World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering

Interaction Of Low-Energy Positrons With Mg Atoms: Elastic Scattering, Bound States, And Annihilation

Mahasen. M. Abdel-Mageed, Hala Saad Zaghloul

Published Oct 1, 2015• 0 citations

Publisher

Abstract

Annihilations, phase shifts, scattering lengths and elastic cross sections of low energy positrons scattering from magnesium atoms were studied using the least-squares variational method (LSVM). The possibility of positron binding to the magnesium atoms is investigated. A trial wave function is suggested to represent e+-Mg elastic scattering and scattering parameters were derived to estimate the binding energy and annihilation rates. The trial function is taken to depend on several adjustable parameters, and is improved iteratively by increasing the number of terms. The present results have the same behavior as reported semi-empirical, theoretical and experimental results. Especially, the estimated positive scattering length supports the possibility of positronmagnesium bound state system that was confirmed in previous experimental and theoretical work.

DOI: 10.5281/zenodo.1109847

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World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering

Interaction Of Low-Energy Positrons With Mg Atoms: Elastic Scattering, Bound States, And Annihilation

Mahasen. M. Abdel-Mageed, Hala Saad Zaghloul

Published Oct 1, 2015• 0 citations

Publisher

Abstract

DOI: 10.5281/zenodo.1109847

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The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at

2.2

eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the

{e}^{+}

-Cd system. The

s

-wave binding energy is estimated to be $126\ifmmode\pm\else\textpm\fi{}42$ meV, with a scattering length of ${A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$

{a}_{0}

, while the threshold annihilation parameter,

{Z}_{\mathrm{eff}}

, was $93.9\ifmmode\pm\else\textpm\fi{}26.5$. The

p

-wave phase shift exhibits a weak shape resonance that results in a peak

{Z}_{\mathrm{eff}}

of $91\ifmmode\pm\else\textpm\fi{}17$ at a collision energy of about $490\ifmmode\pm\else\textpm\fi{}50$ meV.

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.

{Z}_{\mathrm{eff}}(k)

even if the magnitude is incorrect. Analysis of the

{Z}_{\mathrm{eff}}

versus temperature data of Kurz et al. [Phys. Rev. Lett. 77, 2929 (1996)] suggests scattering lengths of $\ensuremath{-}5.6\ifmmode\pm\else\textpm\fi{}{1.0a}_{0},$ $\ensuremath{-}10.3\ifmmode\pm\else\textpm\fi{}{2.0a}_{0},$ and $\ensuremath{-}56\ifmmode\pm\else\textpm\fi{}{15a}_{0}$ for Ar, Kr, and Xe, respectively. Existing bound-state calculations can be used to fix the values of the semi-empirical parameters for a number of metal vapors, resulting in predicted

{Z}_{\mathrm{eff}}

of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of

{Z}_{\mathrm{eff}}(k)

to the complex scattering length are presented.

S

-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result,

a=7.28{a}_{0}

(

{a}_{0}

is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.

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.

The scattering of orthopositronium from He, Ne, Ar,

{\mathrm{Li}}^{+},

{\mathrm{Na}}^{+},

and

{\mathrm{K}}^{+}

is investigated with the fixed-core stochastic variational method. The scattering length for $\mathrm{Ps}\ensuremath{-}\mathrm{He}$ scattering was

{1.57a}_{0},

a value consistent with the threshold cross sections derived from three positron lifetime experiments. The scattering lengths for the $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{N}\mathrm{e}$ and $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{A}\mathrm{r}$ systems were

{1.55a}_{0}

and

{1.79a}_{0},

respectively. That there was only a 15% variation among the scattering lengths is compatible with the experiment of Coleman et al. [J. Phys. B 27, 981 (1994)], who found the low-energy cross sections for He, Ne, and Ar to be about the same size. The scattering lengths for Ps scattering from

{\mathrm{Li}}^{+},

{\mathrm{Na}}^{+},

and

{\mathrm{K}}^{+}

were

{12.9a}_{0},

{28.5a}_{0},

and $\ensuremath{-}{1.9a}_{0}.$ The relatively small magnitude of the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ scattering length strongly supports previous suggestions that the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ system does not support a bound state. The annihilation parameter

{}^{1}{Z}_{\mathrm{eff}}

has also been computed as part of the analysis. The present values of

{}^{1}{Z}_{\mathrm{eff}}

are about 2.5--3 times smaller than the accepted experimental values since short-range electron-positron correlations were not taken into consideration when the annihilation matrix element was evaluated.