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Physical Review A

Low-lying 3Po and 3Se states of Rb−,Cs− , and Fr−

Cristian Bahrim, Uwe Thumm

Published Jan 18, 2000• 72 citations
Publisher

Abstract

Our Dirac R-matrix calculations suggest that none of the heavy alkali-metal negative ions, Rb, Cs, and Fr, has an excited bound state. Their lowest excited state appears to be a multiplet of ${}^{3}{P}_{J}^{o}$-shape resonances, the $J=1$ component of which was recently observed in photodetachment experiments on ${\mathrm{Cs}}^{\ensuremath{-}}.$ We analyze these ${}^{3}{P}_{J}^{o}$ and the ${}^{3}{S}^{e}$ excited negative ion states in partial and converged total scattering cross sections for slow electrons with incident kinetic energies below 120 meV. Our results are in excellent agreement with available experimental data. We also propose a new value for the electron affinity of Fr, provide the scattering length for electronic collisions with Rb, Cs, and Fr, and discuss the nuclear charge dependence of relativistic effects in the resonance profiles.

DOI
10.1103/physreva.61.022722

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Our Dirac R-matrix calculations suggest that none of the heavy alkali-metal negative ions, Rb, Cs, and Fr, has an excited bound state. Their lowest excited state appears to be a multiplet of 3PJo{}^{3}{P}_{J}^{o}3PJo​-shape resonances, the J=1J=1J=1 component of which was recently observed in photodetachment experiments on Cs\ensuremath−.{\mathrm{Cs}}^{\ensuremath{-}}.Cs\ensuremath−. We analyze these 3PJo{}^{3}{P}_{J}^{o}3PJo​ and the 3Se{}^{3}{S}^{e}3Se excited negative ion states in partial and converged total scattering cross sections for slow electrons with incident kinetic energies below 120 meV. Our results are in excellent agreement with available experimental data. We also propose a new value for the electron affinity of Fr, provide the scattering length for electronic collisions with Rb, Cs, and Fr, and discuss the nuclear charge dependence of relativistic effects in the resonance profiles.
We analyze negative-ion resonances in elastic and inelastic total scattering cross sections for slow electron collisions with the heavy-alkali-metal atoms Rb, Cs, and Fr. Our calculations are based on the Dirac RRR-matrix method [Thumm and Norcross, Phys. Rev. A 45, 6349 (1992)]. For incident electrons of up to 2.8 eV kinetic energy, we compare a 3Po{}^{3}{P}^{o}3Po shape resonance and 3Pe,{}^{3}{P}^{e},3Pe, 1P1o,{}^{1}{P}_{1}^{o},1P1o​, and 1D2o{}^{1}{D}_{2}^{o}1D2o​ Feshbach resonances, located below the first excitation threshold of the atomic target in the low-lying spectra of the ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ negative ions, with available experimental data and other calculations. We provide the resonance parameters, partial and converged total elastic and inelastic scattering cross sections, and discuss the relative importance of relativistic effects for the three heavy-alkali-metal targets.
Based on the relativistic Dirac R-matrix method, we calculate angle-dependent and momentum-transfer cross sections for electron scattering by Rb, Cs, and Fr atoms at impact energies below 3 eV. Our results for momentum transfer for ${e}^{\ensuremath{-}}+\mathrm{Rb}$ and Cs collisions are compared with available data from swarm experiments. We find clear evidence for a ${\mathrm{Cs}}^{\ensuremath{-}}{(}^{3}{F}^{o})$ shape resonance at 1.528 eV, in excellent agreement with angle-dependent electron-scattering measurements. We analyze and compare the 3Fo{}^{3}{F}^{o}3Fo shape resonance in ${e}^{\ensuremath{-}}+\mathrm{Rb},$ Cs, and Fr elastic collisions.
We calculate near-threshold photodetachment cross sections for ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ using the Pauli equation method with a model potential describing the effective electron-atom interaction. Parameters of the model potential are fitted to reproduce ab initio scattering phase shifts obtained from Dirac R-matrix calculations. Special care is taken to formulate the boundary conditions near the atomic nucleus for solving the Pauli equation, based on the analytic solution of the Dirac equation for a Coulomb potential. We find a 3P1o{}^{3}{P}_{1}^{o}3P1o​ resonance contribution to the photodetachment cross section of ${\mathrm{Rb}}^{\ensuremath{-}},$ ${\mathrm{Cs}}^{\ensuremath{-}},$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ ions. Our calculated total photodetachment cross sections for Cs agree with experiments after tuning the resonance position by 2.4 meV. For ${\mathrm{Rb}}^{\ensuremath{-}}$ and ${\mathrm{Fr}}^{\ensuremath{-}}$ the resonance contribution is much smaller than for Cs. We therefore also provide angle-differential cross sections and asymmetry parameters which are much more sensitive to the resonant contribution than total cross sections.
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.
Electron-transmission spectroscopy is used to observe structure in the electron-scattering cross section associated with the formation of temporary negative ions and channel-opening effects. A strong ``family'' resemblance is apparent among the resonances of the alkali metals. From published calculations and angular scattering studies, the lower-lying features are known with some confidence. Based on these, plausible assignments for some of the higher-lying resonances are put forth. We propose that the absence of resonances near the Cs 5 2^{2}2D and possibly the Na 4 2^{2}2P and 5 2^{2}2P thresholds is associated with the negative polarizabilities of these excited states.