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Journal of Physics B Atomic Molecular and Optical Physics

Core-valence correlation effects on the ground-state electron affinities of strontium and barium

Dage Sundholm

Published Jun 28, 1995• 14 citations
Publisher

Abstract

The electron affinities of the ground states of Sr and Ba have been calculated using a finite-element multiconfiguration Hartree-Fock method. The valence correlation value for the electron affinity of Sr is 135 meV. Core-valence correlation reduces the electron affinity by 121 meV. By adding relativistic and core-core correlation contributions, the final binding energies of 16 and -6 meV are obtained for Sr -(2) P (1 2)/ and Sr -(2) P (3 2)/, respectively. For Ba, the valence limit is 279 meV, and the core-valence correlation correction is -144 meV. The final binding energies of 113 and 56 meV are obtained for Ba -(2) P (1 2)/ and Ba -(2) P (3 2)/ by adding relativistic and core-core correlation corrections to the core-valence correlation value.

DOI
10.1088/0953-4075/28/12/002

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Physical Review Letters•Jul 17, 1995•25 citations
The electron affinities of the ground states of Sr and Ba have been calculated using a finite-element multiconfiguration Hartree-Fock method. The valence correlation value for the electron affinity of Sr is 135 meV. Core-valence correlation reduces the electron affinity by 121 meV. By adding relativistic and core-core correlation contributions, the final binding energies of 16 and -6 meV are obtained for Sr -(2) P (1 2)/ and Sr -(2) P (3 2)/, respectively. For Ba, the valence limit is 279 meV, and the core-valence correlation correction is -144 meV. The final binding energies of 113 and 56 meV are obtained for Ba -(2) P (1 2)/ and Ba -(2) P (3 2)/ by adding relativistic and core-core correlation corrections to the core-valence correlation value.
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.
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.
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.
Conditional probability distributions for the valence electrons of alkaline-earth atoms in their ground and valence excited states are constructed using large-basis Sturmlan configuration-interaction wave functions for two electrons in frozen, effective-core potentials. The distributions indicate that the ground states of Be, Mg, Ca, Sr, and Ba, and the valence excited states of Be, are much more like linear triatomic molecules, akin to doubly excited He, than like independent-particle systems such as the ground states of He and He-like ions.
We report a theoretical calculation of the relativistic corrections to the binding energy of positronic alkali-metal atoms. The ground state for the positronic alkali-metal atom is a loosely bound state with the structure of an alkali-metal ion surrounded by a positronium cloud. The correlation between the valence electron and positron in the field of a residual core ion is taken into account using a three-body model. Relativistic corrections to the binding energy for positronic alkali-metal atoms are evaluated based on the Breit-Pauli perturbation theory up to the second order of the fine structure constant. The relativistic corrections caused by the interaction between the valence electron and core ion was evaluated from the decomposed expectation values of the perturbation Hamiltonian. We found that the importance of relativistic corrections to the binding energy, namely the ratio of the net relativistic correction in the total binding energy, is remarkably enhanced in the loosely bound states of positronic alkali-metal atoms, where the charge of the valence electron is screened by the positron as positronium in the outermost region, while the electron is released from the positron near the nucleus. The results imply that positronic atoms with a dominant positronium can serve as an apt testing ground for relativistic quantum mechanics.
We have observed a threshold in the electron photodetachment cross section of ${^{88}S\mathrm{r}}^{\ensuremath{-}}$ ions at a photon energy $h\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.820\mathrm{eV}$ and assign it to a ppp-wave transition from the 5s25p2P{5s}^{2}5p^{2}P5s25p2P ground state in ${\mathrm{Sr}}^{\ensuremath{-}}$ to the 5s5p3P5s5p^{3}P5s5p3P state in neutral Sr. The measurement was made with a new technique combining the tunable laser photodetachment threshold method with accelerator mass spectrometry. We determine for the first time the electron affinity of Sr to be $48\ifmmode\pm\else\textpm\fi{}6\mathrm{meV}$, much smaller than predicted in recent calculations. The 2P1/2^{2}P_{1/2}2P1/2​- 2P3/2^{2}P_{3/2}2P3/2​ fine splitting of the ${\mathrm{Sr}}^{\ensuremath{-}}$ ground state is estimated to be $26\ifmmode\pm\else\textpm\fi{}8\mathrm{meV}$.