arXiv:0911.4315 · Physical Review Letters

Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

J. Y. Zhang, Jim Mitroy, Kálmán Varga

Published Nov 24, 2009• 37 citations

Abstract

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).

DOI: 10.1103/physrevlett.103.223202

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arXiv:0911.4315 · Physical Review Letters

Positron Scattering and Annihilation from the Hydrogen Molecule at Zero Energy

J. Y. Zhang, Jim Mitroy, Kálmán Varga

Published Nov 24, 2009• 37 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.103.223202

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 ${a}_{0}$ .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${a}_{0}$.

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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}

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.

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)].

{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.