Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

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

T. T. Gien

Published Jan 1, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/32/9/501

Related papers

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

T. T. Gien

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.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 28, 1998•19 citations

Accurate algebraic coupled-state calculation of positron-hydrogen scattering at low energies

T. T. Gien

Our unexpounded writing in the first paragraph of page L24 of the letter may give a false impression to some about what was really meant. We would like, therefore, to clarify it. We simply intended to stress that the deficiency of the polarizability of H(1s) and of Ps(1s) can be seen more easily at low energies in higher-partial-wave phase shifts of e + -H scattering and in higher-partial-wave elastic cross sections of Ps(1s)-p scattering, and that for the purpose of determining the sequences of S, P, D Feshbach resonances (within the assumption of a degenerate threshold limit at -0.25 Ryd, i.e. when the threshold splitting due to fine-structure and QED corrections is ignored), the use of the E6S coupling scheme is appropriate since this coupling scheme contains the 2s and 2p states of H essential for the degenerate dipole interaction. It is therefore quite obvious that for the calculations in a very narrow range of energy of less than 1 × 10 -2 Ryd beneath the degenerate threshold (resonance region), the use of the E6PS coupling scheme may not be able to yield reliable results for S, P, D scattering, since the scheme cannot handle the resonances properly, due to the absence of the 2s and 2p H states essential for the degenerate dipole interaction. This is, however, of little concern, since the range of energies that we have considered for our various accurate calculations (such as E6PS, E8PS, E6S, ME6S, E8S) is further below the degenerate threshold. Rigorously speaking, even if the 2s and 2p H states are included in the coupling scheme, care concerning the nondegeneracy of threshold might still have to be taken for calculations in the closest vicinity of the threshold.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 1, 1999•1 citation

Feshbach resonances in positron–hydrogen collisions

T. T. Gien

Sequences of Feshbach resonances, predicted by theory to exist below the n = 2 H threshold in positron–hydrogen scattering, that have long evaded all previous numerical searches, were finally located in our close-coupling calculation employing various coupling schemes. The energy ratios and width ratios of the successive resonances of these sequences were, furthermore, found to agree very well with the values predicted by theory.

Canadian Journal of Physics•Jul 1, 1996•10 citations

Tests of the multiconfiguration energy-bound method for Feshbach-type autoionization states of two-electron atoms II. Application to He states between higher thresholds

Erling Holøien, John Midtdal

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.

Journal of Physics B Atomic and Molecular Physics•Jan 1, 1971•16 citations

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

Arindam Basu, Arnab Ghosh

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.

Europhysics Letters (EPL)•Oct 1, 2002•14 citations

Feshbach resonances in positron-hydrogen scattering

Richard J. Drachman

Seiler, Oberoi, and Callaway first located resonances in the positron-hydrogen system below the $n=2$ 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 $1s$, $2s$, and $2p$ eigenstates of hydrogen and the $\stackrel{-}{1s}$ 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 $\stackrel{-}{1s}$ channel. It is concluded that any resonances which may occur in this system must lie closer to the $n=2$ threshold than do the corresponding electron-hydrogen resonances.

Physical Review A•Jul 1, 1975•22 citations
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.
Our unexpounded writing in the first paragraph of page L24 of the letter may give a false impression to some about what was really meant. We would like, therefore, to clarify it. We simply intended to stress that the deficiency of the polarizability of H(1s) and of Ps(1s) can be seen more easily at low energies in higher-partial-wave phase shifts of e + -H scattering and in higher-partial-wave elastic cross sections of Ps(1s)-p scattering, and that for the purpose of determining the sequences of S, P, D Feshbach resonances (within the assumption of a degenerate threshold limit at -0.25 Ryd, i.e. when the threshold splitting due to fine-structure and QED corrections is ignored), the use of the E6S coupling scheme is appropriate since this coupling scheme contains the 2s and 2p states of H essential for the degenerate dipole interaction. It is therefore quite obvious that for the calculations in a very narrow range of energy of less than 1 × 10 -2 Ryd beneath the degenerate threshold (resonance region), the use of the E6PS coupling scheme may not be able to yield reliable results for S, P, D scattering, since the scheme cannot handle the resonances properly, due to the absence of the 2s and 2p H states essential for the degenerate dipole interaction. This is, however, of little concern, since the range of energies that we have considered for our various accurate calculations (such as E6PS, E8PS, E6S, ME6S, E8S) is further below the degenerate threshold. Rigorously speaking, even if the 2s and 2p H states are included in the coupling scheme, care concerning the nondegeneracy of threshold might still have to be taken for calculations in the closest vicinity of the threshold.
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.
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.