Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Variational calculations of s-wave positronium hydrogen scattering

Peter Van Reeth, J W Humberston

Published Apr 29, 2003• 18 citations
Publisher

Abstract

A detailed investigation is made of low energy positronium–hydrogen s-wave elastic scattering, using the Kohn variational method, with very flexible scattering wavefunctions including all inter-particle correlations. The singlet and triplet scattering lengths are calculated and found to be a + = 4.311 a 0 and a − = 2.126 a 0 respectively. The phase shifts are believed to be within less than 0.5% of the exact values, and they are in good agreement with the results of previous calculations.

DOI
10.1088/0953-4075/36/10/303

Related papers

Variational Calculations of Positronium Scattering with Hydrogen

Denton Woods

Positronium-hydrogen (Ps-H) scattering is of interest, as it is a fundamental four-body Coulomb problem. We have investigated low-energy Ps-H scattering below the Ps(n=2) excitation threshold using the Kohn variational method and variants of the method with a trial wavefunction that includes highly correlated Hylleraas-type short-range terms. We give an elegant formalism that combines all Kohn-type variational methods into a single form. Along with this, we have also developed a general formalism for Kohn-type matrix elements that allows us to evaluate arbitrary partial waves with a single codebase. Computational strategies we have developed and use in this work will also be discussed.With these methods, we have computed phase shifts for the first six partial waves for both the singlet and triplet states. The 1S and 1P phase shifts are highly accurate results and could potentially be viewed as benchmark results. Resonance positions and widths for the 1S-, 1P-, 1D-, and 1F-waves have been calculated.We present elastic integrated, elastic differential, and momentum transfer cross sections using all six partial waves and note interesting features of each. We use multiple effective range theories, including several that explicitly take into account the long-range van der Waals interaction, to investigate scattering lengths for the 1,3S and 1,3P partial waves and effective ranges for the 1,3S-wave.

arXiv:1508.05681•Dec 1, 2015•2 citations

Positronium-hydrogen scattering using the stochastic variational method

Igor A. Ivanov, J. Mitroy, Kálmán Varga

The stochastic variational method (SVM) is used in conjunction with stabilization ideas in order to compute low-energy phase shifts. The method is tested by applying it to a simple model problem, and to s-wave positron-hydrogen scattering. The SVM is then applied to the calculation of the s- and p-wave phase shifts for Ps-H scattering. The scattering lengths obtained were ${4.34a}_{0}$ for the electronic-spin-singlet state and ${2.22a}_{0}$ for the triplet state. The present scattering lengths are probably accurate to $\ifmmode\pm\else\textpm\fi{}3%$ and are the most accurate that have so far been computed for the Ps-H systems.

Physical Review A•Feb 5, 2002•31 citations

Detailed investigation of low-energy positronium-hydrogen scattering

Denton Woods, Sandra J. Ward, Peter Van Reeth

We investigate the four-body Coulomb process of low-energy elastic positronium-hydrogen (Ps-H) scattering below the Ps($n=2$) excitation threshold using scattering wave functions that include Hylleraas-type correlation terms. Using the complex Kohn variational method, we compute phase shifts through the $^{1,3}H$ wave and obtain highly accurate $^{1,3}S$- and $^{1,3}P$-wave phase shifts. The complex Kohn variational results compare well to a number of other calculations for this system. We present elastic differential, elastic integrated, and momentum transfer cross sections, and for the singlet, resonances through the $^{1}F$ wave. The differential cross section exhibits interesting features, including a change from slightly backward peaked to forward peaked scattering as the energy of the incident positronium increases and rich structure due to multiple resonances near the Ps($n=2$) threshold. We also give a detailed analysis of the scattering lengths and effective ranges using multiple effective range theories.

Physical Review A•Aug 28, 2015•19 citations

Convergent variational calculation of positronium-hydrogen-atom scattering lengths

Sadhan K Adhikari, Puspajit Mandal

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 ($=3.49\pm 0.20$) and triplet ($=2.46\pm 0.10$) states.

arXiv:physics/0103036•Journal of Physics B Atomic Molecular and Optical Physics•Mar 14, 2001•23 citations

Convergent variational calculation of positronium-hydrogen-atom scattering lengths

Adhikari, S K, Mandal, P

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 ($=3.49\\pm 0.20$) and triplet ($=2.46\\pm 0.10$) states.

•Jan 1, 2001•10 citations

Positronium-hydrogen scattering lengths

B A P Page

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).

Journal of Physics B Atomic and Molecular Physics•May 11, 1976•28 citations
A detailed investigation is made of low energy positronium–hydrogen s-wave elastic scattering, using the Kohn variational method, with very flexible scattering wavefunctions including all inter-particle correlations. The singlet and triplet scattering lengths are calculated and found to be a + = 4.311 a 0 and a − = 2.126 a 0 respectively. The phase shifts are believed to be within less than 0.5% of the exact values, and they are in good agreement with the results of previous calculations.
Positronium-hydrogen (Ps-H) scattering is of interest, as it is a fundamental four-body Coulomb problem. We have investigated low-energy Ps-H scattering below the Ps(n=2) excitation threshold using the Kohn variational method and variants of the method with a trial wavefunction that includes highly correlated Hylleraas-type short-range terms. We give an elegant formalism that combines all Kohn-type variational methods into a single form. Along with this, we have also developed a general formalism for Kohn-type matrix elements that allows us to evaluate arbitrary partial waves with a single codebase. Computational strategies we have developed and use in this work will also be discussed.With these methods, we have computed phase shifts for the first six partial waves for both the singlet and triplet states. The 1S and 1P phase shifts are highly accurate results and could potentially be viewed as benchmark results. Resonance positions and widths for the 1S-, 1P-, 1D-, and 1F-waves have been calculated.We present elastic integrated, elastic differential, and momentum transfer cross sections using all six partial waves and note interesting features of each. We use multiple effective range theories, including several that explicitly take into account the long-range van der Waals interaction, to investigate scattering lengths for the 1,3S and 1,3P partial waves and effective ranges for the 1,3S-wave.
The stochastic variational method (SVM) is used in conjunction with stabilization ideas in order to compute low-energy phase shifts. The method is tested by applying it to a simple model problem, and to s-wave positron-hydrogen scattering. The SVM is then applied to the calculation of the s- and p-wave phase shifts for Ps-H scattering. The scattering lengths obtained were 4.34a0{4.34a}_{0}4.34a0​ for the electronic-spin-singlet state and 2.22a0{2.22a}_{0}2.22a0​ for the triplet state. The present scattering lengths are probably accurate to $\ifmmode\pm\else\textpm\fi{}3%$ and are the most accurate that have so far been computed for the Ps-H systems.
We investigate the four-body Coulomb process of low-energy elastic positronium-hydrogen (Ps-H) scattering below the Ps(n=2n=2n=2) excitation threshold using scattering wave functions that include Hylleraas-type correlation terms. Using the complex Kohn variational method, we compute phase shifts through the 1,3H^{1,3}H1,3H wave and obtain highly accurate 1,3S^{1,3}S1,3S- and 1,3P^{1,3}P1,3P-wave phase shifts. The complex Kohn variational results compare well to a number of other calculations for this system. We present elastic differential, elastic integrated, and momentum transfer cross sections, and for the singlet, resonances through the 1F^{1}F1F wave. The differential cross section exhibits interesting features, including a change from slightly backward peaked to forward peaked scattering as the energy of the incident positronium increases and rich structure due to multiple resonances near the Ps(n=2n=2n=2) threshold. We also give a detailed analysis of the scattering lengths and effective ranges using multiple effective range theories.
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.