pith. sign in

arxiv: 1907.05626 · v1 · pith:5RZFHC6Vnew · submitted 2019-07-12 · ⚛️ nucl-th

Origin of energy shift in kaonic atom and kaon-nucleus interaction

Yutaro Iizawa , Daisuke Jido , Natsumi Ikeno , Junko Yamagata-Sekihara , Satoru Hirenzaki This is my paper

Pith reviewed 2026-05-24 22:19 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords kaonic atomsK^- nucleus optical potentialenergy shiftabsorption widthlevel repulsionnuclear bound statesLambda(1405)
0
0 comments X

The pith

Kaonic-atom data require a K^--nucleus potential with large imaginary part rather than one driven by nuclear-state repulsion.

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

Kaonic atoms exhibit repulsive energy shifts even though the underlying K^-N force is attractive enough to form the Lambda(1405). The authors fit a linear-density optical potential separately to the shift and width of each observed atom and obtain two families of solutions. One family produces a deep real attraction that supports nuclear bound states sharing the atomic quantum numbers; mixing between these states then pushes the atomic level upward. The second family produces a large imaginary (absorptive) strength whose effect on the atomic wave function is itself repulsive. Only the second family simultaneously accounts for the entire body of measured data across many nuclei.

Core claim

In the linear nuclear density approximation the K^- optical potential can be parameterized in two distinct ways that both reproduce individual kaonic-atom data. The first produces deep real attraction sufficient to support nuclear states sharing the atomic quantum numbers; mixing then repels the atomic level upward. The second produces large imaginary strength whose effect on the atomic wave function is also repulsive. Only the second family simultaneously describes the observed shifts and widths across the full range of nuclei, implying that the global K^--nucleus potential for kaonic atoms is characterized by strong absorption rather than by level repulsion with nuclear states.

What carries the argument

Linear-density K^- optical potential with independently fitted real and imaginary strengths for each atom; the distinction between real-part-driven level repulsion and imaginary-part-driven repulsion.

If this is right

  • The picture that repulsive atomic shifts arise from mixing with nuclear states does not hold across the full data set.
  • The K^--nucleus optical potential must carry a large imaginary part.
  • All conventionally used phenomenological potentials already belong to the absorption-dominated class.
  • Nonlinear density corrections leave the conclusion unchanged.

Where Pith is reading between the lines

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

  • Precision data on additional light nuclei could test whether the same absorption-dominated form continues to work at lower densities.
  • The result implies that any attempt to extract the real part of the potential from kaonic atoms will remain coupled to strong absorption effects.
  • If the large imaginary component is confirmed it points toward dominant multi-nucleon absorption channels or strong in-medium broadening of the Lambda(1405).

Load-bearing premise

That independently fitting real and imaginary strengths for each kaonic atom inside the linear-density approximation is enough to identify which global feature of the K^--nucleus interaction is realized.

What would settle it

A new kaonic-atom measurement whose shift and width cannot be reproduced by any large-imaginary linear-density potential but can be fit by a level-repulsion solution would falsify the global preference for the imaginary-dominated family.

Figures

Figures reproduced from arXiv: 1907.05626 by Daisuke Jido, Junko Yamagata-Sekihara, Natsumi Ikeno, Satoru Hirenzaki, Yutaro Iizawa.

Figure 1
Figure 1. Figure 1: FIG. 1. Wavefunctions squared of the atomic states with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The same as in Fig.1, but in the nuclear radial range. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Energy shifts and absorption widths of the atomic [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Atomic dependence of the potential parameters for [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The same as in Fig.4, but for Potential 2. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The same as in Fig.4, but for Potential 3. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Energy shifts (upper plot) and absorption width [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The same in Fig. 7, but for the kaonic atoms with [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Summary of energy shifts of kaonic atoms in the [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The same in Fig. 7, but for Potential 2. [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. The same in Fig. 10, but for Potential 3. [PITH_FULL_IMAGE:figures/full_fig_p010_15.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. The same in Fig. 11, but for the kaonic atoms with [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. The same in Fig. 10, but for Potential 2. [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Energy shifts (upper plot) and absorption width [PITH_FULL_IMAGE:figures/full_fig_p011_16.png] view at source ↗
read the original abstract

