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Physical Review A

Modification of the method of polarized orbitals for electron-alkali-metal scattering: Application to e -Li

A. K. Bhatia, Aaron Temkin, A. Silver, E. C. Sullivan

Published Nov 1, 1978• 30 citations
Publisher

Abstract

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 $e$-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 $^{1}S$ scattering length of $8.69{a}_{0}$. (The $^{3}S$ 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 $^{3}S$ 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.

DOI
10.1103/physreva.18.1935

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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 Li\ensuremath−{\mathrm{Li}}^{\ensuremath{-}}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−9.22a0\ensuremath{-}9.22{a}_{0}\ensuremath−9.22a0​.) 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.
Polarization phenomena in collisions between one-electron (alkali-like) atoms are calculated with density-matrix techniques. The kinetic energies for which this treatment is valid are limited from above by the use of the Born-Oppenheimer approximation, and from below by the assumed degeneracy of the hyperfine states. The basic mechanism for polarization changes is the electron-exchange effect, as suggested by Purcell and Field and by Wittke and Dicke. The special situation of unpolarized targets is treated in some detail. In this case, there are two numbers which characterize the scattering through any angle: the absolute values of certain direct and exchange scattering amplitudes, Fd{F}_{d}Fd​ and Fx{F}_{x}Fx​. All cross sections must be expressible in terms of ∣Fd∣|{F}_{d}|∣Fd​∣ and ∣Fx∣|{F}_{x}|∣Fx​∣, and this is explicitly carried out in two cases of special interest. One refers to the case in which only the electron-spin polarization is measured, and the other to measurements of the polarization of the hyperfine states of the scattered atom. Effects of the identity of the atoms are also studied in detail.
Collisional broadening of nS Rydberg states by K, Rb, and Cs atoms is studied using the adiabatic approach for the $^{3}\mathrm{\ensuremath{\Sigma}}$ quasimolecular state and impulse approximation for all other contributions to the collisional width. The calculations are based on the use of the low-energy phase shifts for electron scattering by alkali metals obtained from ab initio close-coupling calculations and their extrapolation according to the modified effective range theory. We obtain a good agreement for the magnitude of the width with experimental data and satisfactory agreement for the oscillatory part of the width as a function of the principal quantum number. We find that the theory overestimates the amplitude of the oscillations. In the case of Cs as a perturber, the agreement with experimental data is good if we assume the existence of the low-energy 3^{3}3P resonance of ${\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}$. However, recent ab initio bound-state and scattering calculations indicate the existence of the Cs (3{(}^{3}(3P) bound state rather than the resonance.
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.
Projectile-elastic, target-elastic, and full close-coupling approximation models have been employed to investigate scattering of ortho-positronium off Li and Na atoms at low energies. Nine different basis sets for each system have been used to find the relative importance of atomic (target and projectile) states on the elastic scattering parameters and the convergence of the predicted results with added eigen- and pseudostates. The sss-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy k=0.5a.u.k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}k=0.5a.u. and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting sss-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.
The confined variational method is employed to study low-energy electron collisions with a lithium atom, for energies below the 2p2p2p excitation threshold. The accuracy of the phase shifts has been markedly improved in our calculations. From these calculations, we obtain an electron affinity of 4985.6124 ${\mathrm{cm}}^{\ensuremath{-}1}$, in excellent agreement with experiment, validating the accuracy of the approach. A least-squares fit of the phase shifts to effective-range theory yields an SSS-wave scattering length of A=3.02a0A=3.02{a}_{0}A=3.02a0​, where a0{a}_{0}a0​ is the Bohr radius. These results provide a stringent benchmark for future theoretical and experimental investigations. In this study, the sum of all electron spins is considered to be zero.