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Physical Review A

Effect of core-valence electron correlation in low-energy electron scattering with Ca atoms

Jianmin Yuan, C. D. Lin

Published Oct 1, 1998• 14 citations
Publisher

Abstract

$R$-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 $d$-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 $s$- and $p$-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.

DOI
10.1103/physreva.58.2824

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Physical Review Letters•Feb 21, 1994•35 citations
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 Ca\ensuremath−{\mathrm{Ca}}^{\ensuremath{-}}Ca\ensuremath− from 72 to 15 meV, i.e., to a value which is much closer to the experiment.
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.
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.
Electrons are scattered elastically by caesium atoms in a crossed-beam experiment. The dependence of the cross section on collision energy and scattering angle has been measured; the collision energies studied are in the range from 0.8 to 20 eV. Resonant structures are observed in the elastic cross section at an energy of 1.49 eV and around the 6 2 P 1/2 threshold at 1.39 eV. It is believed that the 1.49 eV resonance is due to an autoionising F state of Cs - which is consistent with theoretical predictions. The angular distributions of the elastic cross section agree satisfactorily with theory for collision energies below 2 eV. At higher energies larger deviations from theory are observed.
The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at 2.22.22.2 eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the e+{e}^{+}e+-Cd system. The sss-wave binding energy is estimated to be $126\ifmmode\pm\else\textpm\fi{}42$ meV, with a scattering length of ${A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$a0{a}_{0}a0​, while the threshold annihilation parameter, Zeff{Z}_{\mathrm{eff}}Zeff​, was $93.9\ifmmode\pm\else\textpm\fi{}26.5$. The ppp-wave phase shift exhibits a weak shape resonance that results in a peak Zeff{Z}_{\mathrm{eff}}Zeff​ of $91\ifmmode\pm\else\textpm\fi{}17$ at a collision energy of about $490\ifmmode\pm\else\textpm\fi{}50$ meV.
Relative yields of Ca+{\mathrm{Ca}}^{+}Ca+ and ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ ions from thermal-energy collisions between highly excited Ca∗{\mathrm{Ca}}^{\mathrm{*}}Ca∗ 4snd 1^{1}1D Rydberg atoms and Ca ground-state atoms are measured as a function of n. The collisions take place within an effusive Ca atomic beam. The cross section for a collision resulting in a bound ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ and a ground-state Ca+{\mathrm{Ca}}^{+}Ca+ is expected to be large when the binding energy of the excited Rydberg state nearly matches the electron affinity of Ca. We observe a large increase in positive and negative ions for n=25 only. This result strongly suggests that the binding energy of ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ is 24\ifmmode\pm\else\textpm\fi{}1.4 meV.