pith. sign in

arxiv: 2603.03044 · v2 · pith:IAPVG6FCnew · submitted 2026-03-03 · ⚛️ nucl-th · astro-ph.HE· hep-ph· nucl-ex

Effects of isovector spin-orbit interaction on the charge-weak form factor difference in ⁴⁸Ca, ²⁰⁸Pb, ⁹⁰Zr and ⁶²Ni

Tong-Gang Yue , Zhen Zhang , Lie-Wen Chen This is my paper

Pith reviewed 2026-05-15 16:40 UTC · model grok-4.3

classification ⚛️ nucl-th astro-ph.HEhep-phnucl-ex
keywords isovector spin-orbit interactioncharge-weak form factor differenceSkyrme energy density functionalparity-violating electron scatteringsymmetry energynuclear structure48Ca208Pb
0
0 comments X

The pith

Charge-weak form factor differences in 48Ca and 90Zr respond strongly to isovector spin-orbit strength while those in 208Pb and 62Ni do not.

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

The paper shows that the isovector spin-orbit interaction affects the charge-weak form factor difference in a nucleus-dependent way within extended Skyrme energy density functionals. Nuclei with particular neutron configurations, such as the ten unpaired 1g9/2 neutrons in 90Zr or the structure in 48Ca, exhibit high sensitivity because the interaction modifies the central mean-field potential. In contrast, 208Pb and 62Ni display low sensitivity. A sympathetic reader would care because this distinction points to an experimental approach for separating constraints on the spin-orbit channel from those on the symmetry energy using parity-violating electron scattering.

Core claim

Within the framework of extended Skyrme EDFs, the charge-weak form factor difference ΔF_CW in 48Ca exhibits remarkable sensitivity to the effective isovector spin-orbit interaction, whereas in 208Pb it is much less sensitive. Extending the analysis, 90Zr shows similar sensitivity due to its ten spin-orbit unpaired 1g9/2 neutrons leading to modifications in the central mean-field potential, while 62Ni remains largely insensitive like 208Pb. This structure-driven distinction allows future measurements to target specific nuclei for constraining IVSO strength or probing symmetry energy density dependence.

What carries the argument

The charge-weak form factor difference ΔF_CW, which is sensitive to the isovector spin-orbit interaction through changes in the central mean-field potential induced by unpaired neutrons in specific nuclear shells.

If this is right

  • Future parity-violating electron scattering on 48Ca and 90Zr can constrain the effective IVSO strength.
  • Measurements on 208Pb and 62Ni can provide a cleaner probe of the symmetry energy density dependence with reduced IVSO effects.
  • The sensitivity in 90Zr arises similarly to 48Ca from central potential modifications rather than direct one-body spin-orbit effects.
  • This suggests prioritizing certain nuclei in experiments like MREX at MESA to isolate different nuclear parameters.

Where Pith is reading between the lines

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

  • Similar structure-based selection could apply to other nuclei for disentangling EDF parameters in future work.
  • The findings might inform refinements in Skyrme EDFs by highlighting the role of shell effects in form factor observables.
  • Experimental confirmation could open ways to test isovector components across a broader set of nuclear interactions.

Load-bearing premise

The extended Skyrme energy density functional correctly captures the modifications to the central mean-field potential caused by variations in the isovector spin-orbit strength for these nuclei.

What would settle it

A parity-violating electron scattering experiment on 48Ca or 90Zr that finds no dependence of the charge-weak form factor difference on the isovector spin-orbit strength would contradict the calculated sensitivities.

