pith. sign in

arxiv: 2606.29253 · v1 · pith:ZQO4PAVOnew · submitted 2026-06-28 · ⚛️ physics.atom-ph

Low-energy positron scattering from metastable helium

Ning-Ning Gao , Hui-Li Han , Ting-Yun Shi , Li-Yan Tang This is my paper

Pith reviewed 2026-06-30 02:17 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords positron scatteringmetastable heliumFeshbach resonancesR-matrix methodpositronium formationcross sectionstime-delay matrixhyperspherical coordinates
0
0 comments X

The pith

Positron scattering from metastable helium shows Feshbach resonance series in higher partial waves.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper calculates elastic and positronium-formation cross sections for positrons incident on singlet and triplet metastable helium using the R-matrix propagation method in hyperspherical coordinates. For the triplet target the results match available convergent-close-coupling calculations and follow the expected threshold behavior. Beyond known S-wave features, the work systematically locates Feshbach resonance series in higher partial waves that extend up to highly excited atomic thresholds. The time-delay matrix is used to uncover additional hidden resonances that produce clear structures in the positronium-formation cross sections.

Core claim

The R-matrix propagation method in hyperspherical coordinates locates Feshbach resonance series in higher partial waves for triplet metastable helium; these series reach highly excited thresholds, the time-delay matrix reveals hidden resonances that imprint on positronium-formation cross sections, and the calculated cross sections agree with convergent-close-coupling results while displaying correct threshold behavior.

What carries the argument

R-matrix propagation method in hyperspherical coordinates, which computes eigenphase sums and the time-delay matrix to identify resonances.

If this is right

  • Cross sections for the triplet target agree with convergent-close-coupling results.
  • Feshbach resonance series in higher partial waves extend up to highly excited atomic thresholds.
  • Hidden resonances uncovered by the time-delay matrix produce structures in the positronium-formation cross sections.
  • Near-threshold resonance structures are analyzed through eigenphase sums.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same hyperspherical R-matrix approach could locate analogous resonance series in other light metastable atoms.
  • Structures in positronium-formation cross sections imply that resonance positions must be accounted for when modeling low-energy positronium production rates.
  • If the time-delay matrix technique generalizes, it offers a practical way to detect resonances that are invisible in standard eigenphase plots.

Load-bearing premise

The chosen basis set and propagation parameters produce numerically converged cross sections and locate resonance positions without significant truncation or channel-coupling errors.

What would settle it

An independent high-resolution measurement or calculation of the positronium-formation cross section near the predicted resonance energies that shows no corresponding structures would falsify the resonance identifications.

Figures

Figures reproduced from arXiv: 2606.29253 by Hui-Li Han, Li-Yan Tang, Ning-Ning Gao, Ting-Yun Shi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
read the original abstract

Low-energy positron scattering from singlet and triplet metastable He($1s2s$) is investigated using the $R$-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 $S$-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The manuscript investigates low-energy positron scattering from singlet and triplet metastable He(1s2s) using the R-matrix propagation method in hyperspherical coordinates. Elastic and positronium-formation cross sections are computed, with near-threshold resonance structures analyzed via eigenphase sums and the time-delay matrix. For the triplet target, the cross sections agree with available convergent-close-coupling (CCC) results and follow expected threshold laws. Beyond known S-wave features, Feshbach resonance series in higher partial waves up to highly excited atomic thresholds are identified, and the time-delay matrix reveals hidden resonances that produce structures in the positronium-formation cross sections.

Significance. If the numerical results hold, the work supplies benchmark cross sections and a systematic mapping of resonance series for positron scattering from metastable helium, including higher partial waves and hidden resonances affecting Ps formation. The explicit agreement with independent CCC calculations for the triplet case is a clear strength that externally supports the R-matrix implementation. The application of the time-delay matrix to uncover additional structures is a useful technical contribution to resonance analysis in this system.

major comments (1)
  1. [§3 (Theoretical method)] §3 (Theoretical method): No convergence tests with respect to hyperspherical basis size, number of channels, or propagation parameters are reported, nor are error bars or basis-size details provided. This is load-bearing for the central claims of quantitative agreement with CCC results (abstract and §4) and precise resonance locations, as the R-matrix propagation accuracy cannot be independently verified from the presented material.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comment on the presentation of numerical details. We address the major comment below.

read point-by-point responses

  1. Referee: No convergence tests with respect to hyperspherical basis size, number of channels, or propagation parameters are reported, nor are error bars or basis-size details provided. This is load-bearing for the central claims of quantitative agreement with CCC results (abstract and §4) and precise resonance locations, as the R-matrix propagation accuracy cannot be independently verified from the presented material.

