REVIEW 4 major objections 6 minor 70 references
Neutron skin thickness for $^{208}$Pb from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness for $^{48}$Ca, O, N, C isotopes from reaction and interaction cross sections
T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash
Pith's one-line read A single 14.137 MeV neutron total-cross-section measurement places the 208Pb neutron skin at 0.309 ± 0.057 fm, in agreement with PREX2.
desk verdict A careful folding-model reanalysis that gets PREX2- and CREX-consistent skins, but the 208Pb number rests on one datum with unquantified compound-nucleus effects. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing mechanism is density scaling inside a folding-model optical potential. At low and intermediate energies the paper computes the projectile-target potential by folding a chiral $g$-matrix interaction, which incorporates nuclear-medium effects, with the projectile and target densities; at higher energies it uses a $t$-matrix-based folding model renormalized by a fine-tuning factor $F=0.93766$ calibrated on $^{12}$C+$^{12}$C scattering. The extraction works by scaling the neutron density (and, where needed, the proton density) through $\alpha = \sqrt{\langle r^2\rangle_{\rm scaled}/\langle r^2\rangle}$ until the calculated cross section reproduces the measured one, always holding $r_p$ fixed at its electron-scattering or charge-changing value. The skin value is then the difference between the scaled neutron radius and the fixed proton radius. For $^{48}$Ca the densities used are the D1M-GHFB+AMP self-consistent mean-field densities with angular momentum projection, which the paper shows reproduce the binding energy and matter radius better than the D1S variant.
What would settle it
Measure total neutron cross sections of $^{208}$Pb at several energies between 8 and 20 MeV and analyze them with the same folding model after subtracting compound-nucleus contributions computed with a statistical reaction code; the extraction would be falsified if including those contributions at 14.137 MeV shifts the fitted skin by more than $0.057$ fm, or if the fitted value drifts systematically with energy.
Extended reading notes
Core claim
The central discovery is that one high-precision total cross section at a single energy can pin down a neutron skin. Using the chiral $g$-matrix folding model, the paper scales the neutron density of $^{208}$Pb so that the calculated total cross section reproduces the measured 14.137 MeV value, under the constraint that the proton radius stays at the experimental charge-radius value; this yields $r_{\rm skin}(^{208}{\rm Pb})=0.309\pm0.057$ fm, overlapping PREX2. For $^{48}$Ca, proton reaction cross sections between 23 and 48 MeV, analyzed with the D1M-GHFB+AMP densities and a fine-tuning factor, give $r_{\rm skin}(^{48}{\rm Ca})=0.163\pm0.037$ fm, overlapping CREX; the D1M densities are shown to reproduce the binding energy and matter radius better than the D1S densities. On the isotope chains, the same machinery finds $r_{\rm skin}(^{14}{\rm N})=0.267\pm0.056$ fm and $r_{\rm skin}(^{17}{\rm O})=0.197\pm0.067$ fm, and marks $^{22}$N as halo-like by two quantitative criteria. The paper concludes that each extracted value agrees with the corresponding parity-violation experiment, so cross-section measurements offer an independent route to neutron skins.
Load-bearing premise
The $^{208}$Pb extraction assumes that everything contributing to the measured total cross section at 14.137 MeV, including compound-nucleus formation, is either negligible or correctly described by the folding model; the paper itself notes that compound-nucleus effects appear at low energies and could account for the small difference from PREX2, yet they are not included in the model or in the quoted $0.057$ fm error.
Editorial extensions
If this is right
- A single measured total cross section at 14.137 MeV determines the $^{208}$Pb neutron skin with uncertainty comparable to PREX2, without needing an electron beam.
- Low-energy proton reaction cross sections on $^{48}$Ca give a skin consistent with CREX, so proton scattering can serve as an independent check on parity-violation results.
- Among C, N, O isotopes, $^{14}$N and $^{17}$O stand out as light stable nuclei with thick skins, making them accessible targets for studying skin effects without radioactive beams.
- Minima of $r_m/A^{1/3}$ locate the $N=8$ major shell in N and C isotopes and the $N=14$ subshell in O, N, C, indicating soft cores in light neutron-rich chains.
- $^{22}$N satisfies the paper's two halo criteria and is classified as halo-like, with $H_1=0.148$ and $H_2=0.241$.
Reading between the lines
- If the single-energy extraction is robust, archived total and reaction cross sections across many nuclei could be re-analyzed with the same density-scaling procedure, producing a much wider neutron-skin survey than PREX2 and CREX alone provide; this is an application the paper does not itself make.
- The unmodeled compound-nucleus contribution at 14.137 MeV, which the paper acknowledges may explain the small offset from PREX2, is a concrete place to test the method: including a statistical-model correction could either harden the $0.309$ fm value or reveal a bias larger than the quoted error.
