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arXiv:physics/9911054 · Physical Review A

Positronium–hydrogen-atom scattering in a five-state model

Sadhan K. Adhikari, Priyanka Biswas

Published Mar 1, 1999• 37 citations
arXivHTMLPDF

Abstract

The scattering of orthopositronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for $\mathrm{Ps}(1s)\mathrm{H}(2s,2p)$ and $\mathrm{Ps}(2s,2p)\mathrm{H}(1s)$ excitations using a recently proposed electron-exchange model potential. The higher $(n>~3)$ 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 ${3.72a}_{0}$ and effective range of ${1.67a}_{0},$ whereas the correlations suggest the precise values of ${3.50a}_{0}$ and ${1.65a}_{0}$ for these observables, respectively.

DOI
10.1103/physreva.59.2058

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arXiv:physics/0103035•Journal of Physics B Atomic Molecular and Optical Physics•Apr 3, 2001•10 citations
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\ensuremath{-}1.05\ensuremath−1.05 eV that compares well with the accurate value of \ensuremath−1.067\ensuremath{-}1.067\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.
Calculations are reported for positronium (Ps) scattering by atomic hydrogen (H) in the energy range 0--6.5 eV in a coupled-pseudostate approximation in which excitation and ionization channels of both the Ps and the H are taken into account. The approximation contains an accurate representation of the van der Waals coefficient. Results are presented for phase shifts, scattering lengths, effective ranges, and various cross sections including partial wave, total, and ortho-para conversion cross sections. An analysis of the possible spin transitions is provided and the energy of the positronium hydride (PsH) bound state is determined. Substantial differences are found from earlier work within the frozen target approximation, now clearly confirming the importance of target excitation channels. Good agreement is obtained with recent calculations of S-wave phase shifts and scattering lengths using the stabilization method. Convergence to the exact binding energy for PsH appears to be slow. Resonances corresponding to unstable states of the positron orbiting ${\mathrm{H}}^{\ensuremath{-}}$ are seen in the electronic spin singlet partial waves. The importance of the ${\mathrm{H}}^{\ensuremath{-}}$ formation channel is discussed.
Scattering of ortho positronium (Ps) by cesium and rubidium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s,2s,2p) states using a time-reversal-symmetric regularized electronexchange model potential. We find a narrow S-wave singlet resonance at 5.057 eV of width 0.003 eV in the Ps-Rb system and at 5.067 eV of width 0.003 eV in the Ps-Cs system. Singlet P-wave resonances in both systems are found at 5.3 eV of width 0.4 eV. Singlet D-wave structures are found at 5.4 eV in both systems. The pronounced P- and D-wave resonances in these systems lead to easily detectable local minima in the low-energy elastic cross sections. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Rb and Cs. PACS Number(s): 34.10.+x, 36.10.DrRecent measurements of ortho positronium (Ps) scattering cross section by H2, N2, He, Ne, Ar, C4H10, and C5H12 [1–7] have initiated new theoretical investigations [8–14] in this subject. We suggested [15–17] a regularized, symmetric, nonlocal electron-exchange model
We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the SSS-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The SSS-wave total and ortho-para conversion cross sections are calculated by making use of both 1S^{1}S1S and 3S^{3}S3S results. In the 3S^{3}S3S case, we see no indication of any resonances below the excitation threshold at 5.1 eV.
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.
We investigate ortho-positronium--lithium-atom (Ps-Li) scattering using static-exchange and three-Ps-state coupled-channel calculations. The present three-Ps-state scheme, while closely agreeing with the resonance and binding energies in the Ps-H system, predicts $S\ensuremath{-},$ $P\ensuremath{-},$ and DDD-wave resonances at 4.25 eV, 4.9 eV, and 5.25 eV, respectively, in the electronic spin-singlet channel of Ps-Li scattering. The present calculation also yields a Ps-Li binding in this attractive singlet channel with an approximate binding energy of 0.218 eV, which is in adherence with the recent findings of a chemically stable PsLi system using stocastic variational and quantum Monte Carlo calculations. We further report elastic, $\mathrm{Ps}(2s)\ensuremath{-},$ and Ps(2p)\mathrm{Ps}(2p)Ps(2p)-excitation cross sections at low to medium energies (0.068--30 eV).
Scattering of positronium (Ps) by sodium and potassium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s, 2s, 2p) states using a time-reversal-symmetric regularized electron-exchange model potential fitted to reproduce accurate theoretical results for PsNa and PsK binding energies. We find a narrow S-wave singlet resonance at 4.58 eV of width 0.002 eV in the Ps-Na system and at 4.77 eV of width 0.003 eV in the Ps-K system. Singlet P-wave resonances in both systems are found at 5.07 eV of width 0.3 eV. Singlet D-wave structures are found at 5.3 eV in both systems. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Na and K.