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- W2034275812 abstract "The recently developed improved minimum principle for single-channel scattering is applied to a study of the $s$-wave elastic-scattering phase shift ${ensuremath{eta}}_{0}$ of positrons by atomic hydrogen. The method requires the exact solution of the static one-body equation and of the corresponding static Green's function, and also the orthogonalization of the trial function to the hydrogenic ground-state wave function. The radial part of the trial function $Q{ensuremath{Psi}}_{t}$ is chosen to be of the exponential-polynomial form, with linear and nonlinear variational parameters; to simplify the orthogonalization, $Q{ensuremath{Psi}}_{t}$ is expanded in Legendre polynomials whose argument is the cosine of the angle between the coordinate vectors of the electron and the positron. Rigorous lower bounds are obtained on ${ensuremath{eta}}_{0}$ at various energies. The calculation includes the contributions from hydrogenic states with angular momentum $l$ up to $l=5$. For each energy, an estimate is made by extrapolation of the true contribution to ${ensuremath{eta}}_{0}$ from $0ensuremath{le}lensuremath{le}5$, and this estimate is used in turn to estimate the contribution from $l>5$ to ${ensuremath{eta}}_{0}$. The rigorous lower bounds obtained and the estimates are compared with previous estimates of ${ensuremath{eta}}_{0}$." @default.
- W2034275812 created "2016-06-24" @default.
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- W2034275812 date "1965-10-04" @default.
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- W2034275812 title "Minimum-Principle Calculation of the Positron-Hydrogen<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>s</mml:mi></mml:math>-Wave Phase Shift" @default.
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- W2034275812 doi "https://doi.org/10.1103/physrev.140.a18" @default.
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