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Journal of Physics B Atomic Molecular and Optical Physics

Feshbach resonances below the 2 H excitation threshold in electron - hydrogen scattering

T. T. Gien

Published Dec 28, 1998• 19 citations
Publisher

Abstract

The sequences of S-, P- and D-wave Feshbach resonances in both singlet and triplet electron - hydrogen scatterings were located below the n = 2 H excitation threshold for the first time in an accurate calculation, employing the Harris - Nesbet variational method. The resonance positions and widths of a sequence were found to agree fairly well with the scaling law.

DOI
10.1088/0953-4075/31/24/005

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Physical Review•Jul 1, 1960•54 citations
The sequences of S-, P- and D-wave Feshbach resonances in both singlet and triplet electron - hydrogen scatterings were located below the n = 2 H excitation threshold for the first time in an accurate calculation, employing the Harris - Nesbet variational method. The resonance positions and widths of a sequence were found to agree fairly well with the scaling law.
The positions of these resonances were determined within an implicit assumption of a degenerate threshold limit at -0.25 Ryd for their sequences, i.e. when the various well known threshold-splitting effects are ignored. The positions of these resonances should, therefore, be understood as to be referring to this degenerate threshold limit. For example, the 1 P o (3) and 3 D e (1) resonances, within the degenerate-threshold assumption, are respectively at the positions of 2.378 × 10 -6 Ryd and 3.943 × 10 -6 Ryd from the threshold limit (as point of reference); the threshold limit will change when the threshold-splitting effects are considered.
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.
For pt.I, see abstr. A43029 of 1970. The upper-bound property of the multiconfiguration energy-bound method has also been tested for Feshbach-type autoionization states lying between higher excitation thresholds of one-electron targets. As an illustrative example more compound states associated with the 1 S e closed-channel (Feshbach) resonances for the (e, He + ) scattering system lying between the n=2 and n=3 thresholds, and between the n=3 and n=4 thresholds, have been calculated. The best results so far obtained variationally of the energy positions and the corresponding wave functions are given in the present paper.
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.
Recently developed variational techniques for determining upper bounds on scattering lengths are applied to singlet and triplet scattering of zero-energy electrons by atomic hydrogen. The results obtained are not only rigorous but are in fact somewhat lower and therefore somewhat better than those previously obtained by variational methods. We find that the triplet and singlet scattering lengths, AT{A}_{T}AT​ and AS{A}_{S}AS​ respectively, satisfy the inequalities ${A}_{T}\ensuremath{\leqq}1.91{a}_{0}$ and ${A}_{S}\ensuremath{\leqq}6.23{a}_{0}$, where a0{a}_{0}a0​ is the Bohr radius. The only assumptions involved in the deduction of these results are that there be no bound triplet state and one and only one bound singlet state. The singlet trial function determined during the course of the calculation generates a singlet effective range, r0S{r}_{0S}r0S​, of about 2.7a02.7{a}_{0}2.7a0​. The triplet trial functions which were obtained were not sufficiently accurate to be useful in a determination of the triplet effective range, r0T{r}_{0T}r0T​.