Pith. sign in

REVIEW 3 major objections 5 minor 54 references

By dropping the target–projectile antisymmetrizer, the NCSM/RGM method extends ab initio nuclear scattering to antiproton–nucleus systems, reproducing exact few-body benchmarks for deuteron, triton, and helium-3 targets and yielding converg

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Antiproton-deuteron, antiproton-triton, and antiproton-helium-3 scattering and antiprotonic-atom observables were computed with an adapted ab initio NCSM/RGM method, showing peripheral annihilation at about 2 fm.

T0 review reviewed 2026-08-02 challenge →

load-bearing objection First NCSM/RGM for antiproton-nucleus systems, with careful benchmarks and honest caveats — but the abstract oversells the uncertainty attribution, which the paper's own Faddeev comparisons contradict. the 3 major comments →

arxiv 2602.18162 v2 pith:WXLDMYCW submitted 2026-02-20 nucl-th

Light antiproton-nucleus systems at low energies with the ab initio NCSM/RGM method

Alireza Dehghani , Guillaume Hupin , Sofia Quaglioni , Petr Navr\'atil This is my paper
classification nucl-th PACS 25.43.+t21.60.Cs24.10.-i
keywords antiproton–nucleus scatteringNCSM/RGMab initio methodsoptical potentialscattering lengthsantiprotonic atomsannihilation densitylight nuclei
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

This paper extends the ab initio No-Core Shell Model combined with the Resonating Group Method (NCSM/RGM) to antiproton–nucleus systems. The key adaptation is to remove the antisymmetrizer between target nucleons and the antiproton projectile, which is allowed because antinucleons are not identical to nucleons; this simplifies the formalism substantially, making the norm kernel trivial. The authors compute phase shifts, scattering lengths, antiprotonic-atom level shifts and widths, nuclear quasi-bound energies, and annihilation densities for antiproton + deuteron, triton, and helium-3, benchmarking against exact few-body solutions. Their central claim is that NCSM/RGM can be relied on for antinucleon–nucleus systems, with the dominant residual uncertainty attributed to the antiproton–nucleon interaction itself rather than to the many-body machinery. This matters because low-energy antiproton beams are now being used to probe nuclear surfaces, and this method provides a first-principles path to the observables those experiments measure.

Core claim

The paper claims that NCSM/RGM, with the target–projectile antisymmetrizer removed, is a reliable ab initio tool for antinucleon–nucleus systems. Using a complex optical antiproton–nucleon potential (a real meson-exchange part plus an absorptive term) and a bare chiral two-body nucleon–nucleon interaction, it produces converged low-energy phase shifts, scattering lengths, antiprotonic-atom level shifts and widths, nuclear quasi-bound energies, and annihilation densities for antiproton–deuteron, –triton, and –helium-3. The hard short-range components of the antiproton–nucleon interaction make the harmonic-oscillator expansion of the kernels converge slowly, so the authors introduce regulators

What carries the argument

The central object is the NCSM/RGM wave-function ansatz for an antiproton projectile: the total wave function is expanded as the antiproton in relative motion against a Jacobi-coordinate target state, with the inter-cluster antisymmetrizer dropped. Because the projectile is not identical to target nucleons, the norm kernel collapses to the identity and no exchange kernel appears, simplifying the coupled-channel equations. The Hamiltonian kernel is evaluated in a harmonic-oscillator basis for the relative motion; the hard short-range optical potential keeps matrix elements significant at large radial quantum numbers, so a smooth regulator is applied to the HO functions beyond the interaction

Load-bearing premise

The load-bearing premise is that a single cluster partition — the antiproton moving against the target in its ground state plus a few pseudo-states, with no explicit three-body rearrangement configurations — captures the low-energy dynamics well enough; if configurations such as antiproton–proton–neutron contribute significantly, the quoted scattering lengths and level shifts shift by the observed 4–23%.