Figures

Figures reproduced from arXiv: 2603.03044 by Lie-Wen Chen, Tong-Gang Yue, Zhen Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Single-particle energy levels for [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Orbital contributions to [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Momentum-transfer dependence of ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

The nucleon spin-orbit interaction is a cornerstone of nuclear structure theory, yet its isospin dependence remains insufficiently constrained within modern nuclear energy density functional (EDF) theory. It was recently shown that, within the framework of extended Skyrme EDFs, the charge-weak form factor difference $\Delta F_{\rm CW}$ in $^{48}$Ca exhibits remarkable sensitivity to the effective isovector spin-orbit (IVSO) interaction, whereas $\Delta F_{\rm CW}$ in $^{208}$Pb is much less sensitive to this channel. Extending this analysis to other nuclei, we find that $^{90}$Zr, with its ten spin-orbit unpaired $1\mathrm{g}_{9/2}$ neutrons, displays a $\Delta F_{\rm CW}$ sensitivity to the IVSO strength similar to that of $^{48}$Ca, arising from modifications to the central mean-field potential rather than the one-body spin-orbit potential. In contrast, $^{62}$Ni, like $^{208}$Pb, remains largely insensitive to the IVSO interaction. This structure-driven distinction suggests an experimental strategy: future parity-violating electron scattering measurements, e.g., the MREX experiment at the MESA facility, on $^{48}$Ca and $^{90}$Zr would help constrain the effective IVSO strength, while measurements on $^{208}$Pb and $^{62}$Ni can provide a cleaner probe of the density dependence of the symmetry energy with reduced IVSO sensitivity.

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 / 2 minor

Summary. The paper uses extended Skyrme energy density functionals to study how variations in the isovector spin-orbit (IVSO) strength affect the charge-weak form factor difference ΔF_CW in 48Ca, 208Pb, 90Zr, and 62Ni. It reports that 48Ca and 90Zr (the latter due to its unpaired 1g9/2 neutrons) show strong sensitivity arising from IVSO-induced shifts in the central mean-field potential rather than the one-body spin-orbit term, while 208Pb and 62Ni remain largely insensitive. This leads to a proposed experimental strategy: parity-violating electron scattering on 48Ca and 90Zr (e.g., MREX at MESA) to constrain IVSO, versus 208Pb and 62Ni to probe symmetry-energy density dependence with reduced IVSO contamination.

Significance. If the central-mechanism claim and nucleus-by-nucleus pattern hold under quantitative checks, the work supplies a concrete, structure-based guide for allocating future weak-form-factor measurements to separate IVSO and symmetry-energy effects within EDF frameworks. It also illustrates how a single EDF parameter can produce qualitatively different responses across closed- and open-shell nuclei, which could inform parametrization strategies for isovector channels.

major comments (2)
  1. [Results] The central claim that ΔF_CW sensitivity in 48Ca and 90Zr is driven by central-mean-field modifications (rather than direct spin-orbit contributions) is load-bearing for the experimental strategy, yet the abstract and available description provide no quantitative decomposition (e.g., separate runs with IVSO toggled only in central vs. spin-orbit terms or explicit potential-difference plots). Without such evidence, the reported nucleus-specific pattern cannot be verified as emergent rather than parametrization-dependent.
  2. [Methods] The extended Skyrme EDF framework is asserted to map IVSO strength changes faithfully onto central-potential shifts in these nuclei, but no tests of effective-mass consistency, higher-order density dependencies, or comparison against ab-initio benchmarks are mentioned. If these mappings are incomplete, the predicted distinction between sensitive (48Ca, 90Zr) and insensitive (208Pb, 62Ni) nuclei would not hold.
minor comments (2)
  1. Notation for ΔF_CW should be defined explicitly at first use, including the precise kinematic and isospin weighting employed in the form-factor difference.
  2. The manuscript would benefit from a table listing the specific IVSO strength values varied and the resulting ΔF_CW changes for each nucleus to allow direct 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 the major comments point by point below. Revisions will be incorporated to strengthen the quantitative support for our claims.

read point-by-point responses

  1. Referee: [Results] The central claim that ΔF_CW sensitivity in 48Ca and 90Zr is driven by central-mean-field modifications (rather than direct spin-orbit contributions) is load-bearing for the experimental strategy, yet the abstract and available description provide no quantitative decomposition (e.g., separate runs with IVSO toggled only in central vs. spin-orbit terms or explicit potential-difference plots). Without such evidence, the reported nucleus-specific pattern cannot be verified as emergent rather than parametrization-dependent.

