Physica Scripta

Extrapolated model potential for low-energy scattering of electrons from inert gas atoms, and Be, Mg, Zn, Cd, Hg

S. H. Patil

Published Nov 1, 1996• 2 citations

Abstract

We have developed a model, l -dependent potential to describe the interaction of an electron with inert gas atoms, and Be, Mg, Zn, Cd, Hg, and their isoelectronic sequences. This potential is adjusted so as to produce bound states with experimental binding energies in isoelectronic sequences of Li I, Na I, K I, Rb I, Cs I and B I, Al I, Ga I, In I, Tl I, and extrapolated to get a potential for the interaction of an electron with inert gas atoms, and with Be, Mg, Zn, Cd, Hg. It provides reliable phase shifts and cross sections for e-inert gas atom, e-Be, e-Mg, e-Zn, e-Cd, e-Hg scattering. Particularly interesting are the signs of the scattering lengths, the changes in the signs of the s-wave phase shifts, and p-wave shape resonances at low energies.

DOI: 10.1088/0031-8949/54/5/007

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Physica Scripta

Extrapolated model potential for low-energy scattering of electrons from inert gas atoms, and Be, Mg, Zn, Cd, Hg

S. H. Patil

Published Nov 1, 1996• 2 citations

Publisher

Abstract

DOI: 10.1088/0031-8949/54/5/007

Related papers

A simple potential for low-energy s-wave scattering of electrons from closed-shell atoms

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Physical Review AApr 1, 199425 citations

The configuration-interaction method is applied to the study of positronic zinc

{(e}^{+}\mathrm{Zn})

and positronic cadmium

{(e}^{+}\mathrm{Cd}).

The estimated binding energies and annihilation rates were 0.003 73 hartree and $0.42\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for

{e}^{+}\mathrm{Zn}

and 0.006 10 hartree and $0.56\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}$ for

{e}^{+}\mathrm{Cd}.

The low-energy elastic cross section and

{Z}_{\mathrm{eff}}

were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive

{(14.5a}_{0}

for Zn and

{11.6a}_{0}

for Cd) the differential cross sections are larger at backward angles than at forward angles just above threshold. The possibilities of measuring differential cross sections to confirm positron binding to these atoms is discussed.

s

electrons and to the closed electronic shells of the two atoms. The two-

s

-electron interaction is generated ad hoc phenomenologically from the known hydrogen-hydrogen interatomic potential and the closed-shell interaction from interatomic potentials of two inert atoms corresponding to the cores. The potentials so obtained are in agreement with those constructed from band spectra.

s

-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy

k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.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

s

-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.

{\mathit{p}}_{1/2}

and 6

{\mathit{p}}_{3/2}

states of ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, and 36 meV for the 6

{\mathit{p}}_{1/2}

state of the ${\mathrm{Yb}}^{\mathrm{\ensuremath{-}}}$. A number of prominent p and d resonances are revealed in the scattering phase-shift calculations. These p or d resonances lead to a phenomenon of 100% polarization of the scattered electron beam at appropriate electron energy and scattering angle. A criterion is proposed to measure the strength of the nonlocal correlation potential and to evaluate its ability to create a bound state: FG(r',r)\ensuremath{\Sigma}(r,r')dr dr'>1 is the necessary condition for the formation of a bound state. Here \ensuremath{\Sigma} is the correlation potential and G is the electron Green's function at zero energy.