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Journal of Physics B Atomic Molecular and Optical Physics

Many-body calculation of negative ions using the Dyson equation

Larissa V. Chernysheva, G. F. Gribakin, V. K. Ivanov, Michael Yu. Kuchiev

Published Aug 14, 1988• 117 citations
Publisher

Abstract

A new method of calculating atomic negative ions is developed. It is based on the Dyson equation, and gives the binding energy and the wavefunction of the outer electron in the negative ion. The calculation for He - 1s2s2p 4 P is consistent with experiment. The photodetachment cross section for He - 4 P is calculated for the first time. The phaseshift for p-electron quartet scattering by He 1s2s 3 S is presented. Results for the first calculation of Pd - 4d 10 5s 2 S are reported.

DOI
10.1088/0953-4075/21/15/001

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A new method of calculating atomic negative ions is developed. It is based on the Dyson equation, and gives the binding energy and the wavefunction of the outer electron in the negative ion. The calculation for He - 1s2s2p 4 P is consistent with experiment. The photodetachment cross section for He - 4 P is calculated for the first time. The phaseshift for p-electron quartet scattering by He 1s2s 3 S is presented. Results for the first calculation of Pd - 4d 10 5s 2 S are reported.
The relativistic correlation-potential method was used to calculate binding energies and fine-structure intervals for Pd, Ba, and Yb negative ions and to investigate low-energy electron scattering by Yb, Hg, and Ra atoms. The results for the binding energies are the following: 540 meV for the 5s state of ${\mathrm{Pd}}^{\mathrm{\ensuremath{-}}}$, 190 and 133 meV for the 6p1/2{\mathit{p}}_{1/2}p1/2​ and 6p3/2{\mathit{p}}_{3/2}p3/2​ states of ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and 36 meV for the 6p1/2{\mathit{p}}_{1/2}p1/2​ state of the ${\mathrm{Yb}}^{\mathrm{\ensuremath{-}}}$. A number of prominent p and d resonances are revealed in the scattering phase-shift calculations. These p or d resonances lead to a phenomenon of 100% polarization of the scattered electron beam at appropriate electron energy and scattering angle. A criterion is proposed to measure the strength of the nonlocal correlation potential and to evaluate its ability to create a bound state: FG(r',r)\ensuremath{\Sigma}(r,r')dr dr'>1 is the necessary condition for the formation of a bound state. Here \ensuremath{\Sigma} is the correlation potential and G is the electron Green's function at zero energy.
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.
Binding energies of the ground 1S^{1}S1S states of the alkali negative ions are calculated using the coupled equations of scattering theory, based on semiempirical effective potentials for the neutral atoms. An additional true bound state with configuration 3P^{3}P3P lying just below the first excited state of the neutral atom is predicted for every species except ${\mathrm{Li}}^{\ensuremath{-}}$.
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 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{(}^{1}(1S- $^{3}\mathrm{\ensuremath{-}}$ $^{3}\mathrm{\ensuremath{-}}$ $^{1}\mathrm{\ensuremath{-}}$ $^{1}\mathrm{\ensuremath{-}}$ 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 ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ 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 4s4p3{4\mathrm{s}4\mathrm{p}}^{3}4s4p3P.
Atomic many-body theory methods are used to calculate the fine structure of negative ions formed by binding a p electron into an open shell, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$. This binding is due to a strong correlation potential acting between the electron and the neutral atom. Comparison with experimental data shows that the second order many-body perturbation theory calculation overestimates the correlation potential by 10% to 15%. Scaling factors are introduced in the correlation potential to reproduce experimental binding energies of the lower p1/2{\mathrm{p}}_{1\mathrm{/}2}p1/2​ components. This procedure yields fine-structure intervals in excellent agreement with experiment for ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and allows us to predict that in ${\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}$ the p1/2{\mathrm{p}}_{1\mathrm{/}2}p1/2​ state is bound by 100 meV, and p3/2{\mathrm{p}}_{3\mathrm{/}2}p3/2​ is a resonance at 16 meV in the continuum.