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Physical Review A

Electron scattering by Ca atoms and photodetachment of Ca− ions: An R-matrix study

Jianmin Yuan, L. Fritsche

Published Feb 1, 1997• 26 citations
Publisher

Abstract

We have performed close-coupling calculations on electron scattering by Ca atoms and on photodetachment of ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ ions by using a six-state ${(}^{1}$S- $^{3}\mathrm{\ensuremath{-}}$ $^{3}\mathrm{\ensuremath{-}}$ $^{1}\mathrm{\ensuremath{-}}$ $^{1}\mathrm{\ensuremath{-}}$ $^{1}\mathrm{P}$) R-matrix method. We predict a strong interaction between (${4\mathrm{s}}^{21}$S+\ensuremath{\epsilon}d${)}^{2}$D and (${4\mathrm{s}4\mathrm{p}}^{3}$P+\ensuremath{\epsilon}p${)}^{2}$D channels that gives rise to two relatively broad resonance peaks in the d-wave cross section. In addition, one obtains a strong and a weak peak in the total scattering cross section. Our calculations on the photodetachment cross section of ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ ions yield results that are in good qualitative agreement with the experimental data by allowing for the opening of a detachment channel connected to the excited state ${4\mathrm{s}4\mathrm{p}}^{3}$P.

DOI
10.1103/physreva.55.1020

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We have performed close-coupling calculations on electron scattering by Ca atoms and on photodetachment of Ca\ensuremath−{\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}Ca\ensuremath− ions by using a six-state (1{(}^{1}(1S- 3\ensuremath−^{3}\mathrm{\ensuremath{-}}3\ensuremath− 3\ensuremath−^{3}\mathrm{\ensuremath{-}}3\ensuremath− 1\ensuremath−^{1}\mathrm{\ensuremath{-}}1\ensuremath− 1\ensuremath−^{1}\mathrm{\ensuremath{-}}1\ensuremath− 1P^{1}\mathrm{P}1P) R-matrix method. We predict a strong interaction between (4s21{4\mathrm{s}}^{21}4s21S+\ensuremath{\epsilon}d)2{)}^{2})2D and (4s4p3{4\mathrm{s}4\mathrm{p}}^{3}4s4p3P+\ensuremath{\epsilon}p)2{)}^{2})2D channels that gives rise to two relatively broad resonance peaks in the d-wave cross section. In addition, one obtains a strong and a weak peak in the total scattering cross section. Our calculations on the photodetachment cross section of Ca\ensuremath−{\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}Ca\ensuremath− ions yield results that are in good qualitative agreement with the experimental data by allowing for the opening of a detachment channel connected to the excited state 4s4p3{4\mathrm{s}4\mathrm{p}}^{3}4s4p3P.
Three mutually related problems concerning the interaction of an electron with an alkaline-earth atom are examined. (i) The scattering problem: the phaseshifts for p-electron scattering by Ca, Sr and Ba are calculated. (ii) The negative ion problem: the wavefunction and the binding energy are obtained for the outer electron in Ca - 4s 2 4p, Sr - 5s 2 5p and Ba - 6s 2 6p ions. (iii) The photodetachment problem: the photodetachment cross sections are calculated for the outer electron in each of these ions. The most intriguing feature of these problems is the strong correlational potential, attracting the electron to the atom due to the large dipole polarizabilities of Ca, Sr and Ba. The calculations are performed by means of the Dyson equation of the many-body theory.
The resonance and near-threshold structures of low-energy electron interaction with Sr and Ba atoms have been investigated by carrying out respectively 11-state and 21-state close-coupling calculations within the R-matrix scheme. Part of the core–valence correlation is included by exciting one core electron to the valence orbitals. Results for the low-energy electron scattering and the photodetachment of the negative ions are presented. For Sr, the results show that there is a 2D shape resonance around 0.8 eV above the elastic scattering threshold and a remarkable structure just above the first 3Po excitation threshold. For Ba, two 2D shape resonances are predicted, just above the elastic scattering threshold and the 3D excitation threshold, respectively.
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 3P1o{}^{3}{P}_{1}^{o}3P1o​ 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.
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.
Studies of electron transmission through Ca vapor reveal two prominent resonances in the range 0--4 eV. The energies and widths of these temporary anion states suggest that they may be assigned to the strongly mixed (4${s}^{2}3d3d3d{)}^{2}Dand(4s4D and (4s4Dand(4s4{p}^{2}$)2{)}^{2})2D states of ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$. This interpretation is supported by ab initio configuration-interaction calculations and is consistent with previously unassigned structure observed in the photodetachment cross section.
RRR-matrix calculations have been carried out to investigate the effect of core-valence electron correlation on the scattering of electrons with Ca atoms at low energies. While the major feature of the ddd-wave shape resonance with a peak near 1.3 eV in the total cross section can be reproduced by including only the correlation among the valence electrons, we show that the existence of a low-energy peak near 0.15 eV, which has also been observed experimentally, can be obtained only if the correlations between the valence and core electrons are considered. This low-energy peak is shown not caused by a shape resonance, but rather due to the rapid decrease of the sss- and ppp-wave phase shifts with collision energies. The present result also indirectly supports the previous conclusion that core-valence electron correlation is responsible for bringing the electron affinity of ${\mathrm{Ca}}^{\ensuremath{-}}$ from 72 to 15 meV, i.e., to a value which is much closer to the experiment.