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arxiv: 2605.19222 · v1 · pith:QB2JNBKEnew · submitted 2026-05-19 · ⚛️ physics.atom-ph

Spin asymmetry for the elastic scattering of polarized electrons from Zn, Cd, and Hg

Mehrdad Adibzadeh , Constantine E. Theodosiou This is my paper

Pith reviewed 2026-05-20 03:00 UTC · model grok-4.3

classification ⚛️ physics.atom-ph
keywords spin asymmetrySherman functionelastic scatteringpolarized electronszinccadmiummercury
0
0 comments X

The pith

The calculation method for electron spin asymmetry extends directly to zinc, cadmium, and mercury.

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

This paper extends a prior calculation approach to determine the Sherman functions that quantify spin asymmetry in the elastic scattering of polarized electrons from zinc, cadmium, and mercury atoms. It generates a broad collection of theoretical predictions for different scattering angles and energies. The results show adequate agreement with available experimental measurements and other high-precision theoretical computations. A sympathetic reader cares because accurate spin asymmetry data helps in probing relativistic effects and spin-orbit couplings in atomic collisions.

Core claim

We present an extensive set of theoretical results for spin asymmetry in the form of Sherman functions for the elastic scattering of electrons by zinc, cadmium, and mercury. This study extends the application of our earlier method of calculations, which we previously employed for stable inert gases and alkaline-earth-metals to these three atoms. Our predictions are in adequate agreement with experimental values and precise theoretical results.

What carries the argument

The Sherman function, which describes the degree of spin asymmetry arising from the scattering process.

If this is right

  • The method proves applicable to these atoms without significant modifications.
  • The computed Sherman functions can serve as benchmarks for future experiments.
  • Agreement with data supports the reliability of the approach for these heavier atoms.

Where Pith is reading between the lines

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

  • Similar extensions might work for other atoms with comparable electronic structures.
  • These results could inform the design of experiments using spin-polarized electrons.

Load-bearing premise

The prior calculation method for inert gases and alkaline-earth metals transfers accurately to zinc, cadmium, and mercury without needing major adjustments or losing precision.

What would settle it

An experimental measurement of the Sherman function for electron scattering from mercury at a fixed energy and scattering angle that differs substantially from the predicted value.

Figures

Figures reproduced from arXiv: 2605.19222 by Constantine E. Theodosiou, Mehrdad Adibzadeh.

Figure 1
Figure 1. Figure 1: FIG. 1: Sherman function for electron scattering from zinc at 2, 3, 4 and 5 eV: The legend in the figure describes markers for [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Same as for figure [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparisons between present Sherman function values at 7 and 7.5 eV with those of 66-state RCCC [ [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: A three-dimensional view of Sherman function for electron scattering from zinc. [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Sherman function for electron scattering from cadmium at 0.3, 0.5, 1 and 2 eV: The legend in the figure describes [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Same as for figure [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Same as for figure [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Sherman function for electron scattering from cadmium at scattering angle 110 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: A three-dimensional view of Sherman function for electron scattering from cadmium. [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Sherman function for electron scattering from mercury at 1, 1.5, 1.9 and 2.4 eV: The legend in the figure describes [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Same as for figure [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Same as for figure [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Same as for figure [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p019_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p022_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: FIG. 19: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p023_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: FIG. 20: Sherman function for electron scattering from mercury at 50 [PITH_FULL_IMAGE:figures/full_fig_p024_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: FIG. 21: Same as for figures [PITH_FULL_IMAGE:figures/full_fig_p025_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: FIG. 22: A three-dimensional view of Sherman function for electron scattering from mercury. [PITH_FULL_IMAGE:figures/full_fig_p026_22.png] view at source ↗
read the original abstract

We present an extensive set of theoretical results for spin asymmetry in the form of Sherman functions for the elastic scattering of electrons by zinc, cadmium, and mercury. This study extends the application of our earlier method of calculations, which we previously employed for stable inert gases and alkaline-earth-metals to these three atoms. Our predictions are in adequate agreement with experimental values and precise theoretical results.

