Pith. sign in

REVIEW 4 major objections 5 minor 41 references

Near-threshold neutron resonance widths are set by geometry, not nuclear interior structure.

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 ↗

T0 review · deepseek-v4-flash

2026-08-02 02:00 UTC pith:XZW5ZXA3

load-bearing objection Nice zero-energy square-well insight, but the finite-energy application to broad resonances is not yet quantitatively secure. the 4 major comments →

arxiv 2607.14464 v1 pith:XZW5ZXA3 submitted 2026-07-16 nucl-th nucl-ex

Universal Properties of Near-Threshold Single-Neutron Resonances

Myungkuk Kim , Young-Ho Song , Hans-Werner Hammer , Youngman Kim , Dean Lee , Yuan-Zhuo Ma This is my paper
classification nucl-th nucl-ex MSC 81U0581U3581V35
keywords single-neutron resonancesthreshold universalitydiscrete scale invarianceeffective range expansionsquare-well potentialresonance widthsWoods-Saxon diffusenesscentrifugal barrier
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 paper aims to prove that for a single neutron just above the emission threshold in a partial wave with nonzero orbital angular momentum, the decay width is universal: it depends only on the channel radius, angular momentum, reduced mass, and resonance energy, with no sensitivity to short-distance nuclear details or radial excitation. This claim is derived from a discrete scale invariance of the zero-energy finite square-well potential, which erases the internal wave function's node structure. If correct, the result provides a parameter-free baseline for p-wave and d-wave single-neutron resonance widths across the nuclear chart, and any systematic deviation from this baseline becomes a diagnostic for structure-dependent effects such as surface diffuseness, spectroscopic fragmentation, or core excitation.

Core claim

The authors establish a closed-form, scale-invariant width formula for near-threshold L>0 single-neutron resonances: Γ_L = π(2µE_r)^{L+1/2} (R/2)^{2L-1} / [µ(L+1/2)Γ(L−1/2)Γ(L+1/2)]. It follows from showing that at zero energy the finite square well's effective range is r_L = −(L+1/2)|b_L(R)|, where b_L(R) is the Wigner causality bound; the potential depth and radial node number cancel identically. The cancellation traces to a discrete scale symmetry unique to the square well: rescaling the interior momentum by ratios of spherical Bessel roots maps one radial excitation onto another without changing the surface boundary condition. Applying the formula to observed p-wave and d-wave resonances

What carries the argument

The central object is the zero-energy finite square-well potential and an exact discrete scale symmetry it possesses. At threshold, the interior radial wave function is u(ρ) ∝ ρ j_L(ρ), and the boundary condition j_{L−1}(K_0 R)=0 fixes the interior momentum to Bessel roots χ_{n,L−1}. Rescaling K_0 by the ratio of two Bessel roots maps an n-node state onto an n′-node state with unchanged boundary matching, so the effective range r_L = −(L+1/2)|b_L(R)| and hence the width are independent of radial excitation. The derivation combines the effective-range expansion Γ_L ≈ 2k_r^{2L+1}/(µ|r_L|), the Wigner causality bound b_L(R), and a scale Ward identity that converts the internal normalization int

Load-bearing premise

The prediction rests on applying the zero-energy threshold effective-range formula Γ_L ≈ 2k_r^{2L+1}/(µ|r_L|) to resonances at finite energy, assuming O(k^2) corrections are negligible even for states with Γ/E_r near unity (like 5He) and k_r R_eff ≈ 0.8 (like 9He).

What would settle it

Measure the width of a near-threshold p- or d-wave single-neutron resonance with a well-assigned spin-parity and known radial node number, and compare with Eq. (4); a width deviating from the prediction by more than the stated factor-of-two band, or a clear dependence on radial excitation number at fixed radius and energy, would falsify the universal claim. Alternatively, a high-precision measurement of the effective range r_L at threshold in a system approximating a square well could directly check the relation r_L = −(L+1/2)|b_L(R)| using Eq. (3).