    Authors: We agree that a quantitative decomposition is necessary to substantiate the central claim. In the revised manuscript we will add explicit calculations in which the IVSO strength is varied only in the central mean-field terms while keeping the spin-orbit term fixed, and vice versa. We will also include plots of the resulting differences in the central and spin-orbit potentials for 48Ca and 90Zr. These additions will demonstrate that the sensitivity of ΔF_CW arises from the self-consistent readjustment of the central potential rather than direct one-body spin-orbit effects. revision: yes

  2. Referee: [Methods] The extended Skyrme EDF framework is asserted to map IVSO strength changes faithfully onto central-potential shifts in these nuclei, but no tests of effective-mass consistency, higher-order density dependencies, or comparison against ab-initio benchmarks are mentioned. If these mappings are incomplete, the predicted distinction between sensitive (48Ca, 90Zr) and insensitive (208Pb, 62Ni) nuclei would not hold.

    Authors: The extended Skyrme functional employed here incorporates the IVSO term consistently with the overall density dependence of the EDF, and the self-consistent Hartree-Fock solutions automatically include the effective-mass effects generated by the functional. We will add a brief discussion of the effective-mass values obtained for the four nuclei and their variation with IVSO strength. Systematic tests of higher-order density dependencies and direct comparisons with ab-initio calculations lie outside the scope of the present phenomenological study, which focuses on sensitivities within a single, well-defined EDF framework. The nucleus-specific pattern we report is robust under the parameter variations performed within this model. revision: partial

Circularity Check

1 steps flagged

Minor self-citation of prior EDF sensitivity results; new nucleus-specific calculations remain independent

specific steps
  1. other [Abstract]
    "It was recently shown that, within the framework of extended Skyrme EDFs, the charge-weak form factor difference ΔF_CW in 48Ca exhibits remarkable sensitivity to the effective isovector spin-orbit (IVSO) interaction, whereas ΔF_CW in 208Pb is much less sensitive to this channel. Extending this analysis to other nuclei, we find that 90Zr... displays a ΔF_CW sensitivity to the IVSO strength similar to that of 48Ca..."

    The baseline sensitivity distinction is referenced via self-citation to the authors' earlier work. Because the present manuscript then carries out fresh calculations for the additional nuclei rather than deriving the pattern from the citation alone, the self-reference is minor and does not render the reported results circular.

full rationale

The paper performs explicit parameter variations of the IVSO strength inside an established extended Skyrme EDF and reports the resulting ΔF_CW values for 90Zr and 62Ni. These are direct model outputs rather than quantities forced by construction or renamed fits. The single self-citation to prior work on 48Ca and 208Pb merely supplies context for the extension and does not carry the central claims about nucleus-by-nucleus sensitivity patterns or the proposed experimental strategy.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the extended Skyrme EDF model accurately translates changes in the isovector spin-orbit coupling into modifications of the central potential; the IVSO strength itself functions as a free parameter that is varied to map sensitivity.

free parameters (1)
  • IVSO strength parameter
    The effective isovector spin-orbit coupling constant is varied across a range to quantify its effect on the form factor difference.
axioms (1)
  • domain assumption Extended Skyrme energy density functional framework correctly describes the mean-field potentials in the studied nuclei
    All sensitivity results are obtained inside this modeling framework.

pith-pipeline@v0.9.0 · 5592 in / 1408 out tokens · 35908 ms · 2026-05-15T16:40:09.541609+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    [19], the sensitivity of 48Ca to the IVSO interaction originates from the eight neutrons occupying the 1f 7/2 orbital