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

2 major / 1 minor

Summary. The paper extends the authors' prior method for computing Sherman functions (spin asymmetries) in elastic scattering of polarized electrons, previously applied to inert gases and alkaline-earth atoms, to the targets Zn, Cd, and Hg. It reports an extensive set of theoretical predictions that are stated to be in adequate agreement with experimental values and other precise theoretical results.

Significance. If the central claim holds, the work supplies useful benchmark predictions for spin-dependent scattering from these heavy atoms with filled d-shells, extending the authors' earlier calculations to a new class of targets. No machine-checked proofs, reproducible code, or parameter-free derivations are described.

major comments (2)
  1. [Introduction / Method description] The central claim that the prior method applies directly and accurately to Zn, Cd, and Hg rests on the untested assumption that filled 3d/4d/5d shells do not require major adjustments to the scattering potential, correlation terms, or relativistic corrections. No explicit validation (e.g., comparison of results with and without d-shell contributions or tests against known d-shell effects in related systems) is provided to support transferability.
  2. [Abstract and Results] The abstract asserts 'adequate agreement' with experiment and precise theory, but without quantitative metrics (e.g., mean absolute deviations, chi-squared values, or tabulated comparisons in the results section) it is not possible to assess whether the agreement is sufficient to validate the extended calculations.
minor comments (1)
  1. [Figures and notation] Notation for the Sherman function and any energy-dependent plots should be clarified with explicit definitions and axis labels for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and outline the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [Introduction / Method description] The central claim that the prior method applies directly and accurately to Zn, Cd, and Hg rests on the untested assumption that filled 3d/4d/5d shells do not require major adjustments to the scattering potential, correlation terms, or relativistic corrections. No explicit validation (e.g., comparison of results with and without d-shell contributions or tests against known d-shell effects in related systems) is provided to support transferability.

    Authors: The referee is correct that the manuscript does not contain an explicit side-by-side comparison isolating d-shell contributions. Our relativistic optical-potential framework, detailed in the method section and in our earlier papers on inert gases and alkaline-earth atoms, constructs the scattering potential from the full Dirac-Fock electron density of the target; the filled d shells of Zn, Cd, and Hg are therefore already included in the static and exchange potentials as well as in the correlation and absorption terms. Because the same code and parameter choices were used without modification, the transferability is implicit. Nevertheless, to make this reasoning explicit we will insert a short paragraph in the introduction that recalls how the d-shell electrons enter the potential and notes that independent calculations for these atoms (cited in the paper) employ comparable treatments of the d shells. This addition will directly address the concern about untested assumptions. revision: yes

  2. Referee: [Abstract and Results] The abstract asserts 'adequate agreement' with experiment and precise theory, but without quantitative metrics (e.g., mean absolute deviations, chi-squared values, or tabulated comparisons in the results section) it is not possible to assess whether the agreement is sufficient to validate the extended calculations.

    Authors: We agree that the phrase 'adequate agreement' in the abstract is qualitative and that the results section would be improved by quantitative measures. Although the manuscript already presents graphical comparisons with experiment and with other theories, we will add a new table (or subsection) that reports mean absolute deviations and, where the data permit, root-mean-square deviations between our Sherman-function values and the experimental points as well as selected benchmark calculations. These numbers will be referenced from the abstract and discussed briefly in the text. The revision will allow readers to judge the level of agreement more objectively. revision: yes

Circularity Check

1 steps flagged

Minor self-citation for prior method; new results for Zn/Cd/Hg are independent applications

specific steps
  1. self citation load bearing [Abstract]
    "This study extends the application of our earlier method of calculations, which we previously employed for stable inert gases and alkaline-earth-metals to these three atoms."

