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arXiv:physics/0103095 · Physical Review A

Variational calculation of positronium-helium-atom scattering length

Sadhan K. Adhikari

Published Jul 2, 2001• 11 citations
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Abstract

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 $(4.0\ifmmode\pm\else\textpm\fi{}0.8)\ensuremath{\pi}{a}_{0}^{2}.$

DOI
10.1103/physreva.64.022702

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Physical Review A•May 5, 2021•5 citations
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±\else\textpm\fi0.1)a0.(1.0\ifmmode\pm\else\textpm\fi{}{0.1)a}_{0}.(1.0\ifmmode±\else\textpm\fi0.1)a0​. This corresponds to a zero-energy elastic cross section of (4.0\ifmmode±\else\textpm\fi0.8)\ensuremathπa02.(4.0\ifmmode\pm\else\textpm\fi{}0.8)\ensuremath{\pi}{a}_{0}^{2}.(4.0\ifmmode±\else\textpm\fi0.8)\ensuremathπa02​.
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 (=3.49±0.20=3.49\pm 0.20=3.49±0.20) and triplet (=2.46±0.10=2.46\pm 0.10=2.46±0.10) states.
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.
We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the SSS-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The SSS-wave total and ortho-para conversion cross sections are calculated by making use of both 1S^{1}S1S and 3S^{3}S3S results. In the 3S^{3}S3S case, we see no indication of any resonances below the excitation threshold at 5.1 eV.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.