- The large skin found for the self-conjugate nucleus $^{14}$N is, in the paper's view, a Coulomb effect; a testable extension is to compare the $^{14}$N skin extracted with the same method against density functionals computed with the Coulomb force artificially switched off, to see whether the $0.267$ fm value collapses as expected.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper reanalyzes published cross-section data to extract neutron skin thicknesses using the Kyushu g-matrix folding model for low energies and the Love-Franey t-matrix folding model for intermediate energies. It reports r_skin(208Pb)=0.309±0.057 fm from the single n+208Pb total cross section measured by Foster and Glasgow at 14.137 MeV, r_skin(48Ca)=0.163±0.037 fm from p+48Ca reaction cross sections at 23–48 MeV, and skin values for C, N, and O isotopes from interaction cross sections. The results are compared with PREX2 and CREX values, and 14N and 17O are identified as stable nuclei with relatively large skin thicknesses.
Significance. If the extractions are robust, the paper would provide independent hadronic-scattering checks of the PREX2 and CREX neutron-skin values and would demonstrate the predictive reach of the Kyushu folding model across a wide energy range. The manuscript has genuine strengths: it tests the folding model against p+208Pb and 12C+12C data, compares D1M and D1S Gogny densities for 48Ca, and presents systematic tables of radii and skins for C, N, and O isotopes. However, the quoted uncertainties are almost exclusively experimental; model dependence from the fine-tuning factors and from the choice of densities is acknowledged in Sec. IV but not propagated into the final errors. Because several extractions are one-parameter fits calibrated on the same data, the current significance is limited pending a quantitative treatment of these systematic uncertainties.
major comments (4)
- [III A and IV] The 208Pb extraction is a one-parameter fit to a single total cross section at 14.137 MeV (Fig. 2). The quoted ±0.057 fm propagates only the experimental uncertainty of σ_T, not the model uncertainty. The paper itself states in Sec. IV that compound-nucleus effects appear at low incident energies and that the small difference from PREX2 may come from those effects, yet no systematic uncertainty is assigned. Since any missing contribution to σ_T is absorbed by the neutron-density scaling of Eq. (9), the central value and the PREX2 agreement are not robust at the stated precision. Please model the compound-nucleus contribution or add a quantitative systematic error and weaken the claim accordingly.
- [III C 3] The p+48Ca extraction uses f = 0.968537 obtained by averaging σ_R(exp)/σ_R(ref) over the very data points that are then fitted after scaling the densities. This makes the extracted r_skin partly determined by the fitted f and does not provide an independent check. The quoted ±0.037 fm excludes the model dependence of f and of the density choice (D1M vs D1S). Please quantify the sensitivity of r_skin to f and to the density functional and include those contributions in the final uncertainty.
- [III D and IV] The global factor F = 0.93766 is fitted to 12C+12C data and then applied to C, N, and O isotopes on a 12C target at 710–1020 MeV/u. Section IV notes that a 0.35% change in F shifts r_m by 0.33%, but the tables in Sec. III D quote only the experimental cross-section errors. This omitted F-uncertainty propagates directly into the r_skin values for N, O, and C, including the headline 14N and 17O results. Please propagate the F uncertainty into every reported skin value or state explicitly, with a quantitative argument, why it is negligible.
- [III E 1] The p+14N analysis follows the same ESP-f procedure: f = 0.86196 is the average of σ_R(exp)/σ_R(th) over the same data, and the densities are then scaled to reproduce those data. The resulting r_skin(14N)=0.267±0.056 fm therefore inherits the same circularity and unquantified model dependence. Please clarify what independent information this extraction provides, or remove the strong comparison with PREX2.
minor comments (6)
- [II] The section heading 'MEHOD' should be 'METHOD'.
- [Abstract and text] There are duplicated words such as 'the the σ_T' and 'nuclei having nuclei having'; the manuscript needs careful proofreading.
- [III D] In the opening line of Sec. III D, 'shown blow' should be 'shown below'.
- [III C] In Sec. III C, 'nuleon' should be 'nucleon'.
- [II A] The relation 'Ar2_m = Zr^2_p + N r^2_n' is typeset ambiguously; write A⟨r^2⟩_m = Z⟨r^2⟩_p + N⟨r^2⟩_n to avoid confusion with A times r^2_m.
- [III D 1] The caption of Fig. 17 mentions shell corrections and deformation, but the figure is not referenced in the main text at the point of discussion; please clarify the role of this figure and its connection to the C, N, O skin results.
Circularity Check
Partial circularity: the model-reliability test for the n+208Pb extraction is self-referential, although the central skin values are genuine fits to external data.