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

If this is right

  • Provides a parameter-free, universal benchmark for p-wave and d-wave single-neutron resonance widths in light nuclei, testable against future measurements.
  • The normalized width Γ_L/E_r^{L+1/2} becomes a trace that depends only on core mass and L, enabling a spectroscopic tool to determine or constrain orbital angular momentum from measured energy and width alone.
  • Deviations from the geometric baseline become quantitative indicators of nuclear structure: d-wave suppression tied to surface diffuseness, fragmentation, or non-single-particle strength.
  • The discrete scale invariance predicts exact node independence of threshold widths for square-well systems, which can be probed in controlled few-body experiments or lattice simulations.
  • Extrapolation to heavier dripline systems (e.g., neutron-rich Ca and Sn isotopes) offers a simple baseline to separate universal continuum kinematics from emergent many-body complexity.

Where Pith is reading between the lines

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

  • The same geometric width baseline may apply to any neutral short-range two-body system with a centrifugal barrier, such as cold atoms near a p-wave Feshbach resonance, where the effective-range approximation is well-controlled.
  • The discrete scale invariance suggests an Efimov-like self-similar tower of shape resonances for a square well, with scaling factors given by ratios of Bessel roots; observing finite-energy members of this tower would directly test whether the symmetry survives away from threshold.
  • Because Woods-Saxon diffuseness breaks node independence, real nuclei with even mild surface softness should show systematic node-dependent reductions in width; this could be used to extract internal radial node information from width measurements, turning the baseline into a structure probe.
  • The factor-of-two agreement with experiment may reflect the limit of a purely single-particle, sharp-boundary description; a dedicated correlation analysis of the residuals against known shell closures, pairing, or deformation would reveal whether the scatter is truly random or carries shell-structure information.

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

4 major / 5 minor

Summary. The paper claims to establish universal near-threshold width predictions for L>0 single-neutron resonances. Starting from the effective range expansion and the generalized Bethe integral, the authors derive an analytic square-well relation for the effective range, r_L = -(L+1/2)|b_L(R)|, and hence a closed-form width formula, Eq. (4), that depends only on R, L, µ, and E_r. The node independence is traced to an exact discrete scale invariance of the zero-energy finite square well. The formula is compared with eight observed p- and d-wave resonances in light nuclei and claimed to work within a factor of two. A Woods-Saxon diffuse-surface correction is then introduced to explain d-wave suppression relative to the sharp-boundary baseline.

Significance. If Eq. (4) is quantitatively reliable at the energies of the benchmark states, it would provide a simple, parameter-light geometric baseline for neutron resonance widths and a useful diagnostic for exotic nuclei. The square-well derivation in the Supplemental Material is elegant and mostly internally consistent: the Bessel-integral identity in Eq. (S16) and the dilation-current argument in Sec. S3 cleanly establish node independence at zero energy. I also note that Eq. (4) is not fitted to the experimental widths; the inputs (R_eff from saturation density, µ from masses, E_r from experiment) are external, so the comparison has predictive content. However, the central quantitative claim is not yet secure because the formula is a leading-order threshold result and it is applied to states with k_r R_eff up to ~0.8 and Γ/E_r ~1, where the omitted corrections are comparable to the claimed factor-of-two agreement.

