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Physical Review A

Effect of polarization on photodetachment thresholds

J. Sandström, G. Haeffler, Igor Yu. Kiyan, Uldis Berzinsh, D. Hanstorp, D. J. Pegg, J. C. Hunnell, Sandra J. Ward

Published Nov 16, 2004• 12 citations
Publisher

Abstract

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 $s$ 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.

DOI
10.1103/physreva.70.052707

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We have measured the near-threshold cross sections for the photodetachment of Li\ensuremath−{\mathrm{Li}}^{\ensuremath{-}}Li\ensuremath− into the e\ensuremath−(ks,d)\ensuremath-Li(2p1∕2){e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(2{p}_{1∕2})e\ensuremath−(ks,d)\ensuremath-Li(2p1∕2​), e\ensuremath−(ks,d)\ensuremath-Li(3p){e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{Li}(3p)e\ensuremath−(ks,d)\ensuremath-Li(3p), e\ensuremath−(kp)\ensuremath-Li(3s){e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(3s)e\ensuremath−(kp)\ensuremath-Li(3s), and e\ensuremath−(kp)\ensuremath-Li(4s){e}^{\ensuremath{-}}(kp)\text{\ensuremath{-}}\mathrm{Li}(4s)e\ensuremath−(kp)\ensuremath-Li(4s) continuum channels and the photodetachment of K\ensuremath−{\mathrm{K}}^{\ensuremath{-}}K\ensuremath− into the e\ensuremath−(ks,d)\ensuremath-K(4p3∕2){e}^{\ensuremath{-}}(ks,d)\text{\ensuremath{-}}\mathrm{K}(4{p}_{3∕2})e\ensuremath−(ks,d)\ensuremath-K(4p3∕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)\ensuremath-Li(3p){e}^{\ensuremath{-}}(ks)\text{\ensuremath{-}}\mathrm{Li}(3p)e\ensuremath−(ks)\ensuremath-Li(3p) system.
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.
Photodetachment from negative ions in a static electric field has been studied using ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ and ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$. These experiments were done with greater precision than previous studies and allow a quantitative comparison of data with theory. A 10-keV ion beam was sent through a region with fields of up to 1.5 kV/cm applied parallel to the beam velocity. A pulsed dye-laser beam, perpendicular to the ion beam, photoneutralized the ions. The relative cross sections were measured by detecting the resulting fast neutral atoms. Detachment below threshold and oscillations on the cross section above threshold were observed near the ${\mathrm{S}}^{\mathrm{\ensuremath{-}}}$ threshold at 16 269.5 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ and near the ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$ threshold at 29 138.3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The phase of the oscillations in the data is in good agreement with predictions for s-wave photodetachment in a static electric field, but the amplitude of the oscillations is found to be slightly reduced.
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(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(102P10{\phantom{\rule{0.16em}{0ex}}}^{2}P102P3/2{}_{3/2}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) ${\mathrm{cm}}^{\ensuremath{-}1}$, in agreement with a previous experiment.
We report on the first experimental observation of a new threshold behavior observed in the 5(2)G partial channel in photodetachment of K(-). It arises from the repulsive polarization interaction between the detached electron and the residual K(5(2)G) atom, which has a large negative dipole polarizability. In order to account for the observation in the K(5(2)G) channel, we have developed a semiclassical model that predicts an exponential energy dependence for the cross section. The measurements were made with collinear laser-ion beams and a resonance ionization detection scheme.
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 method of polarized orbitals is modified to treat low-energy scattering of electrons from highly polarizable systems, specifically alkali-metal atoms. The modification is carried out in the particular context of the eee-Li system, but the procedure is general; it consists of modifying the polarized orbital, so that when used in the otherwise orthodox form of the method, it gives (i) the correct electron affinity of the negative ion (in this case ${\mathrm{Li}}^{\ensuremath{-}}$), (ii) the proper (i.e., Levinson-Swan) number of nodes of the associated zero-energy scattering orbital, and (iii) the correct polarizability. A procedure is devised whereby the scattering length can be calculated from the (known) electron affinity without solving the bound-state equation. Using this procedure we adduce a 1S^{1}S1S scattering length of 8.69a08.69{a}_{0}8.69a0​. (The 3S^{3}S3S scattering length is $\ensuremath{-}9.22{a}_{0}$.) The above modifications can also be carried out in the (lesser) exchange adiabatic approximation. However, they lead to qualitatively incorrect 3S^{3}S3S phase shifts. The modified polarized-orbital phase shifts are qualitatively similar to close-coupling and elaborate variational calculations. Quantitative differences from the latter calculations, however, remain; they are manifested most noticeably in the very-low-energy total and differential spin-flip cross sections.