    48Ca and 208Pb As elucidated in Ref. [19], the sensitivity of 48Ca to the IVSO interaction originates from the eight neutrons occupying the 1f 7/2 orbital. This distinction between 48Ca and 208Pb can be traced to the IVSO energy term bIV 2 ˜J· ∇˜ρin Eq. (10). As shown in Ref. [19], in 48Ca, all proton spin-orbit partners are filled, while the neu- tron 1f...

    work page

  2. [2]

    [19] to analyze the contribution of single-particle orbitals to the IVSO term in the energy density (Eq

    90Zr and 62Ni Following the same line of reasoning used in Ref. [19] to analyze the contribution of single-particle orbitals to the IVSO term in the energy density (Eq. (10)), one can infer that nuclei with a spin-orbit pattern analogous to 48Ca, such as 90Zr, should also exhibit sensitivity to the IVSO interaction in their ∆F CW values. Conversely, nu- c...

    work page

  3. [3]

    L. H. Thomas, The motion of a spinning electron, Nature 117, 514 (1926)

    work page 1926

  4. [4]

    P. A. M. Dirac, The quantum theory of the electron, Proc. Roy. Soc. Lond. A117, 610 (1928)

    work page 1928

  5. [5]

    Liang and X.-N

    Z.-T. Liang and X.-N. Wang, Globally polarized quark- gluon plasma in non-central A+A collisions, Phys. Rev. Lett.94, 102301 (2005), [Erratum: Phys.Rev.Lett. 96, 039901 (2006)]

    work page 2005

  6. [6]

    Adamczyket al.(STAR), Global Λ hyperon polariza- tion in nuclear collisions: evidence for the most vortical fluid, Nature548, 62 (2017)

    L. Adamczyket al.(STAR), Global Λ hyperon polariza- tion in nuclear collisions: evidence for the most vortical fluid, Nature548, 62 (2017)

    work page 2017

  7. [7]

    Bihlmayer, P

    G. Bihlmayer, P. Noel, D. V. Vyalikh, E. V. Chulkov, and A. Manchon, Rashba-like physics in condensed matter, Nature Rev. Phys.4, 642– (2022)

    work page 2022

  8. [8]

    K. Y. Bliokh, F. J. Rodr´ ıguez-Fortu˜ no, F. Nori, and A. V. Zayats, Spin–orbit interactions of light, Nature Photon. 9, 796 (2015)

    work page 2015

  9. [9]

    S. A. Goudschmidt and G. H. Uhlenbeck, Spinning elec- trons and the structure of spectra, Nature117, 264 (1926)

    work page 1926

  10. [10]

    M. G. Mayer, On closed shells in nuclei. 2, Phys. Rev. 75, 1969 (1949)

    work page 1969

  11. [11]

    Haxel, J

    O. Haxel, J. H. D. Jensen, and H. E. Suess, On the ”Magic Numbers” in Nuclear Structure, Phys. Rev.75, 1766 (1949)

    work page 1949

  12. [12]

    V. I. Isakov, K. I. Erokhina, H. Mach, M. Sanchez-Vega, and B. Fogelberg, On the difference between proton and neutron spin orbit splittings in nuclei, Eur. Phys. J. A 14, 29 (2002)

    work page 2002

  13. [13]

    Lesinski, M

    T. Lesinski, M. Bender, K. Bennaceur, T. Duguet, and J. Meyer, The Tensor part of the Skyrme energy density functional. I. Spherical nuclei, Phys. Rev. C76, 014312 (2007)

    work page 2007

  14. [14]

    Klupfel, P

    P. Klupfel, P. G. Reinhard, T. J. Burvenich, and J. A. Maruhn, Variations on a theme by Skyrme: A systematic study of adjustments of model parameters, Phys. Rev. C 79, 034310 (2009)

    work page 2009

  15. [15]

    Bender, P.-H

    M. Bender, P.-H. Heenen, and P.-G. Reinhard, Self- consistent mean-field models for nuclear structure, Rev. Mod. Phys.75, 121 (2003)

    work page 2003

  16. [16]

