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Europhysics Letters (EPL)

Feshbach resonances in electron-positronium continuum and the close-coupling model

Arindam Basu, Arnab Ghosh

Published Oct 1, 2002• 14 citations
Publisher

Abstract

A three-state and a six-state close-coupling approximation have been employed to investigate the e − -Ps scattering below the first excitation threshold of the Ps atom. Present s - and p -wave phase shifts and total cross-sections are compared with the corresponding predictions of Ward et al. ( J. Phys. B , 20 (1987) 127). All the Feshbach resonances below the n = 2 threshold, including 3 S e and 3 P e resonances as predicted by Ho ( Phys. Lett. A , 120 (1984) 348 and Phys. Rev. A , 60 (1999) 2834), have been obtained.

DOI
10.1209/epl/i2002-00316-7

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A three-state and a six-state close-coupling approximation have been employed to investigate the e − -Ps scattering below the first excitation threshold of the Ps atom. Present s - and p -wave phase shifts and total cross-sections are compared with the corresponding predictions of Ward et al. ( J. Phys. B , 20 (1987) 127). All the Feshbach resonances below the n = 2 threshold, including 3 S e and 3 P e resonances as predicted by Ho ( Phys. Lett. A , 120 (1984) 348 and Phys. Rev. A , 60 (1999) 2834), have been obtained.
The coupled-channel model [Phys. Rev. A {\bf 59}, 363 (1999)] that yields converged low-energy phase shifts, and exact binding and resonance features in Ps-H [Phys. Rev. A {\bf 59}, 2058 (1999)] is applied to study Ps-He+^++ scattering. Similar to PsH, resonances appear in the S-, P-, D-, etc partial waves in the Ps-He+^++ system but in both the singlet and triplet scattering channels. The latter signifies possible Rydberg states of e+e^+e+ around singlet and triplet helium. The S-wave singlet resonance at 2.79 eV agrees to that predicted earlier in e+e^+e+-He entrance channel (energy difference 16.64 eV) at 19.27 eV [Chem. Phys. Lett. {\bf 262}, 460 (1996)].
A pseudopotential for positronium-atom interaction, based on electron-atom and positron-atom phase shifts, is constructed, and the phase shifts for Ps-Kr and Ps-Ar scattering are calculated. This approach allows us to extend the Ps-atom cross sections, obtained previously in the impulse approximation [I. I. Fabrikant and G. F. Gribakin, Phys. Rev. Lett. 112, 243201 (2014)], to energies below the Ps ionization threshold. Although experimental data are not available in this low-energy region, our results describe well the tendency of the measured cross sections to drop with decreasing velocity at v<1v<1v<1 a.u. Our results show that the effect of the Ps-atom van der Waals interaction is weak compared to the polarization interaction in electron-atom and positron-atom scattering. As a result, the Ps scattering length for both Ar and Kr is positive, and the Ramsauer-Townsend minimum is not observed for Ps scattering from these targets. This makes Ps scattering quite different from electron scattering in the low-energy region, in contrast to the intermediate energy range from the Ps ionization threshold up to $v\ensuremath{\sim}2$ a.u., where the two are similar.
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.
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.
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.