    Authors: We acknowledge that the manuscript as submitted does not report explicit convergence tests or error estimates. While the agreement with independent CCC calculations for the triplet target provides external validation of the implementation, we agree that internal convergence studies are required to substantiate the quantitative claims. In the revised manuscript we will add a dedicated subsection to §3 that specifies the hyperspherical basis sizes, channel numbers, and propagation parameters employed, together with the results of convergence tests with respect to these quantities and estimated uncertainties on the reported cross sections and resonance positions. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper computes elastic and positronium-formation cross sections via the R-matrix propagation method in hyperspherical coordinates, then directly compares the triplet-target results to independent convergent-close-coupling calculations performed by other groups. Resonance positions are extracted from eigenphase sums and the time-delay matrix using standard scattering theory; neither step reduces to a fitted parameter, a self-definition, nor a load-bearing self-citation. The external CCC benchmark supplies independent validation, so the derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, invented entities, or non-standard axioms; all content rests on standard quantum scattering theory.

axioms (1)
  • standard math Standard non-relativistic quantum mechanics and scattering theory apply to low-energy positron-atom collisions.
    The R-matrix method and eigenphase/time-delay analysis presuppose this framework.

pith-pipeline@v0.9.1-grok · 5642 in / 1210 out tokens · 26286 ms · 2026-06-30T02:17:15.432278+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

53 extracted references

  1. [1]

    The eigenphase shifts δi(E) are obtained by diagonalizing the K matrix in Eq

    Eigenphase-sum and time-delay analyses To determine the resonance energies Er and widths Γ, we use the eigenphase-sum method as the primary diagnostic for well-isolated resonances. The eigenphase shifts δi(E) are obtained by diagonalizing the K matrix in Eq. ( 28) and taking the arctangent of its eigenvalues. The total eigenphase sum is then given by [ 91...

  2. [2]

    The first consists of atomic channels, which dissociate into a positron and an excited helium atom, e+ + He ∗

    Narrow Feshbach resonances There are two classes of asymptotic channels in the present systems. The first consists of atomic channels, which dissociate into a positron and an excited helium atom, e+ + He ∗ . The second consists of rearrangement channels, which dissociate into a Ps atom and a He + ion. In the present calculations, the atomic-channel expans...

  3. [3]

    These resonances are indi- cated in bold in Table II

    Resonant structures in Ps-formation cross sections In addition to the narrow Feshbach resonances dis- cussed above, we find several resonant structures with widths of order 10−4 a.u.. These resonances are indi- cated in bold in Table II. A distinctive feature of these states is that they produce pronounced structures in the Ps-formation cross sections, al...

  4. [4]

    The fitted universal scaling parameters α are also listed

    threshold for the e +–He(1s2s 1,3S) systems. The fitted universal scaling parameters α are also listed. Figures 7(a1)–7(c1) and Figs. 8(a1)–8(d1) present the eigenphase-sum spectra, Ps( n = 1, 2) formation cross sec- tions, and dipole resonance energies near the Ps( n = 2 ) threshold for the e +-He(1s2s 3S) ( J = 0 − 2) and e +- He(1s2s 1S) ( J = 0 − 3) s...

  5. [36]

    Ryzhikh and J

    G. Ryzhikh and J. Mitroy, A metastable state of positronic helium , J. Phys. B: At. Mol. Opt. Phys. 31, 3465 (1998)

    1998

  6. [42]

    Mitroy and I

    J. Mitroy and I. A. Ivanov, Positronium scattering from closed-shell atoms and ions , Phys. Rev. A 65, 012509 15 (2001)

    2001

  7. [52]

    Wymer, S

    L. Wymer, S. Kumar, T. J. Gay, S. S. Hodgman, S. J. Buckman, and J. R. Machacek, Excitation of metastable helium atoms by positron impact , Eur. Phys. J. D 80, 12 (2026)

    2026

  8. [53]

    Gao, H.-L

    N.-N. Gao, H.-L. Han, and T.-Y. Shi, Positronium forma- tion and threshold behavior in positron-sodium collisions at low energies , Phys. Rev. A 112, 012810 (2025)

    2025

  9. [54]

    Popovicz Seidel, J

    E. Popovicz Seidel, J. Franz, W. Tenfen, and F. Arretche, Use of single-body potentials to accurately describe virtual positronium formation in positron collisions , Phys. Rev. A 111, 052804 (2025)

    2025

  10. [55]

    Van Reeth and J

    P. Van Reeth and J. W. Humberston, Similarities in the low-energy elastic and Ps formation differential cross- sections for e+−H and e+−He scattering, Atoms 13 (2025)

    2025

  11. [56]

    N. A. Mori, L. H. Scarlett, I. Bray, and D. V. Fursa, Con- vergent close-coupling calculations of positron scattering from neon and argon , Eur. Phys. J. D 78, 19 (2024)

    2024

  12. [57]

