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Journal of Physics B Atomic and Molecular Physics

Positronium-hydrogen scattering lengths

B A P Page

Published May 11, 1976• 28 citations
Publisher

Abstract

A calculation of the zero-energy positronium-hydrogen scattering lengths using the Kohn variational method is presented. Including, in the trial wavefunction up to 35 terms to describe short range effects, the scattering lengths are found to be a + =5.844a 0 (the space symmetric case) and a - =2.319a 0 (the space antisymmetric case).
DOI
10.1088/0022-3700/9/7/011

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We present a variational basis-set calculational scheme for elastic scattering of positronium atom by helium atom in S wave and apply it to the calculation of the scattering length. Highly correlated trial functions with appropriate symmetry are used in this calculation. We report numerical result for the scattering length in atomic unit: $(1.0\ifmmode\pm\else\textpm\fi{}{0.1)a}_{0}.$ This corresponds to a zero-energy elastic cross section of $(4.0\ifmmode\pm\else\textpm\fi{}0.8)\ensuremath{\pi}{a}_{0}^{2}.$
A trial wavefunction, Psi 1 , which contains both linear and nonlinear parameters is constructed using an approximate target wavefunction, Psi 1 is related to a quantity, a v , which becomes the Kohn scattering length if the target wavefunction is exact, through an integral expression corresponding to a slight modification of the usual Kohn variational method. It is conjectured that if the values of a v display a local minimum when all the nonlinear parameters of Psi 1 are varied, then this local minimum value of a v is an upper bound on the exact scattering length. Calculations on the zero-energy positron-helium scattering system using Hylleraas-type approximations to the helium ground-state wavefunction are analysed using this criterion. The use of either a six-parameter or a ten-parameter Hylleraas-type approximation to the helium ground-state wavefunction can give good results in scattering calculations for the positron-helium system at zero energy.
We present a convergent variational basis-set calculational scheme for elastic scattering of positronium atom by hydrogen atom in S wave. Highly correlated trial functions with appropriate symmetry are needed for achieving convergence. We report convergent results for scattering lengths in atomic units for both singlet (=3.49pm0.20=3.49\\pm 0.20=3.49pm0.20) and triplet (=2.46pm0.10=2.46\\pm 0.10=2.46pm0.10) states.