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self citation load bearing
[Section I, Introduction (model reliability for p+208Pb)]
"In Ref. [9], we tested the Kyushu g-matrix folding model for σR on p+208Pb scattering in 20≤Elab≤180 MeV and find that our folding model is reliable there, using the σR(PREX2) calculated with the folding model with the neutron density scaled to r208n(PREX2); note that the r208p calculated with D1S-GHFB+AMP agrees with the r208p(PREX2) of Ref. [5]"
The reliability of the folding model in the energy range relevant to the 208Pb extraction is established by comparing the model with σR(PREX2) values that are themselves calculated with the same folding model after forcing the neutron density to the PREX2 neutron radius. This check compares the model with its own output, so the cited Ref. [9] does not provide independent validation. The citation is load-bearing because it is invoked to justify using the Kyushu g-matrix folding model at 14.137 MeV, even though other external tests (e.g., 12C+12C data) provide some independent support.
full rationale
The central 208Pb and 48Ca skin extractions are not, by themselves, circular: each is obtained by scaling a microscopic density so that a folding-model cross section matches an external measured cross section (Foster-Glasgow σT for 208Pb; Carlson σR for 48Ca), and the comparisons with PREX2 and CREX are external benchmark data rather than inputs of the fit. The p+48Ca fine-tuning factor f=0.968537 is obtained by averaging σR(exp)/σR(ref) over the same data set, but this is a calibration of the model normalization before the density scaling, and the final comparison with CREX remains independent; treating this as a prediction would be an overstatement, so I do not count it as a circular step. The genuine circular element is the validation chain for the folding model in the 208Pb energy range: the paper relies on a prior same-author test in which the model is checked against σR(PREX2) values generated by the model itself. Furthermore, the quoted ±0.057 fm uncertainty omits the compound-nucleus contribution at 14.137 MeV, which the paper itself concedes may explain the residual relative to PREX2; that is an important completeness and systematic-error concern, but it is not circularity. Overall, the central values have independent data content, but the load-bearing model-validation support for the n+208Pb analysis is partly self-referential, warranting a moderate circularity score.
Assumptions & free parameters
free parameters (4)
- F (Love-Franey renormalization factor) =
0.93766
- f (p+48Ca fine-tuning factor) =
0.968537
- f (p+14N fine-tuning factor) =
0.86196
- f (p+16O fine-tuning factor) =
0.92449
assumptions (4)
- domain assumption The Kyushu g-matrix folding model, built from chiral N3LO two-nucleon forces and NNLO three-nucleon forces with cD = -2.5 and cE = 0.25, reliably describes reaction and total cross sections for the systems and energies considered.
- domain assumption The input densities (Gogny-D1M-HFB+AMP for 48Ca, D1S-GHFB+AMP for 208Pb, SLy7 for N isotopes, phenomenological densities for 12C) accurately represent the true ground-state densities.
- standard math The density scaling relation in Eq. (9), which multiplies the radial coordinate by alpha and preserves the density shape, captures how the cross section depends on the matter radius.
- ad hoc to paper The fine-tuning factor F determined from 12C+12C scattering is universal for C, N, O isotopes on a 12C target at energies near 700-1000 MeV/nucleon.
Cite this review
Pith. "Pith review of Neutron skin thickness for $^{208}$Pb from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness for $^{48}$Ca, O, N, C isotopes from reaction and interaction cross sections." pith.science (2026). https://pith.science/paper/KWGGURVA
@misc{pith2026241110690,
author = {Pith},
title = {Pith review of: Neutron skin thickness for $^208$Pb from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness for $^48$Ca, O, N, C isotopes from reaction and interaction cross sections},
year = {2026},
howpublished = {\url{https://pith.science/paper/KWGGURVA}},
note = {Machine review of arXiv:2411.10690}
}
abstract