    Mistry, A

    T. Mistry, A. Haque, B. Mandal, M. Mondal, S. Halder, and M. Purkait, State selective total and angular differen- tial cross sections for positronium formation in e+−He collisions, J. Electron Spectrosc. Relat. Phenom. 275, 147470 (2024)

    2024

  13. [58]

    Li, M.-S

    X.-J. Li, M.-S. Wu, J. Jiang, C.-Z. Dong, J.-Y. Zhang, Z.-C. Yan, and K. Varga, Positron scattering and anni- hilation from helium at low energies , Phys. Rev. A 108, 062816 (2023)

    2023

  14. [59]

    N. A. Mori, L. H. Scarlett, I. Bray, and D. V. Fursa, Con- vergent close-coupling calculations of positron scattering from atomic carbon , Phys. Rev. A 107, 032817 (2023)

    2023

  15. [60]

    J. R. Machacek, S. Hodgman, S. Buckman, and T. J. Gay, A method to measure positron beam polarization using optically polarized atoms , Atoms 11 (2023)

    2023

  16. [61]

    R. P. McEachran and A. D. Stauffer, Positron scattering from helium, J. Phys. B: At. Mol. Opt. Phys. 52, 115203 (2019)

    2019

  17. [62]

    Ratnavelu, M

    K. Ratnavelu, M. J. Brunger, and S. J. Buckman, Rec- ommended Positron Scattering Cross Sections for Atomic Systems, J. Phys. Chem. Ref. Data 48, 023102 (2019)

    2019

  18. [63]

    Yan and Y

    Z.-C. Yan and Y. K. Ho, Triply excited autodissociating resonant states in the positron-helium system , Phys. Rev. A 98, 062702 (2018)

    2018

  19. [64]

    A. S. Kadyrov and I. Bray, Recent progress in the de- scription of positron scattering from atoms using the con- vergent close-coupling theory , J. Phys. B: At. Mol. Opt. Phys. 49, 222002 (2016)

    2016

  20. [65]

    Zecca and L

    A. Zecca and L. Chiari, Structures in positron–atom and molecule total cross sections , Molecular Physics 113, 3615 (2015)

    2015

  21. [66]

    S. J. Brawley, S. E. Fayer, M. Shipman, and G. Laricchia, Positronium production and scattering below its breakup threshold, Phys. Rev. Lett. 115, 223201 (2015)

    2015

  22. [67]

    I. Bray, D. V. Fursa, A. S. Kadyrov, A. V. Lugovskoy, J. S. Savage, A. T. Stelbovics, R. Utamuratov, and M. C. Zammit, Positron scattering on atoms and molecules , J. Phys.: Conf. Ser. 488, 012052 (2014)

    2014

  23. [68]

    Karwasz, D

    G. Karwasz, D. Pliszka, A. Zecca, and R. Brusa, Positron scattering in helium: Virtual-positronium resonances , Nucl. Instrum. Methods Phys. Res. B 240, 666 (2005)

    2005

  24. [69]

    C. M. Surko, G. F. Gribakin, and S. J. Buckman, Low- energy positron interactions with atoms and molecules , J. Phys. B: At. Mol. Opt. Phys. 38, R57 (2005)

    2005

  25. [70]

    Harabati, V

    C. Harabati, V. A. Dzuba, and V. V. Flambaum, Iden- tification of atoms that can bind positrons , Phys. Rev. A 89, 022517 (2014)

    2014

  26. [71]

    M. W. J. Bromley, J. Mitroy, and K. Varga, Positron attachment to the He doubly excited states , Phys. Rev. Lett. 109, 063201 (2012)

    2012

  27. [72]

    J. R. Machacek, R. Boadle, S. J. Buckman, and J. P. Sul- livan, Search for positron quasibound states in the dou- bly excited region of the helium atom , Phys. Rev. A 86, 064702 (2012)

    2012

  28. [73]

    Hanssen, P

    J. Hanssen, P. A. Hervieux, O. A. Fojón, and R. D. Rivarola, Positronium formation in positron-metastable- helium collisions , Phys. Rev. A 63, 012705 (2000)

    2000

  29. [74]

    Utamuratov, A

    R. Utamuratov, A. S. Kadyrov, D. V. Fursa, I. Bray, and A. T. Stelbovics, Convergent close-coupling calculations of positron scattering on metastable helium , Phys. Rev. A 82, 042705 (2010)

    2010

  30. [75]

    Wu, Y.-J

    X.-G. Wu, Y.-J. Cheng, F. Liu, and Y.-J. Zhou, Optical potential approach for positron scattering by metastable 2 3S state of helium￿ , Chin. Phys. B 26, 023401 (2017)

    2017

  31. [76]

    A. U. Hazi, Behavior of the eigenphase sum near a reso- nance, Phys. Rev. A 19, 920 (1979)

    1979

  32. [77]