What would settle it

Extend the NCSM/RGM expansion to include the rearrangement configurations present in the exact few-body solution (e.g., antiproton–proton–neutron or NbarN–nucleus channels) and recompute the antiproton–deuteron scattering length and the 1s level shift/width; if the results move outside the quoted few-percent/4–23% deviation band, the one-partition ansatz is the limiting assumption. Alternatively, measure the 1s level shift and half-width of antiprotonic deuterium with sub-keV precision and compare with the predicted values around 2.4 − 1.3i keV.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • NCSM/RGM becomes a practical ab initio route for antinucleon–nucleus observables, with the absent exchange kernel giving access to larger model spaces than nucleon–nucleus applications.
  • For heavier, more tightly bound targets the single-cluster picture should be more accurate, opening a path toward mid-mass nuclei that few-body methods cannot reach.
  • The annihilation density peaking near the nuclear surface supports using low-energy antiprotons as probes of the nuclear density tail rather than the interior.
  • With Coulomb switched off, the same machinery gives predictions for antineutron scattering on the same targets.
  • The regulator strategy offers a general recipe for treating hard short-range interactions in truncated harmonic-oscillator bases.

Where Pith is reading between the lines

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

  • If the residual 4–23% discrepancy comes from the missing three-body configurations, benchmarking the method against exact solutions for a better-bound target such as helium-4 would be a cleaner test of the underlying optical potential than the weakly bound deuteron.
  • The quasi-bound states are too short-lived to observe directly, but if one lands near a physical threshold it could measurably distort scattering observables — a possibility the paper flags without quantifying.
  • The predicted peripherality of annihilation could be tested by comparing pion-charge yields from different atomic states of the same antiprotonic atom; the paper notes this would connect annihilation observables to proton/neutron density distributions.
  • Applying the same regulator scheme to a softer (evolved) version of the antiproton–nucleon interaction and recovering the same observables without huge model spaces would corroborate that the hard potential, not the method, drives the slow convergence.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper extends the ab initio NCSM/RGM framework to antiproton-nucleus systems. Because the projectile is an antiproton, no target–projectile antisymmetrization is needed, which simplifies the norm kernel and removes exchange terms. The authors implement the formalism for pbar+d, pbar+3H, and pbar+3He using the Kohno–Weise optical NbarN potential and a bare N3LO NN interaction for the target. They compute phase shifts, scattering lengths, antiprotonic-atom level shifts and half-widths (both directly from bound-state R-matrix calculations and through the Trueman formula), nuclear quasi-bound states, cross sections, and annihilation densities. They introduce coordinate-space regulators to suppress finite-model-space artifacts caused by the hard short-range NbarN interaction in the HO expansion, and they benchmark against Faddeev calculations. The central claim is that NCSM/RGM can be relied on for antinucleon-nucleus systems, with residual uncertainties attributed primarily to the NbarN interaction.

Significance. If the method is validated, this would be the first ab initio many-body treatment of low-energy antiproton–nucleus interactions with a microscopic target description, opening a route to systems beyond exact few-body methods (e.g., A ~ 16 for PUMA). The paper contains useful internal consistency checks: bound-state R-matrix results and Trueman-formula results agree well, and Nmax convergence is documented for most observables. The benchmarking against Faddeev is a commendable feature and goes beyond what is typically done for many-body reaction methods. However, the paper's own benchmarks also reveal systematic deviations of 4–23% in A=3 atomic observables, which the text attributes to missing rearrangement configurations. This directly qualifies the strength of the central claim and the abstract's attribution of the dominant residual uncertainty to the NbarN interaction.

