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Physical Review A

S−, P−, and D -wave resonances in positronium–lithium-atom scattering

Priyanka Biswas

Published Dec 8, 1999• 18 citations
Publisher

Abstract

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 $D$-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 $\mathrm{Ps}(2p)$-excitation cross sections at low to medium energies (0.068--30 eV).

DOI
10.1103/physreva.61.012502

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Physical Review A•Feb 27, 2002•52 citations
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−,S\ensuremath{-},S\ensuremath−, P\ensuremath−,P\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, Ps(2s)\ensuremath−,\mathrm{Ps}(2s)\ensuremath{-},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.
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
The scattering of orthopositronium off atomic lithium (Li) target has been investigated using the close-coupling approximation (CCA) with different basis sets. The predictions of different projectile-elastic and target-elastic CCA models have been presented along with static-exchange results. We report the scattering length, the effective range, and the zero-energy cross section for singlet and triplet scattering. The spin averaged zero-energy cross section is significantly improved over the static-exchange prediction by the inclusion of the virtual Ps excitation channels in the basis set. All the present models indicate a binding of lithium-positride (LiPs) in the attractive singlet channel. The low-energy (below first Li excitation threshold) and low order (up to l=2)l=2)l=2) phase shifts are also reported and are found to be variationally consistent. Except the s-wave singlet scattering, other phase shifts are influenced more by the target distortion effect than the projectile inelastic effect. Estimates of the different single-atom excitation cross sections have also been reported along with an estimate of the total cross section. The peak in the total cross-section curve for the present system is not prominent at energies around the Ps inelastic threshold, unlike the Ps-Na case. For incident energy 20 eV or more the Ps ionization is the dominant contributor to the total cross section.
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.
Projectile-elastic, target-elastic, and full close-coupling approximation models have been employed to investigate scattering of ortho-positronium off Li and Na atoms at low energies. Nine different basis sets for each system have been used to find the relative importance of atomic (target and projectile) states on the elastic scattering parameters and the convergence of the predicted results with added eigen- and pseudostates. The sss-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy k=0.5a.u.k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}k=0.5a.u. and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting sss-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.
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.