    The applicability of the framework to atoms with filled d shells is justified by reference to the authors' own prior publications rather than by new verification steps internal to this manuscript.

full rationale

The paper extends a previously published computational method to three new atomic targets. The abstract explicitly frames the work as an application to Zn, Cd, and Hg, with new predictions checked against external experimental data and other theoretical results. No equations or steps are shown to reduce by construction to fitted parameters or prior outputs. The self-reference to the authors' earlier work on inert gases and alkaline-earth atoms is present but does not carry the central claim; the new Sherman-function values constitute independent content validated externally.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are described in the provided text.

pith-pipeline@v0.9.0 · 5583 in / 1001 out tokens · 46899 ms · 2026-05-20T03:00:55.813032+00:00 · methodology

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Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

  1. [1]

    Bartsch, H

    M. Bartsch, H. Geesmann, G. F. Hanne, and J. Kessler, Journal of Physics B: Atomic, Molecular and Optical Physics25, 1511 (1992), URLhttps://dx.doi.org/10.1088/0953-4075/25/7/021

    work page doi:10.1088/0953-4075/25/7/021 1992

  2. [2]

    R. P. McEachran and A. D. Stauffer, Journal of Physics B: Atomic, Molecular and Optical Physics25, 1527 (1992), URL https://dx.doi.org/10.1088/0953-4075/25/7/022

    work page doi:10.1088/0953-4075/25/7/022 1992

  3. [3]

    Kumar, A

    P. Kumar, A. K. Jain, A. N. Tripathi, and S. N. Nahar, Phys. Rev. A49, 899 (1994), URLhttps://link.aps.org/doi/ 10.1103/PhysRevA.49.899

    work page doi:10.1103/physreva.49.899 1994

  4. [4]

    Szmytkowski and J

    R. Szmytkowski and J. E. Sienkiewicz, Journal of Physics B: Atomic, Molecular and Optical Physics27, 555 (1994), URL https://dx.doi.org/10.1088/0953-4075/27/3/019

    work page doi:10.1088/0953-4075/27/3/019 1994

  5. [5]

    C. J. Bostock, D. V. Fursa, and I. Bray, Phys. Rev. A85, 062707 (2012), URLhttps://link.aps.org/doi/10.1103/ PhysRevA.85.062707

    work page 2012

  6. [6]

    S. N. Nahar, Phys. Rev. A43, 2223 (1991), URLhttps://link.aps.org/doi/10.1103/PhysRevA.43.2223

    work page doi:10.1103/physreva.43.2223 1991

  7. [7]

    M. J. Berrington, C. J. Bostock, D. V. Fursa, I. Bray, R. P. McEachran, and A. D. Stauffer, Phys. Rev. A85, 042708 (2012), URLhttps://link.aps.org/doi/10.1103/PhysRevA.85.042708

    work page doi:10.1103/physreva.85.042708 2012

  8. [8]

    M. M. Haque, A. K. Haque, M. A. Uddin, M. Maaza, M. A. R. Patoary, A. K. Basak, and B. C. Saha (Academic Press, 2021), vol. 84 ofAdvances in Quantum Chemistry, pp. 1–72, URLhttps://www.sciencedirect.com/science/article/ pii/S0065327620300046

    work page 2021

  9. [9]

    Deichsel, Zeitschrift f¨ ur Physik164, 156 (1961)

    H. Deichsel, Zeitschrift f¨ ur Physik164, 156 (1961)

    work page 1961

  10. [10]

    Jost and J

    K. Jost and J. Kessler, Zeitschrift f¨ ur Physik195, 1 (1966)

    work page 1966

  11. [11]

    Deichsel, E

    H. Deichsel, E. Reichert, and H. Steidl, Zeitschrift f¨ ur Physik189, 212 (1966)

    work page 1966

  12. [12]

    Eitel, K

    W. Eitel, K. Jost, and J. Kessler, Phys. Rev.159, 47 (1967), URLhttps://link.aps.org/doi/10.1103/PhysRev.159.47

    work page doi:10.1103/physrev.159.47 1967

  13. [13]

    Eitel and J

    W. Eitel and J. Kessler, Zeitschrift f¨ ur Physik A Hadrons and nuclei241, 355 (1971)

    work page 1971

  14. [14]

    Hanne, K

    G. Hanne, K. Jost, and J. Kessler, Zeitschrift f¨ ur Physik252, 141 (1972)

    work page 1972

  15. [15]

    D¨ uweke, N

    M. D¨ uweke, N. Kirchner, E. Reichert, and S. Sch¨ on, Journal of Physics B: Atomic and Molecular Physics9, 1915 (1976), URLhttps://dx.doi.org/10.1088/0022-3700/9/11/017

    work page doi:10.1088/0022-3700/9/11/017 1915

  16. [16]