Foster {\it et al.} measured total neutron cross sections $\sigma_{\rm T}$ of n+$^{208}$Pb scattering at $14.137$MeV. Carlson {\it et al.} measured $\sigma_{\rm R}$ for $p$+$^{48}$Ca scattering in $23 \text{--} 48$MeV. Tanaka {\it et al.} measured $\sigma_{\rm I}$ for $^{42\text{--}51}$Ca + $^{12}$C scattering at 280MeV/u. Bagchi {\it et al.} measured the charge-changing (CC) cross sections and determined proton radii $r_{\rm p}({\rm CC})$ for $^{14,15,17 \text{--} 22}$N from the CC cross sections. Kanungo {\it et al.} measured the CC cross sections and extracted $r_{\rm p}({\rm CC})$ for $^{12\text{--} 19}$C. Kaur {\it et al.} measured the CC cross sections and determined $r_{\rm p}({\rm CC})$ for $^{16,18 \text{--} 24}$O. Our 1st aim is to extract $r_{\rm skin}^{208}$ from the the $\sigma_{\rm T}$ of n+$^{208}$Pb scattering at $14.137$MeV. Our 2nd aim is to determine $r_{\rm skin}^{48}({\rm skin})$ from $\sigma_{\rm R}$ on p+$^{48}$Ca scattering in $E_{\rm lab}=23 \text{--} 48$MeV. Our 3rd aim is to find light stable nuclei having nuclei having large $r_{\rm skin}$. We use the Kyushu $g$-matrix folding model for lower $E_{\rm lab}$ and the folding model based on the Love-Franey $t$-matrix for higher $E_{\rm lab}$. We determine $r_{\rm skin}^{48}({\rm skin})=0.163 \pm 0.037{\rm fm}$ from the $\sigma_{\rm R}$ on p+$^{48}$Ca scattering, using the Kyushu $g$-matrix folding model with the D1M-GHFB+AMP proton and neutron densities. We show that D1M-GHFB+AMP is better than D1S-GHFB+AMP for the matter radius and the binding energy. Our skin value is consistent with $r_{\rm skin}^{48}({\rm CREX})$. For C, N, O isotopes, we find that $r_{\rm skin}= 0.267 \pm 0.056$~fm for $^{14}$N and $r_{\rm skin}= 0.197 \pm 0.067$~fm for $^{17}$O. Our value $r_{\rm skin}^{208}=0.309 \pm 0.057$fm agrees with $r_{\rm skin}^{208}({\rm PREX2})$.
Figures
Figures from the paper (14 more)
Reference graph
Works this paper leans on
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[1]
Comparison between D1S and D1M for 48Ca Figure 5 shows σR as a function of Elab for p+48Ca scat- tering. The results of the D1M-GHFB+AMP densities yield better agreement with the data [17] than those of the D1S- GHFB+AMP densities. This is true for 48Ca+12C scattering at 280 MeV/nuleon [19], as shown in Fig. 6. 800 850 900 950 1000 1050 1100 1150 1200 20 ...
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[2]
48Ca+12C scattering in Elab = 280MeV/u Figure 6 shows σI for 48Ca+12C scattering at 280 MeV/nucleon. Scaling the D1M-GHFB+AMP pro- ton and neutron densities for 48Ca , we can obtain r48 skin(skin) = 0.180 ± 0.058 fm. (11) Since we do not adopt any fine-tuning factor, we use the re- sulting values of Table III as reference values for 48Ca. We can obtain rm...
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[3]
p+48Ca scattering in Elab = 23–48 MeV The σR(ref) calculated with the Kyushu g-matrix fold- ing model with the proton and neutron densities having rp(ref) and rn(ref) are compared with the data [17] in Fig. 7. The fine-tuning factor f is obtained by averag- ing σR(exp)/σR(ref) over Elab. The resulting value is f = 0.968537. The f σR(ref) are scaled so as ...
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[4]
N isotopes We use the data σI [12, 42, 48, 49] for 14–23N+12C scat- tering in 710–1020 MeV/u; see Table 1 of Ref. [12] for the values of σI. Figure 8 shows A dependence of interaction cross sections σI for 14–23N+12C scattering, where A is the mass number. The LF t-matrix folding model overshoots σI [12, 42, 48, 49]. The renormalized F σR(LF) with F = 0 ....
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[5]
O isotopes The same procedure is taken for O isotopes. As shown in Fig. 10, the LF t-matrix folding model overshoots the data σI of Refs. [12, 42, 50] in A = 13 –22. The F σR(LF) with F = 0.93766 reproduce the data in A = 13–22. A FIG. 10. A dependence of interaction cross sections σI for AO+12C scattering. Open circles stand for the results of the LF t-m...
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[6]
C isotopes As for 12C+12C scattering, the F σR(LF) reproduces the data [12, 41] at 790, 950 MeV/u within error-bars, as shown in Fig. 1. The phenomenological proton and neutron densities are scaled so as to reproduce the data under the condition of rp,scaling = rp(exp). The average of two rm values is taken. The projectile 12C densities should be the same...
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[7]
Shell effects We analyzed the data σI [20] on 42−51Ca+12C scattering by using Kyushu (chiral) g-folding model with D1S-GHFB proton and neutron densities with and without AMP. Figure 13 shows our rn of Ref. [20] values as a function of N for 42–51Ca. Our rn values are minimized at N = 28. This is the fact that N = 28 is a major shell. 20+N FIG. 13. N depen...
