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Physical Review A

Configuration-interaction calculations of positron binding to zinc and cadmium

M. W. J. Bromley, Jim Mitroy

Published Jun 13, 2002• 30 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.65.062506

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The configuration-interaction method is applied to the study of positronic zinc (e+Zn){(e}^{+}\mathrm{Zn})(e+Zn) and positronic cadmium (e+Cd).{(e}^{+}\mathrm{Cd}).(e+Cd). The estimated binding energies and annihilation rates were 0.003 73 hartree and 0.42\ifmmode×\else\texttimes\fi109sec\ensuremath−10.42\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}0.42\ifmmode×\else\texttimes\fi109sec\ensuremath−1 for e+Zn{e}^{+}\mathrm{Zn}e+Zn and 0.006 10 hartree and 0.56\ifmmode×\else\texttimes\fi109sec\ensuremath−10.56\ifmmode\times\else\texttimes\fi{}{10}^{9} {\mathrm{sec}}^{\ensuremath{-}1}0.56\ifmmode×\else\texttimes\fi109sec\ensuremath−1 for e+Cd.{e}^{+}\mathrm{Cd}.e+Cd. The low-energy elastic cross section and Zeff{Z}_{\mathrm{eff}}Zeff​ were estimated from a model potential that was tuned to the binding energies and annihilation rates. Since the scattering lengths were positive (14.5a0{(14.5a}_{0}(14.5a0​ for Zn and 11.6a0{11.6a}_{0}11.6a0​ 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.
The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at 2.22.22.2 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+{e}^{+}e+-Cd system. The sss-wave binding energy is estimated to be $126\ifmmode\pm\else\textpm\fi{}42$ meV, with a scattering length of ${A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$a0{a}_{0}a0​, while the threshold annihilation parameter, Zeff{Z}_{\mathrm{eff}}Zeff​, was $93.9\ifmmode\pm\else\textpm\fi{}26.5$. The ppp-wave phase shift exhibits a weak shape resonance that results in a peak Zeff{Z}_{\mathrm{eff}}Zeff​ of $91\ifmmode\pm\else\textpm\fi{}17$ at a collision energy of about $490\ifmmode\pm\else\textpm\fi{}50$ meV.
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.
A two-parameter semiempirical theory of positron scattering and annihilation is developed and used to investigate the behavior of positrons interacting with the rare gases and metal vapors. The two-parameter theory is able to do a reasonable job of reproducing existing cross section and annihilation data for the rare gases. A model-potential calculation that correctly predicts the behavior of the phase shifts will also predict the energy dependence of Zeff(k){Z}_{\mathrm{eff}}(k)Zeff​(k) even if the magnitude is incorrect. Analysis of the Zeff{Z}_{\mathrm{eff}}Zeff​ 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 Zeff{Z}_{\mathrm{eff}}Zeff​ of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of Zeff(k){Z}_{\mathrm{eff}}(k)Zeff​(k) to the complex scattering length are presented.
The scattering of orthopositronium from He, Ne, Ar, Li+,{\mathrm{Li}}^{+},Li+, Na+,{\mathrm{Na}}^{+},Na+, and K+{\mathrm{K}}^{+}K+ is investigated with the fixed-core stochastic variational method. The scattering length for $\mathrm{Ps}\ensuremath{-}\mathrm{He}$ scattering was 1.57a0,{1.57a}_{0},1.57a0​, 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 1.55a0{1.55a}_{0}1.55a0​ and 1.79a0,{1.79a}_{0},1.79a0​, 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 Li+,{\mathrm{Li}}^{+},Li+, Na+,{\mathrm{Na}}^{+},Na+, and K+{\mathrm{K}}^{+}K+ were 12.9a0,{12.9a}_{0},12.9a0​, 28.5a0,{28.5a}_{0},28.5a0​, 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 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ has also been computed as part of the analysis. The present values of 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ 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.
Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the 1s1s1s electron in H, He+{\mathrm{He}}^{+}He+, He, Li2+{\mathrm{Li}}^{2+}Li2+, and Li+{\mathrm{Li}}^{+}Li+. The enhancement factor for a free positron annihilating with He+{\mathrm{He}}^{+}He+ and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of 1.47a01.47{a}_{0}1.47a0​ for Ps-He scattering. Further, enhancement factors for e+{e}^{+}e+-Ne and e+{e}^{+}e+-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of 1.46a01.46{a}_{0}1.46a0​ for Ps-Ne scattering and 1.75a01.75{a}_{0}1.75a0​ for Ps-Ar scattering.
The very large annihilation rates observed at room temperature in positron collisions with certain molecules have instigated the development of several models of positron annihilation based on the role of virtual processes, Feshbach resonances and bound states. One of the outcomes of these models has been the interest they have generated in investigations of the energy dependence of the annihilation cross-section in the vicinity of inelastic thresholds. The aim of this article is to provide a review of these recent studies and to highlight outstanding questions.