    Igarashi and I

    A. Igarashi and I. Shimamura, Stable complex-rotation eigenvalues that correspond to no full resonances in scat- tering: Examples in positron scattering by the helium ion , Phys. Rev. A 70, 012706 (2004)

    2004

  33. [78]

    Igarashi, Broad resonances in H+ and Ps+, Eur

    A. Igarashi, Broad resonances in H+ and Ps+, Eur. Phys. J. D 70, 216 (2016)

    2016

  34. [79]

    C. D. Lin, Hyperspherical coordinate approach to atomic and other coulombic three-body systems , Phys. Rep. 257, 1 (1995)

    1995

  35. [80]

    Bachau, E

    H. Bachau, E. Cormier, P. Decleva, J. E. Hansen, and F. Martín, Applications of B-splines in atomic and molec- ular physics , Rep. Prog. Phys. 64, 1815 (2001)

    2001

  36. [81]

    S. Kang, J. Li, and T.-Y. Shi, Investigation of hydrogenic- donor states confined by spherical quantum dots with B- splines, J. Phys. B: At. Mol. Opt. Phys. 39, 3491 (2006)

    2006

  37. [82]

    J. Wang, J. P. D’Incao, and C. H. Greene, Numerical study of three-body recombination for systems with many bound states , Phys. Rev. A 84, 052721 (2011)

    2011

  38. [83]

    Ryzhikh and J

    G. Ryzhikh and J. Mitroy, A metastable state of 16 positronic helium , J. Phys. B: At. Mol. Opt. Phys. 31, 3465 (1998)

    1998

  39. [84]

    Ren, H.-L

    Z.-Z. Ren, H.-L. Han, and T.-Y. Shi, S-wave resonances in the positron–helium scattering , J. Phys. B: At. Mol. Opt. Phys. 44, 065204 (2011)

    2011

  40. [85]

    Mitroy, Expectation values of the e+He(3Se) system, Phys

    J. Mitroy, Expectation values of the e+He(3Se) system, Phys. Rev. A 72, 032503 (2005)

    2005

  41. [86]

    Ren, H.-L

    Z.-Z. Ren, H.-L. Han, T.-Y. Shi, and J. Mitroy, Structure and resonances of the e+−He(1s2s 3Se) system, J. Phys. B: At. Mol. Opt. Phys. 45, 085002 (2012)

    2012

  42. [87]

    Kramida, Yu

    A. Kramida, Yu. Ralchenko, J. Reader, and and NIST ASD Team, NIST Atomic Spectra Database(ver. 5.12), [Online]. National Institute of Standards and Technology, Gaithersburg, MD. (2024)

    2024

  43. [88]

    T. F. O’Malley, Extrapolation of electron-rare gas atom cross sections to zero energy , Phys. Rev. 130, 1020 (1963)

    1963

  44. [89]

    Mitroy and I

    J. Mitroy and I. A. Ivanov, Positronium scattering from closed-shell atoms and ions , Phys. Rev. A 65, 012509 (2001)

    2001

  45. [90]

    Gao, Quantum-defect theory for −1/r4−type interac- tions, Phys

    B. Gao, Quantum-defect theory for −1/r4−type interac- tions, Phys. Rev. A 88, 022701 (2013)

    2013

  46. [91]

    D.-X. Zhao, K. Hu, M.-S. Wu, J.-Y. Zhang, K.-D. Wang, and Z.-C. Yan, Relativistic effects on positron binding to the triplet state of helium , Phys. Rev. A 113, 042811 (2026)

    2026

  47. [92]

    E. P. Wigner, On the behavior of cross sections near thresholds, Phys. Rev. 73, 1002 (1948)

    1948

  48. [93]

    Yan, Polarizabilities of the rydberg states of helium , Phys

    Z.-C. Yan, Polarizabilities of the rydberg states of helium , Phys. Rev. A 62, 052502 (2000)

    2000

  49. [94]

    Zhang, L.-Y

    Y.-H. Zhang, L.-Y. Tang, X.-Z. Zhang, and T.-Y. Shi, Dynamic dipole polarizabilities for the low-lying triplet states of helium , Phys. Rev. A 92, 012515 (2015)

    2015

  50. [95]

    Gao and C

    H. Gao and C. H. Greene, Energy-dependent vibrational frame transformation for electron–molecule scattering with simplified models , J. Chem. Phys. 91, 3988 (1989)

    1989

  51. [96]

    C. H. Greene, Negative-ion photodetachment in a weak magnetic field , Phys. Rev. A 36, 4236 (1987)

    1987

  52. [97]

    F. T. Smith, Lifetime matrix in collision theory , Phys. Rev. 118, 349 (1960)

    1960

  53. [98]

    Gailitis and R

    M. Gailitis and R. Damburg, The influence of close cou- pling on the threshold behaviour of cross sections of electron-hydrogen scattering, Proc. Phys. Soc. 82, 192 (1963)

    1963