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Journal of Physics B Atomic Molecular and Optical Physics

- low-lying shape resonance rather than a bound state

V. A. Dzuba, G. F. Gribakin

Published Jun 14, 1998• 6 citations
Publisher

Abstract

Strong evidence against stability of the negative ion of ytterbium is presented, and the prediction is made that the lowest negative ion state is a narrow shape resonance in the electron - atom continuum at 20 meV. These results are obtained from the many-body theory calculations with the electron - atom correlation potential appropriately scaled to reproduce the experimental data for the isoelectronic neutral Lu and . They are in agreement with the recent thorough experimental investigation of by the Aarhus group.

DOI
10.1088/0953-4075/31/11/002

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Strong evidence against stability of the negative ion of ytterbium is presented, and the prediction is made that the lowest negative ion state is a narrow shape resonance in the electron - atom continuum at 20 meV. These results are obtained from the many-body theory calculations with the electron - atom correlation potential appropriately scaled to reproduce the experimental data for the isoelectronic neutral Lu and . They are in agreement with the recent thorough experimental investigation of by the Aarhus group.
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 first experimental studies of Os(-) reveal the presence of two very strong resonances. One state is a narrow shape resonance lying only 3.52(12) meV above the ground state detachment threshold, while the other is bound by 11.48(12) meV. Convincing evidence that these states have odd parity is presented, making Os(-) the only known atomic negative ion with bound states of opposite parity. Additionally, the binding energies for the Os(-) ground state ((4)F(e)(9/2)) and first excited state ((4)F(e)(7/2)) are measured to be 1.077 80(12) eV and 0.553(3) eV, respectively.
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.
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.
Strontium, barium and radium are predicted to have stable negative ions of ns2np designation, on the basis of eigenchannel R-matrix calculations performed in LS coupling for the negative ion of each alkaline-earth atom. The calculations also confirm earlier studies indicating that the negative ion of calcium is stable and that corresponding 2P degrees states in beryllium and magnesium are unstable shape resonances. The much larger polarisability of the heavier alkaline earths play a crucial role in binding the additional electron. The analysis uses quantum defect theory in its generalised form appropriate for long-range motion in a dipole polarisation potential.
The negative ion of cerium is investigated experimentally with tunable infrared laser photodetachment spectroscopy and theoretically with relativistic configuration interaction in the continuum formalism. The relative cross section for neutral atom production is measured with a crossed ion-beam--laser-beam apparatus over the photon energy range of 0.54--0.75 eV. A rich resonance spectrum is revealed near the threshold with, at least, 12 peaks observed due to transitions from bound states of ${\mathrm{Ce}}^{\ensuremath{-}}$ to either bound or quasibound excited states of the negative ion. Theoretical calculations of the photodetachment cross sections enable identification of the transitions responsible for the measured peaks. Two of the peaks are due to electric dipole-allowed bound-bound transitions in ${\mathrm{Ce}}^{\ensuremath{-}}$, making cerium only the second atomic negative ion that has been demonstrated to support multiple bound states of opposite parity. In addition, combining the experimental data with the theoretical analysis determines the electron affinity of cerium to be 0.628(10) eV and the fine structure splitting of the ground state of ${\mathrm{Ce}}^{\ensuremath{-}}$ (4H7/2−−4H9/2{}^{4}\phantom{\rule{-0.16em}{0ex}}{H}_{7/2}--{}^{4}\phantom{\rule{-0.16em}{0ex}}{H}_{9/2}4H7/2​−−4H9/2​) to be 0.097 75(4) eV.