major comments (3)
  1. [Abstract & Sec. V.C / Table XI] The abstract states that benchmarking allows the dominant residual uncertainty to be attributed to the NbarN interaction. This is contradicted by Table XI, which shows 4–23% deviations for pbar-3H and 2–15% for pbar-3He relative to Faddeev calculations using the same NbarN interaction. Section V.C explicitly says these discrepancies 'cannot be removed solely by including extra target pseudo-states, indicating that missing configurations are involved.' These are method errors, not NbarN-model uncertainties. The conclusion's statement that NCSM/RGM 'can be relied on' is therefore too strong. Please quantify and separate the method uncertainty from the NbarN uncertainty, or restrict the reliability claim to observables and systems where the missing-configuration effect is demonstrated to be small.
  2. [Eq. (13) and Sec. V.B / Fig. 8] The NCSM/RGM ansatz in Eq. (13) contains only the pbar + target configuration. The paper acknowledges in Sec. V.B that 'the pbar p n dynamics may not be well represented by a pbar+d cluster configuration' and Fig. 8 shows the additional Faddeev configurations that are omitted. For a weakly bound target like the deuteron, this is a structural limitation, and the observed 4–23% deviations in A=3 systems indicate it is not benign. The paper argues the cluster picture improves for more tightly bound targets, but this is an untested extrapolation. Please state explicitly which claimed results are robust within the one-partition ansatz and which are subject to this known, unquantified error.
  3. [Sec. V.A / Fig. 6 vs. Sec. V.C] The regulator parameters r_reg and r_reg,c are essential to the numerical results: they are applied to all A=3 observables reported in Tables VII–XII and Figures 13–16. However, the only regulator-plateau demonstration in the manuscript is for pbar+d (Fig. 6). For pbar+3H and pbar+3He, the reader is referred to Ref. [38] (a PhD thesis) for details, but no in-manuscript evidence is shown that the A=3 results are independent of r_reg within a plateau. Since the regulator modifies the HO wave functions by hand, this is a load-bearing convergence check. Please include at least one regulator-plateau scan for pbar+3He or pbar+3H, or summarize the relevant content of Ref. [38] in the paper.
minor comments (5)
  1. [Table XI caption] The caption should state explicitly that both the NCSM/RGM and Faddeev results use the same NbarN interaction and the same second-order Trueman formula, so the reader immediately sees that the differences are methodological. This is mentioned in the text but not in the table caption.
  2. [Fig. 5 bottom / Table III] The notation 'd+d*' and 'd+2d*' should be defined in the caption or at first use; it is clear from the text only after several readings.
  3. [Table I] The row 'Number of basis functions (n_s)' should clarify that these are Lagrange mesh functions used in the R-matrix solution, not HO basis states.
  4. [Ref. [38]] Reference [38] is a PhD thesis. If it is not publicly available, please provide a URL or a more detailed summary of the regulator-convergence and Nmax-convergence checks that are delegated to it.
  5. [Sec. VI] The sentence 'We expect this uncertainty to shrink as we move towards heavier targets' is a plausible expectation but is not demonstrated in this paper. It would be more precise to say 'we hypothesize' or to give a physical argument based on binding energy and cluster formation.

Circularity Check

0 steps flagged

No significant circularity: the derived observables follow from fixed inputs and are benchmarked against independent Faddeev calculations.

full rationale

The paper's derived quantities — phase shifts, scattering lengths, atomic level shifts and widths, quasibound energies, and annihilation densities — all follow from solving the NCSM/RGM equations (Eq. 31) with fixed inputs: the bare N3LO NN interaction, the Kohno-Weise NbarN optical potential fitted to ppbar data, and NCSM target wave functions. No output is recycled as an input. The Trueman-formula level shifts are not circular predictions: they are one independent route, cross-checked against direct bound-state R-matrix diagonalization, and the paper reports good agreement between the two routes. The Faddeev benchmarks of Refs. [2,3] are external to the present authors and use the same interactions, so they provide an independent test of the many-body truncation. The paper's explicit caveats about missing rearrangement configurations, e.g. 'the pbar p n dynamics may not be well represented by a pbar+d cluster configuration' and the 4-23% deviations in Table XI, weaken or qualify the central reliability claim, but they are a correctness/interpretation concern rather than circularity: the derivations do not reduce to their inputs by construction. Self-citations to the NCSM/RGM formalism and to Ref. [38] for regulator details are not load-bearing, since the formalism is re-derived in the paper and the regulator is validated by Nmax convergence and plateau independence.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The central results rest on an externally fitted optical potential, a hand-chosen regulator scheme, and the assumed completeness of a single-cluster RGM expansion. No new particles, forces, or conserved quantities are introduced. The most consequential assumption is the single-partition ansatz, which the paper's own Faddeev comparisons show is insufficient at the 4-23% level for these light systems.