major comments (4)
  1. [Main text after Eq. (1); Supplemental Eqs. (S9), (S40)] The derivation of Eq. (4) combines the threshold effective range r_L with the pole-width relation Γ_L ≈ 2k_r^{2L+1}/(µ|r_L|). Both are leading order in k_r R. The benchmark set includes 5He with k_r R_eff≈0.50 and Γ/E_r≈0.98, and 9He with k_r R_eff≈0.80. The first omitted penetrability correction in Eq. (S40) is −(k_r R)^2/(2L−1); for 9He this is about −0.65. Replacing the threshold penetrability by the exact one changes that predicted width by a factor ≈2.8, which is larger than the claimed factor-of-two agreement. Please provide an exact finite-E_r square-well calculation, or a quantitative error budget for the O(k^2) terms, and show how Table I changes. Without this, the comparison cannot distinguish the universal square-well baseline from an artifact of the threshold truncation.
  2. [Supplemental Sec. S1, last paragraph; Eq. (S9)] Discrete scale invariance and node independence are proven at exactly E=0. The extension to E_r>0 relies on the effective range expansion. The coefficient r_L is node-independent, but the next-order shape parameter (the k^4 term in Eq. (1)) is uncontrolled and may depend on both n and V0. For k_r R_eff≈0.5–0.8 the truncation is not parametrically small. Please derive the next-order square-well correction or state a quantitative validity criterion that the benchmark states actually satisfy.
  3. [Table I] The text states that the geometric baseline predicts the experimental widths 'within a factor of two across all cases'. For 11Be, the central values give Γ_pred/Γ_exp = 0.2112/0.100 ≈ 2.11. With Γ_exp = 0.10±0.01, the ratio ranges from about 1.92 to 2.35, so the factor-of-two claim is not strictly true for the central value. Also, the 9He entry rests on the unpublished preprint ref. [29] for a very broad resonance; its status should be flagged, and the sensitivity of the comparison to excluding it should be reported.
  4. [Main text, Eq. (4) and R_eff definition] The predictions scale as R_eff^{2L−1}, so d-wave widths scale as R_eff^3. The channel radius R_eff = 1.14(A_core^{1/3}+1) fm is a plausible geometric choice but not uniquely determined; a 10% change in R0 changes d-wave predictions by about 30%. No uncertainty is propagated from R0. Please quantify this sensitivity or justify the normalization to nuclear saturation density against other standard radius choices; otherwise the d-wave agreement in Table I is less informative than stated.
minor comments (5)
  1. [Abstract and conclusion] The phrase 'parameter-free geometric baseline' is overstated because R0, the A_core^{1/3}+1 offset, and the diffuseness a are inputs. Suggest 'parameter-light' or explicitly list the geometric inputs.
  2. [Fig. 1 and Supplemental Sec. S6] The main-text figure shows solid traces, while Sec. S6 describes shaded bands generated from the A_core range. Please clarify the relationship between the two representations and whether Fig. 1 is intended as the L=1,2,3 traces or as a band.
  3. [Main text, p.2] Minor typo: 'Because neutrals-wave interactions' should be 'Because neutral s-wave interactions'.
  4. [References [29]] Ref. [29] is an arXiv preprint dated 2026. For a journal submission, please mark it as preprint/submitted and, if possible, use a published version.
  5. [Eq. (5) and Sec. S5] Equation (5) is derived under WKB and boundary-shift approximations. The main text appropriately calls it semi-quantitative, but the paper should avoid presenting it as a precise prediction without benchmarking against an exact Woods-Saxon calculation for at least one d-wave case.

Circularity Check

0 steps flagged

No significant circularity: the central width formula is derived from an analytic square-well calculation and compared with external data, not fitted to it.

full rationale

The paper's central result, Eq. (4), is obtained by combining the threshold effective-range relation Γ_L ≈ 2k_r^{2L+1}/(μ|r_L|) with the square-well effective range r_L = −(L+1/2)|b_L(R)|, Eq. (3). Equation (3) is derived in the Supplemental Material (S2) from the generalized Bethe integral formula and the explicit zero-energy square-well wave function, with no use of experimental widths. The inputs to Eq. (4) are R_eff from nuclear saturation density, μ from masses, and E_r from experiment; the Table I comparison is a genuine external benchmark, not a fit. The only self-citations (refs. [10,11]) are independently published causality/effective-range bounds; they are not the sole justification for the central formula, which is re-derived analytically for the square well. The paper's admitted caveats—that k_r R_eff can approach ~0.8 and Γ/E_r ~1, making O(k^2) corrections non-negligible—are validity/applicability limitations, not evidence of circular construction. No step reduces by the paper's own equations to a fitted parameter or to a self-referential definition.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central width formula rests on standard effective-range/causality results for L>0 and on the modeling choice that observed near-threshold resonances are single-particle states with an effective square-well channel radius. The only input numbers are standard nuclear parameters (R0 from saturation density, a=0.65 fm), not fitted to the benchmark widths.

