathrm{cm}}^{\ensuremath{-}1}$, in agreement with a previous experiment.

Physical Review A•Nov 11, 2013•4 citations

Static electric-field effects in the photodetachment of Cs− at the 3P resonance region

A.A. Khuskivadze, I. I. Fabrikant, Uwe Thumm

We calculated near-threshold photodetachment cross sections for ${\mathrm{Cs}}^{\ensuremath{-}}$ in the presence of a dc electric field using three different approaches: the frame-transformation method with and without rescattering effects and the Kirchhoff-integral approach. Radial wave functions for the electronic motion were obtained using the Pauli equation method with a model potential describing the effective electron-atom interaction. Our results demonstrate the inadequacy of the frame-transformation method in the ${}^{3}P$ resonance region even for weak fields $(E<10\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}).$ We show that the triplet and singlet contributions to the total cross section can be manipulated by varying the external electric field. This can enhance spin-orbit effects in the photodetachment process and create more favorable conditions in the experiment for the observation of the lowest ${}^{3}P$ resonance in ${\mathrm{Cs}}^{\ensuremath{-}}.$

Physical Review A•Dec 10, 2003•4 citations
We calculate near-threshold photodetachment cross sections for Rb\ensuremath−,{\mathrm{Rb}}^{\ensuremath{-}},Rb\ensuremath−, Cs\ensuremath−,{\mathrm{Cs}}^{\ensuremath{-}},Cs\ensuremath−, and Fr\ensuremath−{\mathrm{Fr}}^{\ensuremath{-}}Fr\ensuremath− using the Pauli equation method with a model potential describing the effective electron-atom interaction. Parameters of the model potential are fitted to reproduce ab initio scattering phase shifts obtained from Dirac R-matrix calculations. Special care is taken to formulate the boundary conditions near the atomic nucleus for solving the Pauli equation, based on the analytic solution of the Dirac equation for a Coulomb potential. We find a 3P1o{}^{3}{P}_{1}^{o}3P1o​ resonance contribution to the photodetachment cross section of Rb\ensuremath−,{\mathrm{Rb}}^{\ensuremath{-}},Rb\ensuremath−, Cs\ensuremath−,{\mathrm{Cs}}^{\ensuremath{-}},Cs\ensuremath−, and Fr\ensuremath−{\mathrm{Fr}}^{\ensuremath{-}}Fr\ensuremath− ions. Our calculated total photodetachment cross sections for Cs agree with experiments after tuning the resonance position by 2.4 meV. For Rb\ensuremath−{\mathrm{Rb}}^{\ensuremath{-}}Rb\ensuremath− and Fr\ensuremath−{\mathrm{Fr}}^{\ensuremath{-}}Fr\ensuremath− the resonance contribution is much smaller than for Cs. We therefore also provide angle-differential cross sections and asymmetry parameters which are much more sensitive to the resonant contribution than total cross sections.
We formulate the boundary conditions near the atomic nucleus for solving the Pauli equation, based on the analytic solution of the Dirac equation for a Coulomb potential. We then integrate the Pauli equation using an effective potential that is adjusted to reproduce Dirac R-matrix scattering phase shifts, and find the (3)P(o)(1) resonance contribution to the photodetachment cross section of Cs-. Our photodetachment cross sections agree with recent experiments by Scheer et al. [Phys. Rev. Lett. 80, 684 (1998)] after tuning the resonance position by 2.4 meV. We also provide angle-differential photodetachment cross sections and the corresponding asymmetry parameter beta near the Cs(6s) threshold.
Our Dirac R-matrix calculations suggest that none of the heavy alkali-metal negative ions, Rb, Cs, and Fr, has an excited bound state. Their lowest excited state appears to be a multiplet of 3PJo{}^{3}{P}_{J}^{o}3PJo​-shape resonances, the J=1J=1J=1 component of which was recently observed in photodetachment experiments on ${\mathrm{Cs}}^{\ensuremath{-}}.$ We analyze these 3PJo{}^{3}{P}_{J}^{o}3PJo​ and the 3Se{}^{3}{S}^{e}3Se excited negative ion states in partial and converged total scattering cross sections for slow electrons with incident kinetic energies below 120 meV. Our results are in excellent agreement with available experimental data. We also propose a new value for the electron affinity of Fr, provide the scattering length for electronic collisions with Rb, Cs, and Fr, and discuss the nuclear charge dependence of relativistic effects in the resonance profiles.