    Albert, C

    K. Albert, C. Christian, T. Heindorff, E. Reichert, and S. Sch¨ on, Journal of Physics B: Atomic and Molecular Physics10, 3733 (1977), URLhttps://doi.org/10.1088/0022-3700/10/18/029

    work page doi:10.1088/0022-3700/10/18/029 1977

  17. [17]

    G. F. Hanne, K. J. Kollath, and W. Wubker, Journal of Physics B: Atomic and Molecular Physics13, L395 (1980), URL https://dx.doi.org/10.1088/0022-3700/13/12/009

    work page doi:10.1088/0022-3700/13/12/009 1980

  18. [18]

    Berger, J

    O. Berger, J. Kessler, K. J. Kollath, R. M¨ ollenkamp, and W. W¨ ubker, Phys. Rev. Lett.46, 768 (1981), URLhttps: //link.aps.org/doi/10.1103/PhysRevLett.46.768

    work page doi:10.1103/physrevlett.46.768 1981

  19. [19]

    M¨ ollenkamp, W

    R. M¨ ollenkamp, W. W¨ ubker, O. Berger, K. Jost, and J. Kessler, Journal of Physics B: Atomic and Molecular Physics17, 1107 (1984), URLhttps://doi.org/10.1088/0022-3700/17/6/022

    work page doi:10.1088/0022-3700/17/6/022 1984

  20. [20]

    Berger and J

    O. Berger and J. Kessler, Journal of Physics B: Atomic and Molecular Physics19, 3539 (1986), URLhttps://dx.doi. org/10.1088/0022-3700/19/21/018

    work page doi:10.1088/0022-3700/19/21/018 1986

  21. [21]

    Kaussen, H

    F. Kaussen, H. Geesmann, G. F. Hanne, and J. Kessler, Journal of Physics B: Atomic and Molecular Physics20, 151 (1987), URLhttps://dx.doi.org/10.1088/0022-3700/20/1/018

    work page doi:10.1088/0022-3700/20/1/018 1987

  22. [22]

    D¨ ummler, M

    M. D¨ ummler, M. Bartsch, H. Geesmann, G. F. Hanne, and J. Kessler, Journal of Physics B: Atomic, Molecular and Optical Physics25, 4281 (1992), URLhttps://dx.doi.org/10.1088/0953-4075/25/20/022

    work page doi:10.1088/0953-4075/25/20/022 1992

  23. [23]

    P. J. Bunyan, Proceedings of the Physical Society81, 816 (1963), URLhttps://doi.org/10.1088/0370-1328/81/5/304

    work page doi:10.1088/0370-1328/81/5/304 1963

  24. [24]

    P. J. Bunyan and J. L. Schonfelder, Proceedings of the Physical Society85, 455 (1965), URLhttps://doi.org/10.1088/ 0370-1328/85/3/306

    work page 1965

  25. [25]

    Fink and A

    M. Fink and A. C. Yates, Atomic Data and Nuclear Data Tables1, 385 (1969), ISSN 0092-640X, URLhttps://www. sciencedirect.com/science/article/pii/S0092640X6980029X. 6

    work page 1969

  26. [26]

    Bartschat, K

    K. Bartschat, K. Blum, P. G. Burke, G. F. Hanne, and N. S. Scott, Journal of Physics B: Atomic and Molecular Physics 17, 3797 (1984), URLhttps://doi.org/10.1088/0022-3700/17/18/016

    work page doi:10.1088/0022-3700/17/18/016 1984

  27. [27]

    Haberland and L

    R. Haberland and L. Fritsche, Journal of Physics B: Atomic and Molecular Physics20, 121 (1987), URLhttps://dx.doi. org/10.1088/0022-3700/20/1/016

    work page doi:10.1088/0022-3700/20/1/016 1987

  28. [28]

    R. P. McEachran and A. D. Stauffer, Journal of Physics B: Atomic and Molecular Physics20, 5517 (1987), URLhttps: //dx.doi.org/10.1088/0022-3700/20/20/027

    work page doi:10.1088/0022-3700/20/20/027 1987

  29. [29]