free parameters (5)
  • Kohno-Weise NbarN optical potential parameters = W0 = 1.2i GeV, R = 0.55 fm, a = 0.2 fm
    The annihilation term is a Woods-Saxon fitted to pbarp total, elastic, and charge-exchange cross sections; the real short-range part is extrapolated by matching to a Woods-Saxon. All annihilation and width predictions inherit these fitted values.
  • Strong-interaction regulator radius r_reg = 10, 12, or 14 fm depending on system
    Hand-chosen Woods-Saxon regulator radius used to remove finite-model-space artifacts; results shown stable over a plateau, but the choice is not uniquely determined by the physics.
  • Short-range Coulomb regulator radius r_reg,c = 5 fm
    Hand-chosen regulator applied to Coulomb kernel contributions expanded in the HO basis; dependence is stated to be weak but the parameter is still introduced ad hoc.
  • Harmonic-oscillator frequency hbar-omega = 20 MeV
    Basis parameter used in both NCSM and NCSM/RGM; convergence is checked, but the value is chosen by hand.
  • R-matrix channel radius a_c and number of Lagrange basis functions n_s = a_c = 30-400 fm; n_s = 100-500
    Numerical parameters of the calculable R-matrix method; varied for atomic versus scattering calculations and checked for convergence, but not uniquely fixed.
axioms (6)
  • domain assumption Nonrelativistic Schrodinger equation with a complex optical potential describes pbar-nucleus scattering including annihilation through a non-Hermitian Hamiltonian.
    Section II introduces V = U + W and treats annihilation implicitly; this is the standard optical-model assumption, not derived in the paper.
  • domain assumption The G-parity rule correctly relates meson-exchange NN and NbarN potentials.
    Eqs. (3)-(4) in Section II; the Kohno-Weise real potential is obtained from the Ueda NN interaction via G-parity transformation.
  • ad hoc to paper The one-partition RGM ansatz consisting of pbar + target-nucleus configurations is sufficient for the claimed low-energy observables; rearrangement channels can be neglected.
    Section V B/V C explicitly acknowledge that the pbar+d configuration may not represent pbar p n dynamics and that missing configurations cannot be repaired by adding target pseudo-states.
  • domain assumption The Kohno-Weise potential, fitted to free pbarp data, transfers unchanged to interactions between an antiproton and nucleons bound in a nucleus.
    Section II and all calculations use the free-space potential without medium modifications; no in-medium correction is discussed.
  • domain assumption Target nuclei are described by NCSM with the bare N3LO Entem-Machleidt NN interaction.
    Section V and Table II; the bare interaction is an input from prior literature, not derived here.
  • domain assumption The Trueman formula truncated at second order is valid for extracting atomic level shifts from effective-range parameters.
    Section IV A uses Eq. (46); the paper checks this against direct bound-state R-matrix calculations, finding agreement at the few-percent level.

reviewed 2026-08-02 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Light antiproton-nucleus systems at low energies with the ab initio NCSM/RGM method." pith.science (2026). https://pith.science/paper/WXLDMYCW

@misc{pith2026260218162,
  author       = {Pith},
  title        = {Pith review of: Light antiproton-nucleus systems at low energies with the ab initio NCSM/RGM method},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WXLDMYCW}},
  note         = {Machine review of arXiv:2602.18162}
}
Share X Bluesky LinkedIn Reddit HN
abstract

The availability of low-energy antiproton beams at the CERN Antiproton Decelerator has renewed interest in using antimatter as a probe of nuclear structure and in forming exotic antiprotonic few-body systems. In this work, we extend the ab initio no-core shell model combined with the resonating group method (NCSM/RGM), which was successfully applied to light-nucleus structure and reactions, to antiproton-nucleus dynamics at low energies. The NCSM/RGM formalism is adapted to antiproton projectiles by removing the requirement of antisymmetrization under exchange of target and projectile constituents, while retaining a fully microscopic description of the nuclear target and the relative motion. We focus on the lightest systems, ${\bar p}+d$, ${\bar p}+{}^3 \mathrm{H}$, and ${\bar p}+{}^3\mathrm{He}$, for which benchmarking against exact solutions of the Schr\"odinger equation enables stringent validation and helps disentangle methodological uncertainties -- e.g., those associated with the choice of configurations included in the NCSM/RGM expansion -- so that the dominant residual uncertainty can be attributed to the $N\bar{N}$ interaction. We compute phase shifts, scattering lengths, cross sections, antiprotonic-atom level shifts and widths, nuclear quasibound energies, and annihilation densities. We find that the hard short-range components of the meson-exchange-based $N\bar{N}$ interaction lead to slow convergence of the NCSM/RGM kernels expanded in a harmonic-oscillator basis, requiring exceptionally large model spaces and posing significant numerical challenges. We discuss practical strategies to mitigate these limitations and assess the impact of missing closed-channel configurations, which is a significant source of uncertainties in very light systems.