We analyze negative-ion resonances in elastic and inelastic total scattering cross sections for slow electron collisions with the heavy-alkali-metal atoms Rb, Cs, and Fr. Our calculations are based on the Dirac RRR-matrix method [Thumm and Norcross, Phys. Rev. A 45, 6349 (1992)]. For incident electrons of up to 2.8 eV kinetic energy, we compare a 3Po{}^{3}{P}^{o}3Po shape resonance and 3Pe,{}^{3}{P}^{e},3Pe, 1P1o,{}^{1}{P}_{1}^{o},1P1o​, and 1D2o{}^{1}{D}_{2}^{o}1D2o​ Feshbach resonances, located below the first excitation threshold of the atomic target in the low-lying spectra of the ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ negative ions, with available experimental data and other calculations. We provide the resonance parameters, partial and converged total elastic and inelastic scattering cross sections, and discuss the relative importance of relativistic effects for the three heavy-alkali-metal targets.
We have measured the near-threshold cross sections for the photodetachment of ${\mathrm{Li}}^{\ensuremath{-}}$ into the ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(2{p}_{1∕2})$, ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(3p)$, ${e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(3s)$, and ${e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(4s)$ continuum channels and the photodetachment of ${\mathrm{K}}^{\ensuremath{-}}$ into the ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{K}(4{p}_{3∕2})$ continuum channel. The data was analyzed using both a top-of-barrier model and a modified effective range theory. Both approaches explicitly take into account the significant polarization potential in the final continuum channels. The study involving both experiment and theory enabled us to investigate the effect of the polarization on near-threshold photodetachment. Furthermore, since photodetachment and electron scattering are related in the half-collision concept, we were able to determine low-energy electron scattering quantities such as phase shifts, elastic cross sections, and sss wave scattering lengths for electron scattering on excited Li and K atoms. The results allowed us to predict a virtual state in the ${e}^{\ensuremath{-}}(ks)\text{\ensuremath{-}}\mathrm{Li}(3p)$ system.
A collinear beam apparatus has been used to study photodetachment of Cs${}^{\ensuremath{-}}$. Partial cross sections were measured using state-selective detection based on a resonance ionization scheme. Several resonances were observed in the Cs(102S10{\phantom{\rule{0.16em}{0ex}}}^{2}S102S), Cs(62F6{\phantom{\rule{0.16em}{0ex}}}^{2}F62F), Cs(62G6{\phantom{\rule{0.16em}{0ex}}}^{2}G62G), and Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) final-state channels below the Cs(102P10{\phantom{\rule{0.16em}{0ex}}}^{2}P102P3/2{}_{3/2}3/2​) channel opening. A model was developed to account for the interference between overlapping resonances. This model is essentially a generalization of the Fano [U. Fano, Phys. Rev. 124, 1866 (1961)] and Shore [B. W. Shore, Phys. Rev. 171, 43 (1968)] parametrizations for single resonances. Resonance parameters were extracted by fitting the model to the data sets. The openings of the Cs(102S10{\phantom{\rule{0.16em}{0ex}}}^{2}S102S) and Cs(62F6{\phantom{\rule{0.16em}{0ex}}}^{2}F62F) channels, where the polarizabilities of the atomic states are large and positive, showed rapid onsets. In the case of the Cs(62G6{\phantom{\rule{0.16em}{0ex}}}^{2}G62G) and Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) channels, on the other hand, the photodetachment cross sections increased slowly with energy. For the Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) channel this is the expected behavior, since it is the result of a large and negative polarizability of the 62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H state. In addition, the excitation of the Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) state with respect to the Cs ground state was found to be 28 356.3(2) ${\mathrm{cm}}^{\ensuremath{-}1}$, in agreement with a previous experiment.
We calculated near-threshold photodetachment cross sections for ${\mathrm{Cs}}^{\ensuremath{-}}$ in the presence of a dc electric field using three different approaches: the frame-transformation method with and without rescattering effects and the Kirchhoff-integral approach. Radial wave functions for the electronic motion were obtained using the Pauli equation method with a model potential describing the effective electron-atom interaction. Our results demonstrate the inadequacy of the frame-transformation method in the 3P{}^{3}P3P resonance region even for weak fields (E<10kV/cm).(E<10\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}).(E<10kV/cm). We show that the triplet and singlet contributions to the total cross section can be manipulated by varying the external electric field. This can enhance spin-orbit effects in the photodetachment process and create more favorable conditions in the experiment for the observation of the lowest 3P{}^{3}P3P resonance in ${\mathrm{Cs}}^{\ensuremath{-}}.$