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[8]
Relation between rm and total binding energy for N isotopes As for N isotopes, the data on β ≡ rmEB/(Aℏc) hardly depend on A for A = 14–22; note that EB/A is the binding energy per nucleon. In fact, the deviation ofβ is much smaller than the average value; namely, β = 0.0977(6) (13) 10 for A = 14–22. This indicates that rm is inversely proportion to EB/A....
Show all 70 references
-
[9]
Figure 16 shows our values on σR and the data [51]
p+ 14N scattering We extract rm(σR) from the data [51] σR(exp) for p+14N scattering, using the Kyushu g-matrix folding model with the Sly7 proton and neutron densities. Figure 16 shows our values on σR and the data [51]. The Kyushu g-matrix folding model with the SLy7 densitie...
-
[10]
[52], the σR have been measured for 12C, 16O tar- gets at 65.5 MeV
p+ 16O scattering In Ref. [52], the σR have been measured for 12C, 16O tar- gets at 65.5 MeV . We first deriveσR(th) with the Kyushu g- matrix folding model with the phenomenological proton and neutron densities of 12C and introduce a fine-tuning factor f as f = σR(exp)/σR(th)...
-
[11]
[56], Li, Luo and Wang compiled the charge radii Rch of 236 nuclei measured by laser spectroscopy experi- ment, and calculated the uncertainties
Deformation for 12,14,16,18C In Ref. [56], Li, Luo and Wang compiled the charge radii Rch of 236 nuclei measured by laser spectroscopy experi- ment, and calculated the uncertainties. From the Rch of Mg isotope chain, the new magic number N = 14 can be ob- served. They introduc...
-
[12]
D1S and SLy7 for rskin on N isotopes The rskin(SLy7) calculated with SLy7 are compared with the rskin(D1S) with D1S in Fig. 19. The rskin(SLy7) are al- most the same as rskin(D1S) except for for 21N. The differ- ence between rskin(SLy7) and rskin(D1S) is appreciable only for 2...
-
[13]
C. J. Horowitz, S. J. Pollock, P. A. Souder, and R. Michaels, Parity violating measurements of neutron densities, Phys. Rev. C 63, 025501 (2001)
2001
-
[14]
Adhikari et al
D. Adhikari et al. (PREX), Accurate Determination of the Neutron Skin Thickness of 208Pb through Parity-Violation in Electron Scattering, Phys. Rev. Lett. 126, 172502 (2021), arXiv:2102.10767 [nucl-ex]
2021 arXiv
-
[15]
Adhikari et al
D. Adhikari et al. (CREX), Precision Determination of the Neu- tral Weak Form Factor of Ca48, Phys. Rev. Lett. 129, 042501 (2022), arXiv:2205.11593 [nucl-ex]
2022 arXiv
-
[16]
Angeli and K
I. Angeli and K. P. Marinova, Table of experimental nuclear ground state charge radii: An update, Atom. Data Nucl. Data Tabl. 99, 69 (2013)
2013
-
[17]
B. A. Brown, Constraints on the Skyrme Equations of State from Properties of Doubly Magic Nuclei, Phys. Rev. Lett. 111, 232502 (2013), arXiv:1308.3664 [nucl-th]
2013 arXiv
-
[18]
Tagami, T
S. Tagami, T. Wakasa, J. Matsui, M. Yahiro, and M. Takechi, Neutron skin thickness of Pb208 determined from the reaction cross section for proton scattering, Phys. Rev. C 104, 024606 (2021), arXiv:2010.02450 [nucl-th]
2021 arXiv
-
[19]
Toyokawa, M
M. Toyokawa, M. Yahiro, T. Matsumoto, and M. Kohno, Effects of chiral three-nucleon forces on 4He-nucleus scattering in a wide range of incident energies, PTEP 2018, 023D03 (2018), arXiv:1712.07033 [nucl-th]
2018 arXiv
-
[20]
Tagami, M
S. Tagami, M. Tanaka, M. Takechi, M. Fukuda, and M. Yahiro, Chiral g-matrix folding-model approach to reaction cross sec- tions for scattering of ca isotopes on a c target, Phys. Rev. C 101, 014620 (2020)
2020
-
[21]
Wakasa, S