The $K^-$-nucleus optical potential is revisited to investigate its global feature phenomenologically. It is a puzzle that the energy shift is found to be repulsive in all of the observed kaonic atom, although the $K^-N$ interaction is known to be so attractive as to form the $\Lambda(1405)$ resonance. To solve this puzzle, we examine the $K^-$ optical potential in the linear density approximation and determine the potential parameters of each kaonic atom so as to reproduce the observed energy shift and absorption width. We find two types of the potentials. One potential has a so large real part as to provide nuclear states with the same quantum number to the atomic state in the last orbit. The level repulsion between the atomic state and the nuclear states takes place due to their mixing, and it makes the atomic state shifted repulsively. The other type of the potential has a large imaginary part and the imaginary part works repulsively for atomic states. We find that only the latter solution reproduce a wide of the observed data, and thus is realized as a $K^-$-nucleus potential for kaonic atom. In the linear nuclear density optical potential, the picture that the repulsive shifts in the atomic states stem from the existence of the nuclear states does not globally stand up. This implies that the $K^-$-nucleus optical potential should have a large imaginary part. We examine some nonlinear density effects and find that the conclusion does not change. We also confirm that the conventionally known optical potentials are categorized into the latter type of the potential.

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 manuscript examines the K^--nucleus optical potential in the linear density approximation to address the puzzle of repulsive energy shifts observed in all kaonic atoms despite the attractive K^-N interaction forming the Lambda(1405). Parameters of the real and imaginary parts are fitted independently for each kaonic atom to reproduce the observed energy shift and absorption width. This yields two classes of solutions: one with a large real part that generates nuclear states with the same quantum numbers, leading to level repulsion and repulsive atomic shifts via mixing; the other with a large imaginary part that itself produces repulsive shifts. The authors conclude that only the large-imaginary solutions reproduce a wide range of the observed data and are thus realized globally, that the nuclear-state repulsion picture does not hold, that nonlinear density effects leave the conclusion unchanged, and that conventional potentials belong to the large-imaginary class.

Significance. If the central claim holds, the work would supply phenomenological evidence that a strongly absorptive optical potential, rather than nuclear-state mixing, accounts for the repulsive shifts, with implications for kaon-nucleus interaction models. The per-atom classification, consistency check with conventional potentials, and nonlinear test provide modest additional support, but the absence of error bars, statistical measures, or a global simultaneous fit limits the strength of the evidence for a single realized potential form.

major comments (2)
  1. [Fitting procedure (method and results sections)] The classification of solutions and the claim that 'only the latter solution reproduce a wide of the observed data' (abstract) rest on independent per-atom fits of real and imaginary strengths in the linear-density approximation. Because each atom receives its own unconstrained parameter pair, this procedure shows that large-imaginary solutions exist for many atoms but does not demonstrate that any single fixed (Re, Im) pair or functional form simultaneously reproduces the full data set, weakening the inference that the large-imaginary solution 'is realized as a K^--nucleus potential' globally.
  2. [Nonlinear density effects section] The nonlinear-density test (final section) inherits the identical per-atom independent fitting structure, so it cannot resolve the gap between per-atom existence of solutions and global consistency of one potential form across all atoms.
minor comments (2)
  1. [Abstract] Typo in abstract: 'reproduce a wide of the observed data' should read 'reproduce a wide range of the observed data'.
  2. [Abstract] The sentence 'the picture that the repulsive shifts in the atomic states stem from the existence of the nuclear states does not globally stand up' is awkwardly phrased; consider rewording for clarity.

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, clarifying the purpose and limitations of our phenomenological approach.

read point-by-point responses

  1. Referee: [Fitting procedure (method and results sections)] The classification of solutions and the claim that 'only the latter solution reproduce a wide of the observed data' (abstract) rest on independent per-atom fits of real and imaginary strengths in the linear-density approximation. Because each atom receives its own unconstrained parameter pair, this procedure shows that large-imaginary solutions exist for many atoms but does not demonstrate that any single fixed (Re, Im) pair or functional form simultaneously reproduces the full data set, weakening the inference that the large-imaginary solution 'is realized as a K^--nucleus potential' globally.