    J. E. Sienkiewicz, Journal of Physics B: Atomic, Molecular and Optical Physics23, 1869 (1990), URLhttps://dx.doi. org/10.1088/0953-4075/23/11/020

    work page doi:10.1088/0953-4075/23/11/020 1990

  30. [30]

    Fritsche, C

    L. Fritsche, C. Kroner, and T. Reinert, Journal of Physics B: Atomic, Molecular and Optical Physics25, 4287 (1992), URLhttps://dx.doi.org/10.1088/0953-4075/25/20/023

    work page doi:10.1088/0953-4075/25/20/023 1992

  31. [31]

    V. I. Kelemen and E. Y. Remeta, Journal of Physics B: Atomic, Molecular and Optical Physics45, 185202 (2012), URL https://dx.doi.org/10.1088/0953-4075/45/18/185202

    work page doi:10.1088/0953-4075/45/18/185202 2012

  32. [32]

    A. K. F. Haque, M. M. Haque, P. P. Bhattacharjee, M. A. Uddin, M. A. R. Patoary, M. I. Hossain, A. K. Basak, M. S. Mahbub, M. Maaza, and B. C. Saha, Journal of Physics Communications1, 035014 (2017), URLhttps://doi.org/10. 1088/2399-6528/aa8bf8

    work page 2017

  33. [33]

    Adibzadeh and C

    M. Adibzadeh and C. E. Theodosiou, Atomic Data and Nuclear Data Tables91, 8 (2005), ISSN 0092-640X, URLhttps: //www.sciencedirect.com/science/article/pii/S0092640X05000343

    work page 2005

  34. [34]

    Adibzadeh and C

    M. Adibzadeh and C. E. Theodosiou, Phys. Rev. A70, 052704 (2004), URLhttps://link.aps.org/doi/10.1103/ PhysRevA.70.052704

    work page 2004

  35. [35]

    Adibzadeh, C

    M. Adibzadeh, C. E. Theodosiou, and N. J. Harmon, Atoms12(2024), ISSN 2218-2004, URLhttps://www.mdpi.com/ 2218-2004/12/6/33

    work page 2024

  36. [36]

    J. B. Furness and I. E. McCarthy, Journal of Physics B: Atomic and Molecular Physics6, 2280 (1973), URLhttps: //dx.doi.org/10.1088/0022-3700/6/11/021

    work page doi:10.1088/0022-3700/6/11/021 1973

  37. [37]

    D. Kolb, W. R. Johnson, and P. Shorer, Phys. Rev. A26, 19 (1982), URLhttps://link.aps.org/doi/10.1103/PhysRevA. 26.19

    work page doi:10.1103/physreva 1982

  38. [38]

    Sherman, Phys

    N. Sherman, Phys. Rev.103, 1601 (1956), URLhttps://link.aps.org/doi/10.1103/PhysRev.103.1601

    work page doi:10.1103/physrev.103.1601 1956

  39. [39]

    Kessler, Rev

    J. Kessler, Rev. Mod. Phys.41, 3 (1969), URLhttps://link.aps.org/doi/10.1103/RevModPhys.41.3

    work page doi:10.1103/revmodphys.41.3 1969

  40. [40]

    Salvat, J

    F. Salvat, J. Fern´ andez-Varea, and W. Williamson, Computer Physics Communications90, 151 (1995), ISSN 0010-4655, URLhttps://www.sciencedirect.com/science/article/pii/001046559500039I

    work page arXiv 1995

  41. [41]

    C. J. Bostock, M. J. Berrington, D. V. Fursa, and I. Bray, Phys. Rev. Lett.107, 093202 (2011), URLhttps://link.aps. org/doi/10.1103/PhysRevLett.107.093202. 7 -0.2 -0.1 0 0.1 0.2 3 eV Bartsch et al. RDW 1 RDW 2 RCCC Present -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0 30 60 90 120 150 180 Angle (deg) 5 eV -0.3 -0.2 -0.1 0 0.1 0.2 0.3S 2 eV -0.4 -0.3 -0.2 ...

    work page doi:10.1103/physrevlett.107.093202 2011