Figures

Figures reproduced from arXiv: 2602.18162 by Alireza Dehghani, Guillaume Hupin, Petr Navr\'atil, Sofia Quaglioni.

Figure 1
Figure 1. Figure 1: FIG. 1. Relative radial HO wave function ( [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effect of the finite-model-space artifacts and their [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic illustration of the naive regularization in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Diagonal ( [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Real (green) and imaginary (red) parts of the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison of our [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Convergence of the ¯p [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Convergence of the ¯p [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Convergence of the ¯p [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Strong-interaction potential kernel [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Real (blue) and imaginary (red) parts of the ¯p [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. ¯p [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Comparison of the ¯p [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗

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

54 extracted references · 19 linked inside Pith

  1. [1]

    28) for theA= 3 system

    Strong Interaction Kernels a.A= 3 We begin by discussing the derivation of the potential kernel (Eq. 28) for theA= 3 system. This derivation is given in Ref. [11] for a system of nucleons. Our deriva- tion is almost the same, with the exception that we omit the permutation operator needed for antisymmetrization. Our objective is to calculate D ϕJ πT ν′n′ ...

  2. [2]

    11) to the Hamiltonian kernel in Eq

    Point-Coulomb Interaction In this section, we discuss our method of obtaining the contribution of the point-Coulomb interaction (Eq. 11) to the Hamiltonian kernel in Eq. 22. For simplicity, we only explain the procedure for the antiproton-deuteron system. The generalization to 3He and 3H targets is more involved but follows the same footsteps. The short- ...

  3. [3]

    Caravitaet al., Arxiv e-Print (2025), arXiv:2503.22471 [nucl-ex]

    R. Caravitaet al., Arxiv e-Print (2025), arXiv:2503.22471 [nucl-ex]

    Pith/arXiv arXiv 2025

  4. [4]

    Lazauskas and J

    R. Lazauskas and J. Carbonell, Phys. Lett. B820, 136573 (2021), Corrigendum: Phys. Lett. B 841, 137936 (2023)

    2021

  5. [5]

    Duerinck and R

    P.-Y. Duerinck and R. Lazauskas, Arxiv e-Print (2026), arXiv:2601.06541 [nucl-th]

    arXiv 2026

  6. [6]

    Duerinck, R

    P.-Y. Duerinck, R. Lazauskas, and J. Dohet-Eraly, Phys. Rev. C108, 054003 (2023)

    2023

  7. [7]

    Vorabbi, M

    M. Vorabbi, M. Gennari, P. Finelli, C. Giusti, and P. Navr´ atil, Phys. Rev. Lett.124, 162501 (2020), arXiv:1906.11984 [nucl-th]

    Pith/arXiv arXiv 2020

  8. [8]

    Aumannet al.(PUMA), Eur

    T. Aumannet al.(PUMA), Eur. Phys. J. A58, 88 (2022)

    2022

  9. [9]

    Hergert, Front

    H. Hergert, Front. in Phys.8, 379 (2020), arXiv:2008.05061 [nucl-th]

    Pith/arXiv arXiv 2020

  10. [10]

    B. R. Barrett, P. Navr´ atil, and J. P. Vary, Prog. Part. Nucl. Phys.69, 131 (2013)

    2013

  11. [11]

    Navr´ atil, G

    P. Navr´ atil, G. P. Kamuntavicius, and B. R. Barrett, Phys. Rev. C61, 044001 (2000), arXiv:nucl-th/9907054

    Pith/arXiv arXiv 2000

  12. [12]