    M. M. Sharma, G. Lalazissis, J. Konig, and P. Ring, Isospin Dependence of the Spin-Orbit Force and Effective Nuclear Potentials, Phys. Rev. Lett.74, 3744 (1995)

    work page 1995

  17. [17]

    Reinhard and H

    P.-G. Reinhard and H. Flocard, Nuclear effective forces and isotope shifts, Nuclear Physics A584, 467488 (1995)

    work page 1995

  18. [18]

    J. P. Ebran, A. Mutschler, E. Khan, and D. Vrete- nar, Spin-orbit interaction in relativistic nuclear struc- ture models, Phys. Rev. C94, 024304 (2016)

    work page 2016

  19. [19]

    Vautherin and D

    D. Vautherin and D. M. Brink, Hartree-Fock calculations with Skyrme’s interaction. 1. Spherical nuclei, Phys. Rev. C5, 626 (1972)

    work page 1972

  20. [20]

    Adhikariet al.(CREX), Precision Determination of the Neutral Weak Form Factor of Ca48, Phys

    D. Adhikariet al.(CREX), Precision Determination of the Neutral Weak Form Factor of Ca48, Phys. Rev. Lett. 129, 042501 (2022)

    work page 2022

  21. [21]

    T.-G. Yue, Z. Zhang, and L.-W. Chen, Evidence for strong isovector nuclear spin-orbit interaction, Sci. Bull. 10.1016/j.scib.2026.01.062 (2024)

    work page doi:10.1016/j.scib.2026.01.062 2026

  22. [22]

    Reinhard, X

    P.-G. Reinhard, X. Roca-Maza, and W. Nazarewicz, Combined Theoretical Analysis of the Parity-Violating Asymmetry for Ca48 and Pb208, Phys. Rev. Lett.129, 232501 (2022)

    work page 2022

  23. [23]

    Y¨ uksel and N

    E. Y¨ uksel and N. Paar, Implications of parity-violating electron scattering experiments on 48Ca (CREX) and 208Pb (PREX-II) for nuclear energy density functionals, Phys. Lett. B836, 137622 (2023)

    work page 2023

  24. [24]

    Zhang and L.-W

    Z. Zhang and L.-W. Chen, Bayesian inference of the sym- metry energy and the neutron skin in Ca48 and Pb208 from CREX and PREX-2, Phys. Rev. C108, 024317 (2023)

    work page 2023

  25. [25]

    Mondal and F

    C. Mondal and F. Gulminelli, Nucleonic metamodeling in light of multimessenger, PREX-II, and CREX data, Phys. Rev. C107, 015801 (2023)

    work page 2023

  26. [26]

    Tagami, T

    S. Tagami, T. Wakasa, and M. Yahiro, Slope parame- ters determined from CREX and PREX2 (published in Results in Physics) 10.48550/arXiv.2210.03313 (2022)

    work page doi:10.48550/arxiv.2210.03313 2022

  27. [27]

    Miyatsu, M.-K

    T. Miyatsu, M.-K. Cheoun, K. Kim, and K. Saito, Can the PREX-2 and CREX results be understood by rel- ativistic mean-field models with the astrophysical con- straints?, Phys. Lett. B843, 138013 (2023)

    work page 2023

  28. [28]

    Sammarruca, The Neutron Skin of 48Ca and 208Pb: A Critical Analysis, Symmetry16, 34 (2024)

    F. Sammarruca, The Neutron Skin of 48Ca and 208Pb: A Critical Analysis, Symmetry16, 34 (2024)

    work page 2024

  29. [29]

    Papakonstantinou, Nuclear symmetry energy and the PREX-CREX neutron skin puzzle within the KIDS framework (2022) arXiv:2210.02696 [nucl-th]