T. Wakasa, S. Tagami, J. Matsui, M. Takechi, and M. Yahiro, Neutron-skin values and matter and neutron radii determined from reaction cross sections of proton scattering on C12, Ca40,48, Ni58, and Pb208, Phys. Rev. C 107, 024608 (2023), arXiv:2211.16688 [nucl-th]
2023 arXiv
-
[22]
Matsuzaki, S
M. Matsuzaki, S. Tagami, and M. Yahiro, Neutron skin thick- ness of Pb208, Sn116,120,124, and Ca40 determined from reac- tion cross sections of He4 scattering, Phys. Rev. C104, 054613 (2021), arXiv:2107.06441 [nucl-th]
2021 arXiv
-
[23]
D. G. Foster and D. W. Glasgow, Neutron total cross sections, 2.5-15 mev. i. experimental, Phys. Rev. C3, 576 (1971)
1971
-
[24]
Ozawa, T
A. Ozawa, T. Suzuki, and I. Tanihata, Nuclear size and related topics, Nucl. Phys. A 693, 32 (2001)
2001
-
[25]
Bagchi et al., Neutron skin and signature of the N = 14 shell gap found from measured proton radii of 17−22N, Phys
S. Bagchi et al., Neutron skin and signature of the N = 14 shell gap found from measured proton radii of 17−22N, Phys. Lett. B 790, 251 (2019), arXiv:1901.09707 [nucl-ex]
2019 arXiv
-
[26]
Kaur et al., Proton distribution radii of 16−24O: signatures of new shell closures and neutron skin, Phys
S. Kaur et al., Proton distribution radii of 16−24O: signatures of new shell closures and neutron skin, Phys. Rev. Lett. 129, 142502 (2022), arXiv:2209.00722 [nucl-ex]
2022 arXiv
-
[27]
Kanungo et al., Proton Distribution Radii of 12−19C Illumi- nate Features of Neutron Halos, Phys
R. Kanungo et al., Proton Distribution Radii of 12−19C Illumi- nate Features of Neutron Halos, Phys. Rev. Lett. 117, 102501 (2016), arXiv:1608.08697 [nucl-ex]
2016 arXiv
-
[28]
A. V . Dobrovolsky et al., Nuclear matter distributions in the neutron-rich carbon isotopes 14−17C from intermediate-energy proton elastic scattering in inverse kinematics, Nucl. Phys. A 1008, 122154 (2021), arXiv:2101.10687 [nucl-ex]
2021
-
[29]
R. F. Carlson, A. J. Cox, N. E. Davison, T. Eliyakut-Roshko, R. H. McCamis, and W. T. H. v. Oers, Proton total reaction cross-sections for Ca-42, Ca-44, and Ca-48 between 21 and 48 MeV, Phys. Rev. C 49, 3090 (1994)
1994
-
[30]
Tagami, M
S. Tagami, M. Tanaka, M. Takechi, M. Fukuda, and M. Yahiro, Chiral g-matrix folding-model approach to reaction cross sec- tions for scattering of Ca isotopes on a C target, Phys. Rev. C 101, 014620 (2020), arXiv:1911.05417 [nucl-th]
2020 arXiv
-
[31]
Tanaka et al., Swelling of Doubly Magic 48Ca Core in Ca Isotopes beyond N = 28, Phys
M. Tanaka et al., Swelling of Doubly Magic 48Ca Core in Ca Isotopes beyond N = 28, Phys. Rev. Lett. 124, 102501 (2020), arXiv:1911.05262 [nucl-ex]
2020 arXiv
-
[32]
Takechi, T
M. Takechi, T. Wakasa, S. Tagami, J. Matsui, and M. Yahiro, Reanalyzes for 42–51ca scattering on a 12c target at 280 mev/nucleon based on chiral g folding mode with gogny- d1s hartree–fock–bogoliubov densities, Results in Physics 31, 104923 (2021)
2021
-
[33]
Gonzalez-Boquera, M
C. Gonzalez-Boquera, M. Centelles, X. Vi ˜nas, and L. M. Rob- ledo, New Gogny interaction suitable for astrophysical applica- tions, Phys. Lett. B 779, 195 (2018), arXiv:1712.06735 [nucl- th]
2018 arXiv
-
[34]
Tagami, T
S. Tagami, T. Wakasa, M. Takechi, J. Matsui, and M. Yahiro, Neutron skin in 48ca determined from p+48ca and 48ca+12c scattering, Results in Physics 33, 105155 (2022)
2022
-
[35]
Tagami, T
S. Tagami, T. Wakasa, and M. Yahiro, 12c+12c scattering as the reference system for reaction cross section, Results in Physics 51, 106675 (2023)
2023
-
[36]
Wakasa, S
T. Wakasa, S. Tagami, and M. Yahiro, Skin values of 208pb and 48ca determined from reaction cross sections, Results in Physics 43, 106101 (2022)
2022
-
[37]
W. G. Love and M. A. Franey, Phys. Rev. C 24, 1073 (1981)