    Quaglioni and P

    S. Quaglioni and P. Navr´ atil, Phys. Rev. Lett.101, 092501 (2008), arXiv:0804.1560 [nucl-th]

    Pith/arXiv arXiv 2008

  13. [13]

    Quaglioni and P

    S. Quaglioni and P. Navr´ atil, Phys. Rev. C79, 044606 (2009), arXiv:0901.0950 [nucl-th]

    Pith/arXiv arXiv 2009

  14. [14]

    Navr´ atil, S

    P. Navr´ atil, S. Quaglioni, G. Hupin, C. Romero- Redondo, and A. Calci, Phys. Scripta91, 053002 (2016), arXiv:1601.03765 [nucl-th]

    Pith/arXiv arXiv 2016

  15. [15]

    Navr´ atil, J

    P. Navr´ atil, J. P. Vary, and B. R. Barrett, Phys. Rev. C 62, 054311 (2000)

    2000

  16. [16]

    Navratil, in169th Course of International School of Physics ’Enrico Fermi’: Nuclear Structure far from Sta- bility: New Physics and New Technology(2007) pp

    P. Navratil, in169th Course of International School of Physics ’Enrico Fermi’: Nuclear Structure far from Sta- bility: New Physics and New Technology(2007) pp. 147– 183, arXiv:0711.2702 [nucl-th]

    Pith/arXiv arXiv 2007

  17. [17]

    Y. C. Tang, M. LeMere, and D. R. Thompsom, Phys. Rept.47, 167 (1978)

    1978

  18. [18]

    Atkinson, K

    M. Atkinson, K. Kravvaris, S. Quaglioni, and P. Navr´ atil, Phys. Lett. B860, 139189 (2025)

    2025

  19. [19]

    Orfanidis and V

    S. Orfanidis and V. Rittenberg, Nucl. Phys. B59, 570 (1973)

    1973

  20. [20]

    Richard, Front

    J.-M. Richard, Front. in Phys.8, 6 (2020), arXiv:1912.07385 [nucl-th]

    Pith/arXiv arXiv 2020

  21. [21]

    Richard, Nucleon-Antinucleon Interaction, in Handbook of Nuclear Physics, edited by I

    J.-M. Richard, Nucleon-Antinucleon Interaction, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer, Singapore, 2023) pp. 1–22, arXiv:2205.02529 [nucl-th]

    Pith/arXiv arXiv 2023

  22. [22]

    Klempt, F

    E. Klempt, F. Bradamante, A. Martin, and J. M. Richard, Phys. Rept.368, 119 (2002)

    2002

  23. [23]

    T. E. O. Ericson and W. Weise,Pions and nuclei(Claren- don Press, Oxford, UK, 1988)

    1988

  24. [24]

    Carbonell, G

    J. Carbonell, G. Hupin, and S. Wycech, Eur. Phys. J. A 59, 259 (2023), arXiv:2309.14831 [nucl-th]

    Pith/arXiv arXiv 2023

  25. [25]

    El-Bennich, M

    B. El-Bennich, M. Lacombe, B. Loiseau, and S. Wycech, Phys. Rev. C79, 054001 (2009), arXiv:0807.4454 [nucl- th]

    Pith/arXiv arXiv 2009

  26. [26]

    Richard and M

    J.-M. Richard and M. E. Sainio, Phys. Lett. B110, 349 (1982)

    1982

  27. [27]

    Kohno and W

    M. Kohno and W. Weise, Nucl. Phys. A454, 429 (1986). 24

    1986

  28. [28]

    Zhou and R

    D. Zhou and R. G. E. Timmermans, Phys. Rev. C86, 044003 (2012)

    2012

  29. [29]

    L.-Y. Dai, J. Haidenbauer, and U.-G. Meißner, JHEP07, 078, arXiv:1702.02065 [nucl-th]

    Pith/arXiv arXiv

  30. [30]

    Ueda, Prog

    T. Ueda, Prog. Theor. Phys.62, 1670 (1979)

    1979

  31. [31]

    G. P. Kamuntaviˇ cius, R. K. Kalinauskas, B. R. Barrett, S. Mickeviˇ cius, and D. Germanas, Nucl. Phys. A695, 191 (2001), arXiv:nucl-th/0105009