free parameters (4)
  • R_0 (channel radius parameter) = 1.14 fm
    Derived from saturation density ρ0=0.16 fm^-3; not fitted to the eight widths, but the prediction scales as R^{2L-1}, so the choice matters.
  • Valence-nucleon offset in R_eff = R_0(A_core^{1/3}+1) = 1 (dimensionless)
    A modeling choice for the channel radius; not independently constrained by the data. A different offset changes Γ.
  • Woods-Saxon diffuseness a = 0.65 fm
    Standard nuclear surface diffuseness used in the Eq. (5) suppression estimate; not fitted here.
  • Radial node number n for d-wave suppression estimate = 0
    The WS suppression factor depends on χ_{n,L-1}; the paper quotes n=0 for d-wave. Higher n would give stronger suppression.
axioms (6)
  • standard math Effective range expansion k^{2L+1} cot δ_L = -1/a_L + (1/2) r_L k^2 + ... is valid for L>0 near threshold
    Invoked in Eq. (1) of the main text.
  • domain assumption Causality bounds and generalized Wigner bound r_L ≤ b_L(R) from refs [8-11]
    Used to fix the exterior bound b_L(R) in Eq. (2); results are cited, not rederived.
  • domain assumption Zero-energy exterior wavefunction is a pure r^{-L} scaling branch with logarithmic derivative -L at r=R
    Boundary matching in Supplemental S1 and S3.
  • domain assumption Resonance pole is narrow and isolated so E_pole ≈ E_r - iΓ_L/2 and Γ_L ≈ 2k_r^{2L+1}/(µ|r_L|) with O(k^2) corrections negligible
    Used for the width formula and the data comparison; questionable for broad resonances such as 5He and 9He.
  • domain assumption Observed near-threshold states are predominantly single-neutron shape resonances describable by a one-body potential with channel radius R_eff
    Defines the benchmark set in Table I; fragmented or ambiguous states are excluded.
  • domain assumption WKB approximation for the Woods-Saxon normalization difference and barrier action deficit
    Derivation of Eq. (5) in Supplemental S5.

pith-pipeline@v1.3.0-alltime-deepseek · 12662 in / 19069 out tokens · 180224 ms · 2026-08-02T02:00:56.156517+00:00 · methodology

0 comments
read the original abstract

We establish universal width predictions for near-threshold single-neutron resonances in $L > 0$ partial waves. Our results go beyond Wigner's well-known scaling behavior of cross sections near threshold. We show that the finite square-well potential exhibits discrete scale invariance at zero energy. From this fact, we derive an analytic baseline for the resonance width that depends only on geometry, angular momentum, and resonance energy, and not on internal short-distance nuclear details or radial excitation. This is a nontrivial property that is unique to the finite square-well potential and does not occur for other potentials. Application to observed p-wave and d-wave resonances demonstrates that the square-well result provides a robust baseline. We show that discrete scale invariance erases radial-node information in the sharp-boundary limit, but realistic Woods-Saxon diffuseness breaks this invariance, suppressing the reduced width by a factor sensitive to the internal radial excitation. These results provide a simple geometric benchmark for identifying when observed neutron resonances are controlled by universal threshold physics and when they exhibit systematic deviations driven by structure-dependent effects.

Figures

Figures reproduced from arXiv: 2607.14464 by Dean Lee, Hans-Werner Hammer, Myungkuk Kim, Young-Ho Song, Youngman Kim, Yuan-Zhuo Ma.

Figure 1
Figure 1. Figure 1: FIG. 1. Normalized resonance width Γ [PITH_FULL_IMAGE:figures/full_fig_p004_1.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

41 extracted references · 12 linked inside Pith

  1. [1]

    A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido, Structure and reactions of quantum halos, Rev. Mod. Phys.76, 215 (2004)

    2004

  2. [2]

    Ab-initio nuclear structure and nuclear re- actions

    assuming the lowest radial mode (n= 0,χ 0,1 ≈4.49), the WS diffuseness yields a geometric suppression factor of roughly 1.8. Applying this estimate provides a geo- metric mechanism for width suppression relative to the sharp-boundary limit. However, given that the baseline geometric estimate already works within a factor of two for the data, we view this ...

    2024

  3. [3]

    E. P. Wigner, On the Behavior of Cross Sections Near Thresholds, Phys. Rev.73, 1002 (1948)

    1948

  4. [4]

    Braaten and H

    E. Braaten and H. W. Hammer, Universality in few-body systems with large scattering length, Phys. Rept.428, 259 (2006), arXiv:cond-mat/0410417

    Pith/arXiv arXiv 2006

  5. [5]

    R. Higa, H. W. Hammer, and U. van Kolck, alpha alpha Scattering in Halo Effective Field Theory, Nucl. Phys. A 809, 171 (2008), arXiv:0802.3426 [nucl-th]

    Pith/arXiv arXiv 2008

  6. [6]

    C. H. Schmickler, H. W. Hammer, and A. G. Volosniev, Universal physics of bound states of a few charged parti- cles, Phys. Lett. B798, 135016 (2019), arXiv:1904.00913 [nucl-th]