1981
-
[38]
F. A. . Brieva and J. Rook, Nucl. Phys. A291, 299 (1977)
1977
-
[39]
K. Amos, P. J. Dortmans, H. V . von Geramb, S. Karataglidis, and J. Raynal, Advances in Nuclear Physics, edited by J. W. Negele and E. V ogt, V ol. 25 (Plenum, New York, 2000) p. 275
2000
-
[40]
Furumoto, Y
T. Furumoto, Y . Sakuragi, and Y . Yamamoto, Phys. Rev. C78, 044610 (2008)
2008
-
[41]
Minomo, T
K. Minomo, T. Sumi, M. Kimura, K. Ogata, Y . R. Shimizu, and M.Yahiro, Phys. Rev. Lett.108, 052503 (2012)
2012
-
[42]
T. Sumi, K. Minomo, S. Tagami, M. Kimura, T. Matsumoto, K. Ogata, Y . R. Shimizu, and M. Yahiro, Deformation of Ne iso- topes in the island-of-inversion region, Phys. Rev. C85, 064613 (2012), arXiv:1201.2497 [nucl-th]
2012 arXiv
-
[43]
Egashira, K
K. Egashira, K. Minomo, M. Toyokawa, T. Matsumoto, and M. Yahiro, Microscopic optical potentials for 4He scattering, Phys. Rev. C 89, 064611 (2014), arXiv:1404.2735 [nucl-th]
2014 arXiv
-
[44]
Watanabe et al., Ground-state properties of neutron-rich Mg isotopes, Phys
S. Watanabe et al., Ground-state properties of neutron-rich Mg isotopes, Phys. Rev. C 89, 044610 (2014), arXiv:1404.2373 [nucl-th]
2014 arXiv
-
[45]
Toyokawa, K
M. Toyokawa, K. Minomo, M. Kohno, and M. Yahiro, Roles of chiral three-nucleon forces in nucleon–nucleus scattering, J. Phys. G 42, 025104 (2015), [Erratum: J.Phys.G 44, 079502 (2017)], arXiv:1404.6895 [nucl-th]
2015 arXiv
-
[46]
Toyokawa, M
M. Toyokawa, M. Yahiro, T. Matsumoto, K. Minomo, K. Ogata, and M. Kohno, Microscopic calculations based on chiral two- and three-nucleon forces for proton- and 4He-nucleus scatter- ing, Phys. Rev. C92, 024618 (2015), [Erratum: Phys.Rev.C 96, 059905 (2017)], arXiv:1507.02807 [nucl-th]
2015 arXiv
-
[47]
Kohno, Phys
M. Kohno, Phys. Rev. C 88, 064005 (2013)
2013
-
[48]
H. V . von Gerambet al., Phys. Rev. C 44, 73 (1991)
1991
-
[49]
Amos and P
K. Amos and P. J. Dortmans, Phys. Rev. C 49, 1309 (1994)
1994
-
[50]
de Vries, C
H. de Vries, C. W. de Jager, and C. de Vries, NUCLEAR CHARGE-DENSITY-DISTRIBUTION PARAMETERS, At. Data Nucl. Data Tables 36, 495 (1987)
1987
-
[51]
Chabanat, P
E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaef- fer, A Skyrme parametrization from subnuclear to neutron star densities. 2. Nuclei far from stablities, Nucl. Phys. A 635, 231 (1998), [Erratum: Nucl.Phys.A 643, 441–441 (1998)]. 14
1998
-
[52]
Schunck et al., Solution of the Skyrme- Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis
N. Schunck et al., Solution of the Skyrme- Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): A new version of the program, Comput. Phys. Commun. 216, 145 (2017), arXiv:1612.05314 [nucl-th]
2017 arXiv
-
[53]
Tanihata, T
I. Tanihata, T. Kobayashi, O. Yamakawa, S. Shimoura, K. Ekuni, K. Sugimoto, N. Takahashi, T. Shimoda, and H. Sato, Measurement of Interaction Cross-Sections Using Iso- tope Beams of Be and B and Isospin Dependence of the Nuclear Radii, Phys. Lett. B 206, 592 (1988)
1988
-
[54]
Ozawa et al., Measurements of interaction cross sections for light neutron-rich nuclei at relativistic energies and determina- tion of effective matter radii, Nucl
A. Ozawa et al., Measurements of interaction cross sections for light neutron-rich nuclei at relativistic energies and determina- tion of effective matter radii, Nucl. Phys. A 691, 599 (2001)
2001
-
[55]
Takechi et al., Reaction cross sections at intermediate ener- gies and Fermi-motion effect, Phys
M. Takechi et al., Reaction cross sections at intermediate ener- gies and Fermi-motion effect, Phys. Rev. C 79, 061601 (2009)
2009
-
[56]
Ingemarsson, J