    Authors: The per-atom fitting procedure is deliberately chosen to classify the two possible types of solutions that can reproduce the data for each individual kaonic atom. This reveals a consistent pattern: for a wide range of atoms, only the large-imaginary solutions provide acceptable fits to both the energy shift and absorption width, while the large-real solutions (relying on nuclear-state mixing) fail to do so consistently or lead to unphysical results. This classification supports our conclusion that the large-imaginary class is the one realized globally as the K^--nucleus potential. We acknowledge that a single simultaneous global fit with fixed parameters across all atoms would provide additional support, but the current study focuses on identifying the dominant phenomenological type, which is also consistent with conventional potentials. revision: no

  2. Referee: [Nonlinear density effects section] The nonlinear-density test (final section) inherits the identical per-atom independent fitting structure, so it cannot resolve the gap between per-atom existence of solutions and global consistency of one potential form across all atoms.

    Authors: The nonlinear-density test applies the same per-atom classification to examine whether density-dependent corrections alter the preference for large imaginary parts. We find that the conclusion remains unchanged, reinforcing that the linear-density result captures the essential global feature. While this does not constitute a global simultaneous fit, it demonstrates the robustness of the large-imaginary class under nonlinear effects. revision: no

Circularity Check

0 steps flagged

No significant circularity; phenomenological classification of per-atom fits

full rationale

The paper determines real and imaginary strengths independently for each kaonic atom to reproduce its observed shift and width in the linear-density approximation, classifies the resulting solutions into two types, and reports that the large-imaginary class accommodates a wider set of atoms. This is a direct enumeration of fitting outcomes rather than a derivation in which a claimed result (e.g., a prediction or global potential) is shown by the paper's own equations to be identical to the fitted inputs. No self-citation is invoked as a load-bearing uniqueness theorem, no ansatz is smuggled, and no quantity is renamed as a first-principles result. The analysis remains self-contained within its stated phenomenological scope.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on two free parameters per atom fitted to data and on the domain assumption of linear density dependence; no new entities are postulated.

free parameters (2)
  • real part of optical potential
    Adjusted independently for each kaonic atom to reproduce the measured energy shift and width.
  • imaginary part of optical potential
    Adjusted independently for each kaonic atom to reproduce the measured energy shift and width.
axioms (1)
  • domain assumption K^- optical potential is linear in nuclear density
    Invoked as the starting approximation for the global phenomenological study.

pith-pipeline@v0.9.0 · 5838 in / 1271 out tokens · 30390 ms · 2026-05-24T22:19:22.138448+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

53 extracted references · 53 canonical work pages

  1. [1]

    Unfolded

    5i)(ρN (r)/ρ 0) MeV) in the previous section. This is a natural result because the potential (13) is similar to the phenomenological potential is Ref [1] and it has already universality to reproduce a wide range of the ob- served kaonic atoms. -0.2 0 0.2 0.4 22 24 26 28 30 -Shift [keV] Atomic number Co Ni Cu1 Cu2 0 0.5 1 1.5 2 2.5 22 24 26 28 30 Width [ke...

    work page

  2. [2]

    Friedman, A

    E. Friedman, A. Gal and C. J. Batty, Nucl. Phys. A 579, 518 (1994)

    work page 1994

  3. [3]

    C. J. Batty, E. Friedman and A. Gal, Phys. Rept. 287, 385 (1997)

    work page 1997

  4. [4]

    Friedman and A

    E. Friedman and A. Gal, Phys. Rept. 452, 89 (2007)

    work page 2007

  5. [5]

    C. J. Batty, Nucl. Phys. A 372, 418 (1981)

    work page 1981

  6. [6]

    Friedman and A

    E. Friedman and A. Gal, Phys. Lett. B 459, 43 (1999)

    work page 1999

  7. [7]

