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Physical Review A

Orthopositronium-lithium scattering using a close-coupling approximation at low and medium energies

Ajoy Chakraborty, Prabal K. Sinha, Arnab Ghosh

Published Jun 7, 2002• 9 citations
Publisher

Abstract

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 $l=2)$ 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.

DOI
10.1103/physreva.65.062504

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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
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.
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.
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).
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.
Low-energy elastic and inelastic scattering in the Ps(1s1s1s)-Ps(2s2s2s) channel is treated in a four-body hyperspherical coordinate calculation. Adiabatic potentials are calculated for triplet-triplet, singlet-singlet, and singlet-triplet spin symmetries in the spin representation of coupled electrons and coupled positrons, with total angular momentum L=0L=0L=0 and parity equal to +1+1+1. The sss-wave scattering lengths for the asymptotic Ps(1s1s1s)-Ps(2s2s2s) channel are calculated for each spin configuration. Results obtained for the sss-wave scattering lengths are ${a}_{\mathrm{TT}}=7.3(2){a}_{0}\ensuremath{-}i0.02(1){a}_{0}, {a}_{\mathrm{SS}}=13.2(2){a}_{0}\ensuremath{-}i0.9(2){a}_{0}$, and aST=9.7(2)a0{a}_{\mathrm{ST}}=9.7(2){a}_{0}aST​=9.7(2)a0​ for each spin configuration. Spin recoupling is implemented to extract the scattering lengths for collisions of Ps in different spin configurations through properly symmetrized unitary transformations. Calculations of experimentally relevant scattering lengths and cross sections are carried out for Ps atoms initially prepared in different uncoupled spin states.
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.
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)].