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arXiv:1803.03026 · Physical Review A

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

J.-Y. Zhang, M.-S. Wu, Ying Qian, Xiang Gao, Yihan Yang, Kálmán Varga, Z.-C. Yan, Udo Schwingenschlögl

Published Sep 3, 2019• 18 citations
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Abstract

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)].

DOI
10.1103/physreva.100.032701

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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)].
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 ${e}^{\ifmmode\pm\else\textpm\fi{}}$ 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 ${e}^{\ensuremath{-}}$-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.
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.
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 scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for Ps(1s)H(2s,2p)\mathrm{Ps}(1s)\mathrm{H}(2s,2p)Ps(1s)H(2s,2p) and Ps(2s,2p)H(1s)\mathrm{Ps}(2s,2p)\mathrm{H}(1s)Ps(2s,2p)H(1s) excitations using a recently proposed electron-exchange model potential. The higher (n> 3)(n>~3)(n> 3) excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts, elastic, Ps and H excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range, and resonance energy obtained in various model calculations. These correlations suggest that if a Ps-H dynamical model yields the correct result for one of these four observables, it is expected to lead to the correct result for the other three. The present model, which is constructed so as to reproduce the Ps-H resonance at 4.01 eV, automatically yields a Ps-H bound state at $\ensuremath{-}1.05$ eV that compares well with the accurate value of $\ensuremath{-}1.067$ eV. The model leads to a singlet scattering length of 3.72a0{3.72a}_{0}3.72a0​ and effective range of 1.67a0,{1.67a}_{0},1.67a0​, whereas the correlations suggest the precise values of 3.50a0{3.50a}_{0}3.50a0​ and 1.65a0{1.65a}_{0}1.65a0​ for these observables, respectively.
Abstract The study of collision between metastable positronium (Ps) and antihydrogen ( H ¯ ) is crucial for precision experiments involving H ¯ . In this paper, we investigate the elastic scattering between H ¯ and Ps(2s) by combining the confined variational method with the projection method, for scattering energies from 0.0245 eV to 0.068 eV. Our calculations provide accurate phase shifts and cross sections for the 1,3 S and 1,3 P symmetries. Near the binding threshold, the rapid increase in the total cross section may be attributed to the P-wave resonance effect. Additionally, we determined the S-wave scattering lengths to be 9.34 a 0 and 5.81 a 0 for singlet and triplet elastic scattering, respectively.
We have investigated the elastic scattering of positronium atoms by hydrogen atoms below the excitation threshold at 5.1 eV, limiting the investigation to the spin-zero (singlet) state of the two electrons. Nonresonant SSS-wave phase shifts have been obtained from normalizable trial functions by extracting the center-of-mass wave function and examining its spatial behavior. An effective-range expansion is fitted to the phase shifts and the previously obtained positronium-hydride bound-state energy to yield a scattering length $a\ensuremath{\cong}5.3{a}_{0}$ compared with Fraser's corrected exchange result, a=7.28a0a=7.28{a}_{0}a=7.28a0​ (a0{a}_{0}a0​ is the Bohr radius). The stabilization method suggests that a resonance occurs at a scattering energy of 4.5 eV, about 0.6 eV below the excitation threshold. Using the complex rotation method, we have obtained evidence confirming the existence of the resonance and an estimate of its width of about 6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ eV.