    Friedman and A

    E. Friedman and A. Gal, Nucl. Phys. A 881, 150 (2012)

    work page 2012

  8. [8]

    Friedman and A

    E. Friedman and A. Gal, Nucl. Phys. A 899, 60 (2013)

    work page 2013

  9. [9]

    Gal, Nucl

    A. Gal, Nucl. Phys. A 914, 270 (2013)

    work page 2013

  10. [10]

    Barnea and E

    N. Barnea and E. Friedman, Phys. Rev. C 75, 022202 (2007)

    work page 2007

  11. [11]

    Cieply, E

    A. Cieply, E. Friedman, A. Gal and J. Mares, Nucl. Phys. A 696, 173 (2001)

    work page 2001

  12. [12]

    Koch, Phys

    V. Koch, Phys. Lett. B 337, 7 (1994)

    work page 1994

  13. [13]

    Schaffner, J

    J. Schaffner, J. Bondorf and I. N. Mishustin, Nucl. Phys. A 625, 325 (1997)

    work page 1997

  14. [14]

    T. Waas, N. Kaiser and W. Weise, Phys. Lett. B 365, 12 (1996)

    work page 1996

  15. [15]

    T. Waas, N. Kaiser and W. Weise, Phys. Lett. B 379, 34 (1996)

    work page 1996

  16. [16]

    Waas and W

    T. Waas and W. Weise, Nucl. Phys. A 625, 287 (1997)

    work page 1997

  17. [17]

    Ohnishi, Y

    A. Ohnishi, Y. Nara and V. Koch, Phys. Rev. C 56, 2767 (1997)

    work page 1997

  18. [18]

    Lutz, Phys

    M. Lutz, Phys. Lett. B 426, 12 (1998)

    work page 1998

  19. [19]

    Tsushima, K

    K. Tsushima, K. Saito, A. W. Thomas and S. V. Wright, Phys. Lett. B 429, 239 (1998); Phys. Lett. B 436, 453(E) (1998)

    work page 1998

  20. [20]

    Sibirtsev and W

    A. Sibirtsev and W. Cassing, Nucl. Phys. A 641, 476 (1998)

    work page 1998

  21. [21]

    Ramos and E

    A. Ramos and E. Oset, Nucl. Phys. A 671, 481 (2000)

    work page 2000

  22. [22]

    Hirenzaki, Y

    S. Hirenzaki, Y. Okumura, H. Toki, E. Oset and A. Ramos, Phys. Rev. C 61, 055205 (2000)

    work page 2000

  23. [23]

    A. Baca, C. Garcia-Recio and J. Nieves, Nucl. Phys. A 673, 335 (2000)

    work page 2000

  24. [24]

    Tolos, A

    L. Tolos, A. Ramos, A. Polls and T. T. S. Kuo, Nucl. Phys. A 690, 547 (2001)

    work page 2001

  25. [25]

    Tolos, A

    L. Tolos, A. Ramos and A. Polls, Phys. Rev. C 65, 054907 (2002)

    work page 2002

  26. [26]

    C. L. Korpa and M. F. M. Lutz, Acta Phys. Hung. A 22, 21 (2005). 12

    work page 2005

  27. [27]

    Tolos, A

    L. Tolos, A. Ramos and E. Oset, Phys. Rev. C 74, 015203 (2006)

    work page 2006

  28. [28]

    Yamagata and S

    J. Yamagata and S. Hirenzaki, Eur. Phys. J. A31, 255 (2007)

    work page 2007

  29. [29]

    Tolos, D

    L. Tolos, D. Cabrera and A. Ramos, Phys. Rev. C 78, 045205 (2008)

    work page 2008

  30. [30]

    Weise and R

    W. Weise and R. Hartle, Nucl. Phys. A 804, 173 (2008)

    work page 2008

  31. [31]

    Cieply, E

    A. Cieply, E. Friedman, A. Gal, D. Gazda and J. Mares, Phys. Rev. C 84, 045206 (2011)

    work page 2011

  32. [32]

