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

Physical Review A

Scattering of near-zero-energy electrons and positrons by H2

Jun-Yi Zhang, Y.-J. Yang, Ying Qian, Zhiwei Yan, Udo Schwingenschlögl

Published Apr 15, 2014• 6 citations
Publisher

Abstract

The parameters for $S$-wave elastic scattering of near-zero-energy electrons and positrons by ${H}_{2}$ molecules are calculated using the stabilization method with explicitly correlated Gaussians. The confined variational method is applied to optimize the Gaussians to describe the short-range interaction of incident ${e}^{\ifmmode\pm\else\textpm\fi{}}$ with ${H}_{2}$ in the fixed-nuclei approximation. For ${e}^{+}$-${H}_{2}$ scattering the scattering length of previous work [Phys. Rev. Lett. 103, 223202 (2009)] is substantially improved. More importantly, for ${e}^{\ensuremath{-}}$-${H}_{2}$ scattering, from first principles, the scattering length is computed as a function of the internuclear distance. In the case that the two nuclei are at the equilibrium distance the results are in a good agreement with values derived from fitting experimental total and diffusion cross sections to the modified effective range theory.

DOI
10.1103/physreva.89.042703

Related papers

Stochastic variational calculation of zero-energy positron scattering from H, He, and H2

J. Y. Zhang, J. Mitroy

The confined variational method is used to generate a set of energy-optimized explicitly correlated Gaussians to describe positrons interacting with H, He and the ${\mathrm{H}}_{2}$ molecule. These basis functions are then used in a Kohn variational calculation of the scattering lengths and zero-energy annihilation parameters, ${Z}_{\mathrm{eff}}$. The results for the H and He atoms are consistent with previous high-quality variational calculations while the annihilation parameter for ${\mathrm{H}}_{2}$ is consistent with experiment. An extensive tabulation of the ${\mathrm{H}}_{2}$ scattering parameters as a function of internuclear distance confirm the existence of a virtual state at $R\ensuremath{\approx}3.4$${a}_{0}$. The scattering length was $\ensuremath{-}$2.71${a}_{0}$ and ${Z}_{\mathrm{eff}}$ was 15.7 at the mean ${\mathrm{H}}_{2}$ internuclear distance of 1.45${a}_{0}$.

Physical Review A•Feb 18, 2011•28 citations

Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

J. Y. Zhang, Jim Mitroy, Kálmán Varga

The confined variational method is used to generate a basis of correlated Gaussians to describe the interaction region wave function for positron scattering from the H2 molecule. The scattering length was approximately = -2.7a(0) while the zero energy Z(eff) of 15.7 is compatible with experimental values. The variation of the scattering length and Z(eff) with internuclear distance was surprisingly rapid due to virtual state formation at R approximately = 3.4a(0).

arXiv:0911.4315•Physical Review Letters•Nov 24, 2009•37 citations

S -wave elastic scattering of o -Ps from H2 at low energy

J.-Y. Zhang, M.-S. Wu, Ying Qian +5 more

The confined variational method is applied to investigate the low-energy elastic scattering of orthopositronium from ${\text{H}}_{2}$ by first-principles quantum mechanics. Describing the correlations with explicitly correlated Gaussians, we obtain accurate $s$-wave phase shifts and pickoff annihilation parameters for different incident momenta. By a least-squares fit of the data to the effective-range theory, we determine the $s$-wave scattering length ${A}_{S}=2.02{a}_{0}$ and the zero-energy value of the pickoff annihilation parameter, ${}^{1}{Z}_{\text{eff}}=0.1839$. The obtained ${}^{1}{Z}_{\text{eff}}$ agrees well with the precise experimental value of 0.186(1) [G. L. Wright et al., J. Phys. B 16, 4065 (1983)] and the obtained ${A}_{S}$ agrees well with the value of $2.1(2){a}_{0}$ estimated from the average experimental momentum-transfer cross section for positronium energy below 0.3 eV [F. Saito et al., J. Phys. B 36, 4191 (2003)].

arXiv:1803.03026•Physical Review A•Sep 3, 2019•18 citations

Faddeev calculation of e− -Ps scattering lengths

Andrei A. Kvitsinsky, Jaume Carbonell, Claude Gignoux

The modified Faddeev equations in configuration space are applied to solve numerically the problem of the zero-energy elastic scattering of an electron by positronium at zero angular momentum. The singlet and triplet scattering lengths are calculated and zero-energy limits of elastic and ortho-para conversion cross sections are established. The results confirm and improve previous variational estimations of these parameters.

Physical Review A•Aug 1, 1992•27 citations

Calculation of spin-polarized positronium-helium (2 S3) and electron-helium (2 S3) scattering

Yi Zhang, M.-S. Wu, Ying Qian +2 more

Low-energy properties of spin-polarized electron-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ and spin-polarized positronium-helium $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ 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 $(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ 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 $\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the $S$-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium$(2\phantom{\rule{0.16em}{0ex}}^{3}S)$ scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.

