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Physical Review A

Expectation values of the e+He(Se3) system

Jim Mitroy

Published Sep 21, 2005• 20 citations
Publisher

Abstract

Close to converged energies and expectation values for ${e}^{+}\mathrm{He}(^{3}S^{e})$ are computed using a ground state wave function consisting of 1500 explicitly correlated Gaussians. The best estimate of the ${e}^{+}\mathrm{He}(^{3}S^{e})$ energy was $\ensuremath{-}2.250\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$, which has a binding energy of $0.000\phantom{\rule{0.2em}{0ex}}595\phantom{\rule{0.2em}{0ex}}08\phantom{\rule{0.3em}{0ex}}\text{hartree}$ against dissociation into $\mathrm{Ps}+{\mathrm{He}}^{+}$. The $2\ensuremath{\gamma}$ annihilation rate for the spin doublet state was $5.713\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The estimated annihilation rate with the core ${\mathrm{He}}^{+}$ electron was $2.506\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$. The derived enhancement factor for annihilation with the ${\mathrm{He}}^{+}(1s)$ core was 2.29, just over 10% smaller than the enhancement factor derived from analyses of annihilation during ${e}^{+}\text{\ensuremath{-}}{\mathrm{He}}^{+}$ scattering. The diffuse nature of the wave function, with well separated ${\mathrm{He}}^{+}$ and Ps subsystems, is demonstarted to be on the threshold of satisfying the formal criteria that define a quantum halo state.

DOI
10.1103/physreva.72.032503

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