    Sekihara, J

    T. Sekihara, J. Yamagata-Sekihara, D. Jido, and Y. Kanada-En’yo, Phys. Rev. C 86, 065205 (2012)

    work page 2012

  33. [33]

    Yamagata-Sekihara, N

    J. Yamagata-Sekihara, N. Ikeno, H. Nagahiro, D. Jido, and S. Hirenzaki, Nucl. Phys. A914, 344 (2013)

    work page 2013

  34. [34]

    Kishimoto, Phys

    T. Kishimoto, Phys. Rev. Lett. 83, 4701 (1999)

    work page 1999

  35. [35]

    Kishimoto et al

    T. Kishimoto et al. , Prog. Theor. Phys. Suppl. 149, 264 (2003)

    work page 2003

  36. [36]

    Kishimoto et al

    T. Kishimoto et al. , Prog. Theor. Phys. 118, 181 (2007)

    work page 2007

  37. [37]

    Ikuta, M

    K. Ikuta, M. Arima and K. Masutani, Prog. Theor. Phys. 108, 917 (2002)

    work page 2002

  38. [38]

    Yamagata, H

    J. Yamagata, H. Nagahiro, Y. Okumura, and S. Hiren- zaki, Prog. Theor. Phys. 114, 301 (2005); 114, 905(E) (2005)

    work page 2005

  39. [39]

    Yamagata, H

    J. Yamagata, H. Nagahiro, and S. Hirenzaki, Phys. Rev. C76, 014604 (2006)

    work page 2006

  40. [40]

    Yamagata, H

    J. Yamagata, H. Nagahiro, R. Kimura, and S. Hirenzaki, Phys. Rev. C76, 045204 (2007)

    work page 2007

  41. [41]

    Yamagata-Sekihara, D

    J. Yamagata-Sekihara, D. Jido, H. Nagahiro, and S. Hirenzaki, Phys. Rev. C80, 045204 (2009)

    work page 2009

  42. [42]

    Koike and T

    T. Koike and T. Harada, Phys. Lett. B 652, 262 (2007); Nucl. Phys. A 804, 231 (2008)

    work page 2007

  43. [43]

    V. K. Magas, J. Yamagata-Sekihara, S. Hirenzaki, E. Oset and A. Ramos, Phys. Rev. C 81, 024609 (2010)

    work page 2010

  44. [44]

    Ichikawa et al

    Y. Ichikawa et al. , JPS Conf. Proc. 13, 020007 (2017); talk given in the 13th International Conference on Hy- pernuclear and Strange Particle Physics (HYP2018)

    work page 2017

  45. [45]

    Kaiser, P

    N. Kaiser, P. B. Siegel and W. Weise, Nucl. Phys. A 594, 325 (1995)

    work page 1995

  46. [46]

    Oset and A

    E. Oset and A. Ramos, Nucl. Phys. A 635, 99 (1998)

    work page 1998

  47. [47]

    R. H. Dalitz, T. C. Wong and G. Rajasekaran, Phys. Rev. 153, 1617 (1967)

    work page 1967

  48. [48]

    Hyodo and D

    T. Hyodo and D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012)

    work page 2012

  49. [49]

    C. W. De Jager, H. De Vries and C. De Vries, Atom. Data Nucl. Data Tabl. 14, 479 (1974); Atom. Data Nucl. Data Tabl. 16, 580(E) (1975)

    work page 1974

  50. [50]

    De Vries, C

    H. De Vries, C. W. De Jager and C. De Vries, Atom. Data Nucl. Data Tabl. 36, 495 (1987)

    work page 1987

  51. [51]

    Backenstoss et al

    G. Backenstoss et al. , Phys. Lett. 38B, 181 (1972); G. Backenstoss, J. Egger, H. Koch, H. P. Povel, A. Schwitter and L. Tauscher, Nucl. Phys. B 73, 189 (1974)

    work page 1972

  52. [52]

    C. J. Batty et al. , Nucl. Phys. A 329, 407 (1979)

    work page 1979

  53. [53]

    P. D. Barnes et al. , Nucl. Phys. A 231, 477 (1974)

    work page 1974