Optics and Spectroscopy

Resonances in the scattering of ultraslow electrons at alkali atoms

I. I. Fabrikant

Published Aug 1, 1982• 0 citations

Abstract

A theory for the effective radius for scattering at strongly polarized atoms is constructed that permits us to extrapolate the results of calculations for the scattering phases for energies E> or approx. =0.1 eV to a region of lower energies. The proposed theory in contrast with that used earlier does not put a requirement on the smallness of ..cap alpha..E, where ..cap alpha.. is the polarizability of the atom, and, therefore, is valid in a broader region. The theory is used for the parametrization of /sup 3/P resonances in the scattering of electrons at alkali atoms and for finding the binding energies. It is shown that extrapolation of the phases known up to the present of the scattering of electrons at Cs atoms leads to the existence of a bound /sup 3/P state of Cs instead of a /sup 3/P resonance. One possible cause of such a result involves the use of atomic wave functions, which overestimate the polarizability of the Cs atom.

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Optics and Spectroscopy

Resonances in the scattering of ultraslow electrons at alkali atoms

I. I. Fabrikant

Published Aug 1, 1982• 0 citations

OpenAlex

Abstract

Related papers

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Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali-metal atoms, Rb and Cs, for the $nS, n{P}_{\textonehalf{},\phantom{\rule{0.16em}{0ex}}3/2}$, and $n{D}_{3/2,\phantom{\rule{0.16em}{0ex}}5/2}$ states with large principal quantum numbers up to $n=50$ . The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semiempirical core-polarization potential. The obtained results are compared with those from a simpler semiempirical approach and with available experimental data.Calculations of the static electric-dipole scalar and tensor polarizabilities are presented for two alkali-metal atoms, Rb and Cs, for the $nS, n{P}_{\textonehalf{},\phantom{\rule{0.16em}{0ex}}3/2}$, and $n{D}_{3/2,\phantom{\rule{0.16em}{0ex}}5/2}$ states with large principal quantum numbers up to $n=50$. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semiempirical core-polarization potential. The obtained results are compared with those from a simpler semiempirical approach and with available experimental data.

arXiv:1608.04515Physical Review ASep 6, 201631 citations

^{3}

P resonance of ${\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}$. However, recent ab initio bound-state and scattering calculations indicate the existence of the Cs

{(}^{3}

P) bound state rather than the resonance.

{n}^{2}P

) excitation functions have been normalized to the Born theory in the high-energy limit. Comparisons are made with other measurements and calculations. The polarizations and total cross sections for H, Li, Na, K, Rb, and Cs are also compared with each other in reduced units to investigate systematic behavior.

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.

^{3}

P) state is a resonance rather than a bound state.

n{D}_{3/2,\phantom{\rule{0.16em}{0ex}}5/2}

states with large principal quantum numbers up to

n=50

. The calculations are performed within an effective one-electron approximation, based on the Dirac-Fock Hamiltonian with a semiempirical core-polarization potential. The obtained results are compared with those from a simpler semiempirical approach and with available experimental data.