    Pith/arXiv arXiv 2001

  32. [32]

    Carbonell, J.-M

    J. Carbonell, J.-M. Richard, and S. Wycech, Z. Phys. A 343, 325 (1992)

    1992

  33. [33]

    H. A. Bethe,Elementary nuclear theory(John Wiley & Sons, 1956)

    1956

  34. [34]

    C. J. Batty, Rept. Prog. Phys.52, 1165 (1989)

    1989

  35. [35]

    T. L. Trueman, Nucl. Phys.26, 57 (1961)

    1961

  36. [36]

    Carbonell, G

    J. Carbonell, G. Ihle, and J. M. Richard, Z. Phys. A334, 329 (1989)

    1989

  37. [37]

    Descouvemont and D

    P. Descouvemont and D. Baye, Rept. Prog. Phys.73, 036301 (2010), arXiv:1001.0678 [nucl-th]

    Pith/arXiv arXiv 2010

  38. [38]

    Hesse, J

    M. Hesse, J. M. Sparenberg, F. Van Raemdonck, and D. Baye, Nucl. Phys. A640, 37 (1998)

    1998

  39. [39]

    D. R. Entem and R. Machleidt, Phys. Rev. C68, 041001 (2003), arXiv:nucl-th/0304018

    Pith/arXiv arXiv 2003

  40. [40]

    Dehghani,Reactions with antiprotons in the theory of cold nuclear collisions, Ph.D

    A. Dehghani,Reactions with antiprotons in the theory of cold nuclear collisions, Ph.D. thesis, Paris-Saclay Univer- sity (2025)

    2025

  41. [41]

    Hupin, S

    G. Hupin, S. Quaglioni, and P. Navr´ atil, Phys. Rev. Lett. 114, 212502 (2015), arXiv:1412.4101 [nucl-th]

    Pith/arXiv arXiv 2015

  42. [42]

    Navratil and S

    P. Navratil and S. Quaglioni, Phys. Rev. C83, 044609 (2011), arXiv:1102.2042 [nucl-th]

    Pith/arXiv arXiv 2011

  43. [43]

    Augsburgeret al., Phys

    M. Augsburgeret al., Phys. Lett. B461, 417 (1999)

    1999

  44. [44]

    Gottaet al., Nucl

    D. Gottaet al., Nucl. Phys. A660, 283 (1999)

    1999

  45. [45]

    Yanet al., Phys

    Y. Yanet al., Phys. Lett. B659, 555 (2008), Erratum: Phys. Lett. B 665, 425–425 (2008)

    2008

  46. [46]

    Zenoniet al., Phys

    A. Zenoniet al., Phys. Lett. B461, 413 (1999)

    1999

  47. [47]

    Aghai-Khozaniet al., Nucl

    H. Aghai-Khozaniet al., Nucl. Phys. A970, 366 (2018)

    2018

  48. [48]

    Navr´ atil, Phys

    P. Navr´ atil, Phys. Rev. C70, 014317 (2004)

    2004

  49. [49]

    Loiseau and S

    B. Loiseau and S. Wycech, Phys. Rev. C102, 034006 (2020), arXiv:2007.01775 [nucl-th]

    Pith/arXiv arXiv 2020

  50. [50]

    Bianconiet al., Phys

    A. Bianconiet al., Phys. Lett. B492, 254 (2000)

    2000

  51. [51]

    S. K. Bogner, R. J. Furnstahl, and R. J. Perry, Phys. Rev. C75, 061001 (2007)

    2007

  52. [52]

    Bogner, R

    S. Bogner, R. Furnstahl, and R. Perry, Ann. Phys.323, 1478 (2008)

    2008

  53. [53]

    A. D. Martin and T. D. Spearman,Elementary particle theory(North Holland Publishing Company, 1970)

    1970

  54. [54]

    V. K. Khersonskii, A. N. Moskalev, and D. A. Varshalovich,Quantum theory of angular momemtum (World Scientific Publishing Company, 1988)

    1988

This paper was first reviewed by deepseek-v4-flash on August 2, 2026.