A. Ingemarsson, J. Nyberg, P. Renberg, O. Sundberg, R. Carl- son, A. Cox, A. Auce, R. Johansson, G. Tibell, D. T. Khoa, and R. Warner, New results for reaction cross sections of inter- mediate energy particles on targets from 9be to 208pb, Nuclear Physics A 676, 3 (2000)
2000
-
[57]
Bonin, N
B. Bonin, N. Alamanos, B. Berthier, G. Bruge, H. Faraggi, J. Lugol, W. Mittig, L. Papineau, A. Yavin, J. Arvieux, L. Far- vacque, M. Buenerd, and W. Bauhoff, Alpha-nucleus elastic scattering at intermediate energies, Nuclear Physics A 445, 381 (1985)
1985
-
[58]
Kameyama, M
H. Kameyama, M. Kamimura, and Y . Fukushima, Coupled- rearrangement-channel Gaussian-basis variational method for trinucleon bound states, Phys. Rev. C 40, 974 (1989)
1989
-
[59]
Hiyama, B
E. Hiyama, B. F. Gibson, and M. Kamimura, Four-body cal- culation of the first excited state of He-4 using a realistic nn interaction: He-4(e, e-prime) He-4(02+) and the monopole sum rule, Phys. Rev. C 70, 031001 (2004)
2004
-
[60]
Ozawa et al., Interaction cross-sections and radii of mass number A = 17 isobars (N-17, F-17, and Ne-17), Phys
A. Ozawa et al., Interaction cross-sections and radii of mass number A = 17 isobars (N-17, F-17, and Ne-17), Phys. Lett. B 334, 18 (1994)
1994
-
[61]
Chulkov et al., Interaction cross-sections and matter radii of A = 20 isobars, Nucl
L. Chulkov et al., Interaction cross-sections and matter radii of A = 20 isobars, Nucl. Phys. A 603, 219 (1996)
1996
-
[62]
Ozawa, I
A. Ozawa, I. Tanihata, T. Kobayashi, Y . Sugahara, O. Ya- makawa, K. Omata, K. Sugimoto, D. Olson, W. Christie, and H. Wieman, Interaction cross sections and radii of light nuclei, Nucl. Phys. A 608, 63 (1996)
1996
-
[63]
Carlson, A
R. Carlson, A. Cox, T. Nasr, M. De Jong, D. Ginther, D. Hasell, A. Sourkes, W. van Oers, and D. Margaziotis, Measurements of proton total reaction cross sections for 6li, 7li, 14n, 20ne and 40ar between 23 and 49 mev, Nuclear Physics A445, 57 (1985)
1985
-
[64]
Ingemarsson, J
A. Ingemarsson, J. Nyberg, P. Renberg, O. Sundberg, R. Carl- son, A. Auce, R. Johansson, G. Tibell, B. Clark, L. Kurth Kerr, and S. Hama, Reaction cross sections for 65 mev protons on targets from 9be to 208pb, Nuclear Physics A 653, 341 (1999)
1999
-
[65]
The value for 6He is taken from Ref. [58]. The value for 11Li is calculated from rm = 3.12 ± 0.16 fm [12, 41] and rp = 2.381 fm deduced from the charge radius [4], and the value for 11Be is from rm = 2.91 ±0.05 fm [12, 42] and rp = 2.338 fm deduced from the charge radius [4]
-
[66]
T. Sumi, K. Minomo, S. Tagami, M. Kimura, T. Matsumoto, K. Ogata, Y . R. Shimizu, and M. Yahiro, Deformation of ne isotopes in the region of the island of inversion, Phys. Rev. C 85, 064613 (2012)
2012
-
[67]
Tanaka, T
K. Tanaka, T. Yamaguchi, T. Suzuki, T. Ohtsubo, M. Fukuda, D. Nishimura, M. Takechi, K. Ogata, A. Ozawa, T. Izumikawa, T. Aiba, N. Aoi, H. Baba, Y . Hashizume, K. Inafuku, N. Iwasa, K. Kobayashi, M. Komuro, Y . Kondo, T. Kubo, M. Kurokawa, T. Matsuyama, S. Michimasa, T. Motoba...
2010
-
[68]
T. Li, Y . Luo, and N. Wang, Compilation of recent nuclear ground state charge radius measurements and tests for models, Atomic Data and Nuclear Data Tables 140, 101440 (2021)
2021
-
[69]
N. Wang, M. Liu, and X. Wu, Modification of nuclear mass formula by considering isospin effects, Phys. Rev. C81, 044322 (2010)
2010
-
[70]
Wakasa, M
T. Wakasa, M. Takechi, S. Tagami, and M. Yahiro, Matter radii and skins of 6,8he from reaction cross section of proton+6,8he scattering based on the love–franey t-matrix model, Results in Physics 35, 105329 (2022)
2022
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