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Physical Review A

Fine structure of Ca− , Sr− , Ba− , and Ra− from the many-body theory calculation

V. A. Dzuba, G. F. Gribakin

Published Mar 1, 1997• 17 citations
Publisher

Abstract

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 ${\mathrm{p}}_{1\mathrm{/}2}$ 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 ${\mathrm{p}}_{1\mathrm{/}2}$ state is bound by 100 meV, and ${\mathrm{p}}_{3\mathrm{/}2}$ is a resonance at 16 meV in the continuum.

DOI
10.1103/physreva.55.2443

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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, Ca\ensuremath−{\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}Ca\ensuremath−, Sr\ensuremath−{\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}Sr\ensuremath−, Ba\ensuremath−{\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}Ba\ensuremath−, and Ra\ensuremath−{\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}Ra\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 Ca\ensuremath−{\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}Ca\ensuremath−, Sr\ensuremath−{\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}Sr\ensuremath−, and Ba\ensuremath−{\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}Ba\ensuremath−, and allows us to predict that in Ra\ensuremath−{\mathrm{Ra}}^{\mathrm{\ensuremath{-}}}Ra\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.
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.
The binding energies of the 4s24p2P{4s}^{2}4p^{2}P4s24p2P ground state in ${\mathrm{Ca}}^{\ensuremath{-}}$ have been determined by means of state-selective photoionization of Ca atoms produced in s-wave photodetachment to be $24.55\ifmmode\pm\else\textpm\fi{}0.10$ meV for the J=1/2J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2J=1/2 and $19.73\ifmmode\pm\else\textpm\fi{}0.10$ meV for the J=3/2J\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3/2J=3/2 component. The sensitivity of the detection technique applied has also made it possible to disprove previous claims for the observation of a metastable ${4s4p}^{2}^{4}P$ state in ${\mathrm{Ca}}^{\ensuremath{-}}$.
The binding energy and fine-structure splitting of the ground state of the ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$n(${5\mathrm{s}}^{2}5p5p5p{\mathrm{}}^{2}$P) ion have been measured by means of the laser photodetachment threshold technique combined with state-selective detection of neutral atoms using resonant ionization spectroscopy. We find binding energies of 32.17\ifmmode\pm\else\textpm\fi{}0.03 meV (J=3/2) and 52.06\ifmmode\pm\else\textpm\fi{}0.06 meV (J=1/2), yielding a fine-structure splitting of 19.89\ifmmode\pm\else\textpm\fi{}0.07 meV. This represents an improvement of two orders of magnitude compared to the recent data based on a combination of laser photodetachment and accelerator mass spectroscopy [D. Berkovits et al., Phys. Rev. Lett. 75, 414 (1995)].
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.
Within the framework of the close-coupling method, ab initio calculations of parameters of multichannel quantum-defect theory have been carried out for several Rydberg series of Ca, Sr, and Ba. A local-density approximation, commonly used in solid-state calculations, including self-consistent, self-energy corrections, was made to the exchange-correlation potential. Good agreement with experimental values of multichannel quantum-defect theory parameters is obtained, permitting accurate prediction of highly excited-state binding energies.
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.