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Physical Review A

Observation of thresholds and overlapping resonances below the 10 2P1/2 and 2P3/2 thresholds in the photodetachment of Cs −

Anton O. Lindahl, Johan Rohlén, Hannes Hultgren, D. J. Pegg, C. W. Walter, D. Hanstorp

Published Nov 11, 2013• 4 citations
Publisher

Abstract

A collinear beam apparatus has been used to study photodetachment of Cs${}^{\ensuremath{-}}$. Partial cross sections were measured using state-selective detection based on a resonance ionization scheme. Several resonances were observed in the Cs($10{\phantom{\rule{0.16em}{0ex}}}^{2}S$), Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}F$), Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}G$), and Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) final-state channels below the Cs($10{\phantom{\rule{0.16em}{0ex}}}^{2}P$${}_{3/2}$) channel opening. A model was developed to account for the interference between overlapping resonances. This model is essentially a generalization of the Fano [U. Fano, Phys. Rev. 124, 1866 (1961)] and Shore [B. W. Shore, Phys. Rev. 171, 43 (1968)] parametrizations for single resonances. Resonance parameters were extracted by fitting the model to the data sets. The openings of the Cs($10{\phantom{\rule{0.16em}{0ex}}}^{2}S$) and Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}F$) channels, where the polarizabilities of the atomic states are large and positive, showed rapid onsets. In the case of the Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}G$) and Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) channels, on the other hand, the photodetachment cross sections increased slowly with energy. For the Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) channel this is the expected behavior, since it is the result of a large and negative polarizability of the $6{\phantom{\rule{0.16em}{0ex}}}^{2}H$ state. In addition, the excitation of the Cs($6{\phantom{\rule{0.16em}{0ex}}}^{2}H$) state with respect to the Cs ground state was found to be 28 356.3(2) ${\mathrm{cm}}^{\ensuremath{-}1}$, in agreement with a previous experiment.

DOI
10.1103/physreva.88.053410

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A collinear beam apparatus has been used to study photodetachment of Cs\ensuremath−{}^{\ensuremath{-}}\ensuremath−. Partial cross sections were measured using state-selective detection based on a resonance ionization scheme. Several resonances were observed in the Cs(102S10{\phantom{\rule{0.16em}{0ex}}}^{2}S102S), Cs(62F6{\phantom{\rule{0.16em}{0ex}}}^{2}F62F), Cs(62G6{\phantom{\rule{0.16em}{0ex}}}^{2}G62G), and Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) final-state channels below the Cs(10{\phantom{\rule{0.16em}{0ex}}}^{2}P$${}_{3/2}) channel opening. A model was developed to account for the interference between overlapping resonances. This model is essentially a generalization of the Fano [U. Fano, Phys. Rev. 124, 1866 (1961)] and Shore [B. W. Shore, Phys. Rev. 171, 43 (1968)] parametrizations for single resonances. Resonance parameters were extracted by fitting the model to the data sets. The openings of the Cs(102S10{\phantom{\rule{0.16em}{0ex}}}^{2}S102S) and Cs(62F6{\phantom{\rule{0.16em}{0ex}}}^{2}F62F) channels, where the polarizabilities of the atomic states are large and positive, showed rapid onsets. In the case of the Cs(62G6{\phantom{\rule{0.16em}{0ex}}}^{2}G62G) and Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) channels, on the other hand, the photodetachment cross sections increased slowly with energy. For the Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) channel this is the expected behavior, since it is the result of a large and negative polarizability of the 62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H state. In addition, the excitation of the Cs(62H6{\phantom{\rule{0.16em}{0ex}}}^{2}H62H) state with respect to the Cs ground state was found to be 28 356.3(2) cm\ensuremath−1{\mathrm{cm}}^{\ensuremath{-}1}cm\ensuremath−1, in agreement with a previous experiment.
We 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 then integrate the Pauli equation using an effective potential that is adjusted to reproduce Dirac R-matrix scattering phase shifts, and find the (3)P(o)(1) resonance contribution to the photodetachment cross section of Cs-. Our photodetachment cross sections agree with recent experiments by Scheer et al. [Phys. Rev. Lett. 80, 684 (1998)] after tuning the resonance position by 2.4 meV. We also provide angle-differential photodetachment cross sections and the corresponding asymmetry parameter beta near the Cs(6s) threshold.
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.
We have measured the near-threshold cross sections for the photodetachment of ${\mathrm{Li}}^{\ensuremath{-}}$ into the ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(2{p}_{1∕2})$, ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(3p)$, ${e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(3s)$, and ${e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(4s)$ continuum channels and the photodetachment of ${\mathrm{K}}^{\ensuremath{-}}$ into the ${e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{K}(4{p}_{3∕2})$ continuum channel. The data was analyzed using both a top-of-barrier model and a modified effective range theory. Both approaches explicitly take into account the significant polarization potential in the final continuum channels. The study involving both experiment and theory enabled us to investigate the effect of the polarization on near-threshold photodetachment. Furthermore, since photodetachment and electron scattering are related in the half-collision concept, we were able to determine low-energy electron scattering quantities such as phase shifts, elastic cross sections, and sss wave scattering lengths for electron scattering on excited Li and K atoms. The results allowed us to predict a virtual state in the ${e}^{\ensuremath{-}}(ks)\text{\ensuremath{-}}\mathrm{Li}(3p)$ system.
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 ${\mathrm{Cs}}^{\ensuremath{-}}.$ 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.
A Feshbach resonance associated with the 1s3s4s4S{1s3s4s}^{4}S1s3s4s4S state of He${}^{\ensuremath{-}}$ has been observed in the He(1s2s3S){(1s2s}^{3}S)(1s2s3S) + ${e}^{\ensuremath{-}}(\ensuremath{\epsilon}s)$ partial photodetachment cross section. The residual He(1s2s3S){(1s2s}^{3}S)(1s2s3S) atoms were resonantly ionized and the resulting He+{}^{+}+ ions were detected in the presence of a small background. A collinear laser-ion beam apparatus was used to attain both high resolution and sensitivity. We measured a resonance energy Er=2.959255(7){E}_{\mathrm{r}}=2.959255(7)Er​=2.959255(7) eV and a width $\ensuremath{\Gamma}=0.19(3)$ meV, in agreement with a recent calculation.
The photodetachment cross section of has been measured in the photon energy range 2.9-3.3 eV in order to investigate doubly excited states. Measurements were made channel specific by selectively detecting the residual He atoms left in a particular excited state following detachment. Three Feshbach resonances were found in the partial cross section: a resonance below the threshold and two resonances below the threshold. The measured energies of these doubly excited states are 2.959 260(6), 3.072(7) and 3.264 87(5) eV. The corresponding widths are found to be 0.20(2), 50(5) and 0.61(5) meV. The measured energies agree well with recent theoretical predictions for the , and states, respectively, but the widths deviate noticeably from calculations for and states.