    P. Papakonstantinou, Nuclear symmetry energy and the PREX-CREX neutron skin puzzle within the KIDS framework (2022) arXiv:2210.02696 [nucl-th]

    work page arXiv 2022

  30. [30]

    Kumar, S

    M. Kumar, S. Kumar, V. Thakur, R. Kumar, B. K. Agrawal, and S. K. Dhiman, CREX- and PREX-II- motivated relativistic interactions and their implications for the bulk properties of nuclear matter and neutron stars, Phys. Rev. C107, 055801 (2023)

    work page 2023

  31. [31]

    J. M. Lattimer, Constraints on Nuclear Symmetry En- ergy Parameters, Particles6, 30 (2023)

    work page 2023

  32. [32]

    Liliani, A

    N. Liliani, A. M. Nugraha, J. P. Diningrum, and A. Su- laksono, Tensor and isovector–isoscalar terms of relativis- tic mean field model: Impacts on neutron-skin thickness, charge radius, and nuclear matter, Nucl. Phys. A1042, 122812 (2024)

    work page 2024

  33. [33]

    Kunjipurayil, J

    A. Kunjipurayil, J. Piekarewicz, and M. Salinas, Role of the isovector spin-orbit potential in mitigating the CREX-PREX dilemma, Phys. Rev. C112, 014310 (2025)

    work page 2025

  34. [34]

    T. Zhao, Z. Lin, B. Kumar, A. W. Steiner, and M. Prakash, Characterizing the nuclear models informed by PREX and CREX: A view from Bayesian inference, Phys. Rev. Res.7, 043335 (2025)

    work page 2025

  35. [35]

    Qiu, T.-G

    M. Qiu, T.-G. Yue, Z. Zhang, and L.-W. Chen, Resolving the PREX-CREX puzzle in covariant density functional theory, (2025)

    work page 2025

  36. [36]

    Chamel, S

    N. Chamel, S. Goriely, and J. M. Pearson, Further explo- rations of Skyrme-Hartree-Fock-Bogoliubov mass formu- las. XI. Stabilizing neutron stars against a ferromagnetic collapse, Phys. Rev. C80, 065804 (2009)

    work page 2009

  37. [37]

    Stancu, D

    F. Stancu, D. M. Brink, and H. Flocard, The tensor part of Skyrme’s interaction, Phys. Lett. B68, 108 (1977)

    work page 1977

  38. [38]

    Chabanat, J

    E. Chabanat, J. Meyer, P. Bonche, R. Schaeffer, and P. Haensel, A Skyrme parametrization from subnuclear to neutron star densities, Nucl. Phys. A627, 710 (1997)

    work page 1997

  39. [39]

    Zhang and L.-W

    Z. Zhang and L.-W. Chen, Extended Skyrme interactions for nuclear matter, finite nuclei and neutron stars, Phys. Rev. C94, 064326 (2016)

    work page 2016

  40. [40]

    M. V. Stoitsov, J. Dobaczewski, W. Nazarewicz, and P. Ring, Axially deformed solution of the Skyrme- Hartree-Fock-Bogolyubov equations using the trans- 10 formed harmonic oscillator basis: The Program HF- BTHO (v1.66p), Comput. Phys. Commun.167, 43 (2005)

    work page 2005

  41. [41]

    Reinhard, X

    P.-G. Reinhard, X. Roca-Maza, and W. Nazarewicz, In- formation Content of the Parity-Violating Asymmetry in Pb208, Phys. Rev. Lett.127, 232501 (2021)

    work page 2021

  42. [42]

    Achaet al.(HAPPEX), Precision Measurements of the Nucleon Strange Form Factors at Q**2 ˜ 0.1-GeV**2, Phys

    A. Achaet al.(HAPPEX), Precision Measurements of the Nucleon Strange Form Factors at Q**2 ˜ 0.1-GeV**2, Phys. Rev. Lett.98, 032301 (2007)

    work page 2007

  43. [43]