    Pith/arXiv arXiv 2019

  7. [7]

    Mochizuki and Y

    S. Mochizuki and Y. Nishida, Universal bound states and resonances with Coulomb plus short-range poten- tials, Phys. Rev. C110, 064001 (2024), arXiv:2408.06011 [nucl-th]

    Pith/arXiv arXiv 2024

  8. [8]

    H. M. Nussenzveig, The poles of the s-matrix of a rect- angular potential well of barrier, Nuclear Physics11, 499 (1959)

    1959

  9. [9]

    E. P. Wigner, Lower Limit for the Energy Derivative of the Scattering Phase Shift, Phys. Rev.98, 145 (1955)

    1955

  10. [10]

    D. R. Phillips and T. D. Cohen, How short is too short? Constraining contact interactions in nucleon-nucleon scattering, Phys. Lett. B390, 7 (1997), arXiv:nucl- th/9607048

    arXiv 1997

  11. [11]

    H. W. Hammer and D. Lee, Causality and universality in low-energy quantum scattering, Phys. Lett. B681, 500 (2009), arXiv:0907.1763 [nucl-th]

    Pith/arXiv arXiv 2009

  12. [12]

    Hammer and D

    H.-W. Hammer and D. Lee, Causality and the effec- tive range expansion, Annals Phys.325, 2212 (2010), arXiv:1002.4603 [nucl-th]

    Pith/arXiv arXiv 2010

  13. [13]

    Efimov, Energy levels arising from resonant two-body forces in a three-body system, Phys

    V. Efimov, Energy levels arising from resonant two-body forces in a three-body system, Phys. Lett. B33, 563 (1970)

    1970

  14. [14]

    V. N. Efimov, Weakly-Bound State of 3 Resonantly- Interacting Particles, Sov. J. Nucl. Phys.12, 589 (1971)

    1971

  15. [15]

    Kraemer, M

    T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H.-C. N¨ agerl,et al., Evidence for efimov quantum states in an ultracold gas of caesium atoms, Nature440, 315 (2006)

    2006

  16. [16]

    Braaten and H.-W

    E. Braaten and H.-W. Hammer, Efimov physics in cold atoms, Annals of Physics322, 120 (2007)

    2007

  17. [17]

    Efimov, Giant trimers true to scale, Nature Physics5, 533 (2009)

    V. Efimov, Giant trimers true to scale, Nature Physics5, 533 (2009)

    2009

  18. [18]

    Hammer and L

    H.-W. Hammer and L. Platter, Efimov states in nuclear and particle physics, Annual Review of Nuclear and Par- ticle Science60, 207 (2010)

    2010

  19. [19]

    J. Wang, J. P. D’Incao, B. Esry, and C. H. Greene, Ori- gin of the three-body parameter universality in efimov physics, Physical review letters108, 263001 (2012)

    2012

  20. [20]

    Nishida and S

    Y. Nishida and S. Tan, Liberating efimov physics from three dimensions, Few-Body Systems51, 191 (2011)

    2011

  21. [21]

    Nishida and D

    Y. Nishida and D. Lee, Weakly bound molecules trapped with discrete scaling symmetries, Physical Re- view A—Atomic, Molecular, and Optical Physics86, 032706 (2012)

    2012

  22. [22]

    Kunitski, S

    M. Kunitski, S. Zeller, J. Voigtsberger, A. Kalinin, L. P. H. Schmidt, M. Sch¨ offler, A. Czasch, W. Sch¨ ollkopf, R. E. Grisenti, T. Jahnke,et al., Observation of the efi- mov state of the helium trimer, Science348, 551 (2015)

    2015

  23. [23]

    Naidon and S

    P. Naidon and S. Endo, Efimov physics: a review, Re- ports on Progress in Physics80, 056001 (2017)

    2017

  24. [24]

    Kievsky, M

    A. Kievsky, M. Gattobigio, L. Girlanda, and M. Viviani, Efimov physics and connections to nuclear physics, An- nual Review of Nuclear and Particle Science71, 465 (2021)

    2021

  25. [25]

    Bringas, M

    F. Bringas, M. T. Yamashita, and T. Frederico, Tri- atomic continuum resonances for large negative scatter- ing lengths, Phys. Rev. A69, 040702 (2004), arXiv:cond- mat/0312291

    arXiv 2004

  26. [26]

