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Physical Review A

S -wave resonances in positron-lithium scattering below the Li (n=4) thresholds

Hui-Li Han, Zhen-Xiang Zhong, Xianzhou Zhang, Ting-Yun Shi

Published Oct 22, 2008• 21 citations
Publisher

Abstract

We have calculated $S$-wave resonances in the positron-lithium system using the stabilization method in the framework of hyperspherical coordinates. Resonances below the Li $(n=4)$ thresholds have been investigated. We have located the previously known $S$-wave resonances by Roy and Ho [J. Phys. B 35, 2149 (2002)] and observed relatively good agreement for the resonance positions. In addition, one Feshbach resonance associated with the Ps $(n=2)$ threshold is also identified.

DOI
10.1103/physreva.78.044701

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We have calculated SSS-wave resonances in the positron-lithium system using the stabilization method in the framework of hyperspherical coordinates. Resonances below the Li (n=4)(n=4)(n=4) thresholds have been investigated. We have located the previously known SSS-wave resonances by Roy and Ho [J. Phys. B 35, 2149 (2002)] and observed relatively good agreement for the resonance positions. In addition, one Feshbach resonance associated with the Ps (n=2)(n=2)(n=2) threshold is also identified.
We have performed a three-body calculation for investigation of S-wave resonances in the positron–helium scattering in the hyperspherical coordinates. B-splines are used to obtain accurate hyperspherical potential curves and channel functions. An adiabatical hyperspherical approach is used to predict semi-quantitatively the position of the resonances. A multichannel calculation with the stabilization method is also used to extract accurately the positions and widths of resonances. We find four resonances associated with the He + –Ps( n = 2) channel. The resonance parameters for the lowest two resonances are in reasonable agreement with the calculations of Kar and Ho ( 2004 J. Phys. B: At. Mol. Opt. Phys. 37 3177 ), and two more new resonances below the Ps( n = 2) threshold are identified.
Low-energy positron scattering from singlet and triplet metastable He(1s2s1s2s1s2s) is investigated using the RRR-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are reported, and near-threshold resonance structures are analyzed in terms of eigenphase sums and the time-delay matrix. For the triplet target, the calculated cross sections are in agreement with available convergent-close-coupling results and display the expected threshold behavior. Beyond the known SSS-wave features, Feshbach resonance series in higher partial waves extending up to highly excited atomic thresholds are systematically identified. The time-delay matrix further uncovers hidden resonances that produce obvious structures in the positronium-formation cross sections.
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.
Seiler, Oberoi, and Callaway first located resonances in the positron-hydrogen system below the n=2n=2n=2 inelastic threshold, using the algebraic close-coupling method without including the open positronium channel. Several other calculations including both open channels have failed to find any resonances. In an attempt to clarify the situation, a calculation has been performed which is an extension of the work of Seiler, Oberoi, and Callaway. A wave function including the 1s1s1s, 2s2s2s, and 2p2p2p eigenstates of hydrogen and the 1s−\stackrel{-}{1s}1s− ground state of positronium was used in a calculation that is a simplification of the usual close-coupling technique and that resembles the optical-potential method. In this approximation it is found that the lowest resonance of Seiler, Oberoi, and Callaway is destroyed by opening the 1s−\stackrel{-}{1s}1s− channel. It is concluded that any resonances which may occur in this system must lie closer to the n=2n=2n=2 threshold than do the corresponding electron-hydrogen resonances.