    J. Liu, R. D. McKeown, and M. J. Ramsey-Musolf, Global Analysis of Nucleon Strange Form Factors at Low Q**2, Phys. Rev. C76, 025202 (2007)

    work page 2007

  44. [44]

    Alexandrou, S

    C. Alexandrou, S. Bacchio, M. Constantinou, J. Finken- rath, K. Hadjiyiannakou, K. Jansen, and G. Koutsou, Nucleon strange electromagnetic form factors, Phys. Rev. D101, 031501 (2020)

    work page 2020

  45. [45]

    Adhikariet al.(PREX), Accurate Determination of the Neutron Skin Thickness of 208Pb through Parity- Violation in Electron Scattering, Phys

    D. Adhikariet al.(PREX), Accurate Determination of the Neutron Skin Thickness of 208Pb through Parity- Violation in Electron Scattering, Phys. Rev. Lett.126, 172502 (2021)

    work page 2021

  46. [46]

    Bender, K

    M. Bender, K. Rutz, P. G. Reinhard, and J. A. Maruhn, Pairing gaps from nuclear mean field models, Eur. Phys. J. A8, 59 (2000)

    work page 2000

  47. [47]

    National Nuclear Data Center, information extracted from the NuDat database,https://www.nndc.bnl.gov/ nudat/

    work page

  48. [48]

    Schlimmeet al., The MESA physics program, EPJ Web Conf.303, 06002 (2024)

    S. Schlimmeet al., The MESA physics program, EPJ Web Conf.303, 06002 (2024)

    work page 2024

  49. [49]

    Esseret al., Beam-Normal Single-Spin Asymmetry in Pb208 at Low Energy: Discrepancy Resolved or New Kinematic Puzzle?, Phys

    A. Esseret al., Beam-Normal Single-Spin Asymmetry in Pb208 at Low Energy: Discrepancy Resolved or New Kinematic Puzzle?, Phys. Rev. Lett.135, 232502 (2025)

    work page 2025

  50. [50]

    Galet al., Nuclear Dependence of Beam Normal Sin- gle Spin Asymmetry in Elastic Scattering from Nuclei, (2024)

    C. Galet al., Nuclear Dependence of Beam Normal Sin- gle Spin Asymmetry in Elastic Scattering from Nuclei, (2024)

    work page 2024

  51. [51]

    Ozawa, T

    A. Ozawa, T. Kobayashi, K. Suzuki, K. Yoshida, and I. Tanihata, A new magic number, N=16, Near to the neutron drip-line, Phys. Rev. Lett.84, 5493 (2000)

    work page 2000

  52. [52]

    Bechevaet al., N=14 Shell Closure in O-22 Viewed through a Neutron Sensitive Probe, Phys

    E. Bechevaet al., N=14 Shell Closure in O-22 Viewed through a Neutron Sensitive Probe, Phys. Rev. Lett.96, 012501 (2006)

    work page 2006

  53. [53]

    K. Yako, H. Sagawa, and H. Sakai, Neutron skin thickness of Zr-90 determined by charge exchange reactions, Phys. Rev. C74, 051303 (2006)

    work page 2006

  54. [54]

    Zhanget al.(Super-FRS), A new approach for deduc- ing rms proton radii from charge-changing reactions of neutron-rich nuclei and the reaction-target dependence, Sci

    J. Zhanget al.(Super-FRS), A new approach for deduc- ing rms proton radii from charge-changing reactions of neutron-rich nuclei and the reaction-target dependence, Sci. Bull.69, 1647 (2024)

    work page 2024

  55. [55]

    Hasan, M

    Z. Hasan, M. Imran, A. A. Usmani, and Z. A. Khan, Theoretical investigation of charge-changing cross sec- tion and interaction cross section for Be, B, C, N, O, and F isotopes on C12 at 200–1050 MeV/nucleon, Phys. Rev. C111, 064601 (2025)

    work page 2025