    Deltuva, Energies and widths of Efimov states in the three-boson continuum, Phys

    A. Deltuva, Energies and widths of Efimov states in the three-boson continuum, Phys. Rev. C102, 034003 (2020), arXiv:2101.12654 [cond-mat.quant-gas]

    Pith/arXiv arXiv 2020

  27. [27]

    Dietz, H.-W

    S. Dietz, H.-W. Hammer, S. K¨ onig, and A. Schwenk, Three-body resonances in pionless effective field the- ory, Phys. Rev. C105, 064002 (2022), arXiv:2109.11356 [nucl-th]

    Pith/arXiv arXiv 2022

  28. [28]

    D. R. Tilley, C. M. Cheves, J. L. Godwin, G. M. Hale, H. M. Hayes, J. H. Kelley, C. G. Sheu, and H. R. Weller, Energy levels of light nucleiA= 5, 6, 7, Nucl. Phys. A 708, 3 (2002)

    2002

  29. [29]

    Caoet al., Recoil proton tagged knockout reaction for 8He, Phys

    Z. Caoet al., Recoil proton tagged knockout reaction for 8He, Phys. Lett. B707, 46 (2012)

    2012

  30. [30]

    Sun, Y. L. and others, Observation of a broadp- wave resonant state in 9He, arXiv preprint (2026), arXiv:2602.07810 [nucl-ex]

    arXiv 2026

  31. [31]

    Kondoet al., Low-lying resonant states in 13Be, Phys

    Y. Kondoet al., Low-lying resonant states in 13Be, Phys. Lett. B690, 245 (2010)

    2010

  32. [32]

    Corsiet al., Structure of 13Be studied in proton knockout from 14B, Phys

    A. Corsiet al., Structure of 13Be studied in proton knockout from 14B, Phys. Lett. B797, 134843 (2019), arXiv:1908.09459 [nucl-ex]

    Pith/arXiv arXiv 2019

  33. [33]

    Revelet al.(SAMURAI21 collaboration), Extending the southern shore of the island of inversion to 28F, Phys

    A. Revelet al.(SAMURAI21 collaboration), Extending the southern shore of the island of inversion to 28F, Phys. Rev. Lett.124, 152502 (2020)

    2020

  34. [34]

    D. S. Delion and S. Ghinescu, Systematics of neutron emission, J. Phys. G52, 055105 (2025), arXiv:2311.08180 [nucl-th]

    Pith/arXiv arXiv 2025

  35. [35]

    J. H. Kelley, E. Kwan, J. E. Purcell, C. G. Sheu, and H. R. Weller, Energy levels of light nucleiA= 11, Nucl. Phys. A880, 88 (2012)

    2012

  36. [36]

    Snyderet al., First observation of the unbound nucleus 15Be, Phys

    J. Snyderet al., First observation of the unbound nucleus 15Be, Phys. Rev. C88, 031303 (2013)

    2013

  37. [37]

    Kondoet al., Nucleus 26O: A Barely Unbound Sys- tem beyond the Drip Line, Phys

    Y. Kondoet al., Nucleus 26O: A Barely Unbound Sys- tem beyond the Drip Line, Phys. Rev. Lett.116, 102503 (2016)

    2016

  38. [38]

    C. R. Hoffmanet al., Determination of theN= 16 halo shell closure at the oxygen drip line, Phys. Rev. Lett. 100, 152502 (2008), arXiv:0801.3855 [nucl-ex]

    Pith/arXiv arXiv 2008

  39. [39]

    A. M. Lane and R. G. Thomas, R-Matrix Theory of Nu- clear Reactions, Rev. Mod. Phys.30, 257 (1958)

    1958

  40. [40]

    S. A. Gurvitz and G. Kaelbermann, The Decay Width and the Shift of a Quasistationary State, Phys. Rev. Lett. 59, 262 (1987)

    1987

  41. [41]

    theoretical range

    N. Michel, W. Nazarewicz, M. Ploszajczak, and T. Vertse, Shell Model in the Complex Energy Plane, J. Phys. G36, 013101 (2009), arXiv:0810.2728 [nucl-th]. 6 Supplemental Material S1. DISCRETE SCALE INV ARIANCE AND NODE INDEPENDENCE The independence of the threshold resonance width on the internal radial excitation is a consequence of a discrete scale symme...

    Pith/arXiv arXiv 2009