Physical Review A•May 5, 2021•5 citations

Elastic scattering of hydrogen atoms at low temperatures

Michael J. Jamieson, A. Dalgarno, John N. Yukich

The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of ${\mathrm{H}}_{2}$. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41${\mathit{a}}_{0}$ for the singlet case and 1.91${\mathit{a}}_{0}$ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$ but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{2}$, with a different fit to the triplet potential between 12${\mathit{a}}_{0}$ and 15${\mathit{a}}_{0}$. A more accurate triplet-state potential is needed at these separations.

Physical Review A•Dec 1, 1992•53 citations
The parameters for SSS-wave elastic scattering of near-zero-energy electrons and positrons by H2{H}_{2}H2​ molecules are calculated using the stabilization method with explicitly correlated Gaussians. The confined variational method is applied to optimize the Gaussians to describe the short-range interaction of incident e\ifmmode±\else\textpm\fi{e}^{\ifmmode\pm\else\textpm\fi{}}e\ifmmode±\else\textpm\fi with H2{H}_{2}H2​ in the fixed-nuclei approximation. For e+{e}^{+}e+-H2{H}_{2}H2​ scattering the scattering length of previous work [Phys. Rev. Lett. 103, 223202 (2009)] is substantially improved. More importantly, for e\ensuremath−{e}^{\ensuremath{-}}e\ensuremath−-H2{H}_{2}H2​ scattering, from first principles, the scattering length is computed as a function of the internuclear distance. In the case that the two nuclei are at the equilibrium distance the results are in a good agreement with values derived from fitting experimental total and diffusion cross sections to the modified effective range theory.
The confined variational method is used to generate a set of energy-optimized explicitly correlated Gaussians to describe positrons interacting with H, He and the H2{\mathrm{H}}_{2}H2​ molecule. These basis functions are then used in a Kohn variational calculation of the scattering lengths and zero-energy annihilation parameters, Zeff{Z}_{\mathrm{eff}}Zeff​. The results for the H and He atoms are consistent with previous high-quality variational calculations while the annihilation parameter for H2{\mathrm{H}}_{2}H2​ is consistent with experiment. An extensive tabulation of the H2{\mathrm{H}}_{2}H2​ scattering parameters as a function of internuclear distance confirm the existence of a virtual state at $R\ensuremath{\approx}3.4$a0{a}_{0}a0​. The scattering length was $\ensuremath{-}2.712.712.71{a}_{0}$ and Zeff{Z}_{\mathrm{eff}}Zeff​ was 15.7 at the mean H2{\mathrm{H}}_{2}H2​ internuclear distance of 1.45a0{a}_{0}a0​.
The confined variational method is applied to investigate the low-energy elastic scattering of orthopositronium from H2{\text{H}}_{2}H2​ by first-principles quantum mechanics. Describing the correlations with explicitly correlated Gaussians, we obtain accurate sss-wave phase shifts and pickoff annihilation parameters for different incident momenta. By a least-squares fit of the data to the effective-range theory, we determine the sss-wave scattering length AS=2.02a0{A}_{S}=2.02{a}_{0}AS​=2.02a0​ and the zero-energy value of the pickoff annihilation parameter, 1Zeff=0.1839{}^{1}{Z}_{\text{eff}}=0.18391Zeff​=0.1839. The obtained 1Zeff{}^{1}{Z}_{\text{eff}}1Zeff​ agrees well with the precise experimental value of 0.186(1) [G. L. Wright et al., J. Phys. B 16, 4065 (1983)] and the obtained AS{A}_{S}AS​ agrees well with the value of 2.1(2)a02.1(2){a}_{0}2.1(2)a0​ estimated from the average experimental momentum-transfer cross section for positronium energy below 0.3 eV [F. Saito et al., J. Phys. B 36, 4191 (2003)].
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.
The elastic scattering of two hydrogen atoms interacting at very small energies is explored numerically using the most accurate potential-energy curves available for the X $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ and $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{u}}^{+}$ states of H2{\mathrm{H}}_{2}H2​. The scattering lengths and low-temperature-averaged cross sections are determined and compared with previous calculations. The scattering lengths are 0.41a0{\mathit{a}}_{0}a0​ for the singlet case and 1.91a0{\mathit{a}}_{0}a0​ for the triplet. The predicted total triplet cross section at 2 K is 5.5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2 but it could be lower, at 4.8\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm2{\mathrm{cm}}^{2}cm2, with a different fit to the triplet potential between 12a0{\mathit{a}}_{0}a0​ and 15a0{\mathit{a}}_{0}a0​. A more accurate triplet-state potential is needed at these separations.