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arxiv: 2605.20056 · v1 · pith:XZR7SGVNnew · submitted 2026-05-19 · ⚛️ nucl-th

Deformed neutron halo nuclei and soft dipole excitations in the 40<A<90 mass region

Xiao Lu , Cong Pan , Hiroyuki Sagawa , Xiang-Xiang Sun , Shan-Gui Zhou This is my paper

Pith reviewed 2026-05-20 03:28 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords deformed neutron halo nucleisoft dipole excitationsmedium-heavy mass regionhalo wave functionnuclear deformationcontinuum effectsE1 responsesingle-particle structure
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0 comments X

The pith

Dipole response detects the halo component in deformed nuclei between mass 40 and 90.

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

The paper applies a deformed relativistic Hartree-Bogoliubov approach in continuum to examine neutron halo nuclei in the 40 to 90 mass range. Three specific candidates receive close study: silicon-43, titanium-69, and chromium-75. The analysis reveals distinctive patterns in the separate proton and neutron densities for candidate s-wave and p-wave halos, patterns shaped by mixing with higher angular momentum states. It establishes that the soft electric dipole response serves as a sensitive indicator of the halo portion of the single-particle wave function and supplies information on both the orbital configuration and the size of the deformation. Confirmation through low-energy dipole measurements would open a practical route to locating deformed halo systems in this mass window.

Core claim

The dipole response is a highly sensitive observable to detect the halo component of the single-particle wave function in a deformed halo nucleus, and it helps identify the configuration and the magnitude of deformation for halo nuclei in the 40 < A < 90 mass region. Unique features appear in the decoupled densities of possible s- and p-wave deformed halo nuclei, shaped by large high-l configurations.

What carries the argument

soft electric dipole (E1) excitations, which act as a probe that isolates the halo portion of the single-particle wave function in the presence of deformation and continuum effects

If this is right

  • Decoupled densities for s- and p-wave halos exhibit distinct features driven by high-l mixing that differ from spherical cases.
  • The three selected nuclei 43Si, 69Ti, and 75Cr display halo characteristics amenable to dipole-based identification of orbital and deformation details.
  • Low-energy dipole strength provides an observable that distinguishes halo components more clearly than ground-state properties alone.
  • Experimental searches for deformed halos in the medium-heavy region gain a concrete diagnostic through the low-lying E1 response.

Where Pith is reading between the lines

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

  • Similar dipole measurements could be extended to neighboring nuclei to map how deformation thresholds affect halo formation across the mass region.
  • The approach may connect to studies of neutron skins or cluster structures if the same sensitivity to wave-function tails appears in other observables.
  • Facilities capable of low-energy photon or Coulomb excitation experiments could prioritize these mass-40 to 90 candidates for halo searches.

Load-bearing premise

The deformed relativistic Hartree-Bogoliubov theory in continuum correctly reproduces the continuum and deformation contributions that control halo formation and the resulting dipole strength.

What would settle it

A precise measurement of the low-energy E1 strength distribution in 43Si, 69Ti, or 75Cr that either shows or fails to show the predicted enhancement and shape tied to the halo wave-function tail would test the claimed sensitivity.

Figures

Figures reproduced from arXiv: 2605.20056 by Cong Pan, Hiroyuki Sagawa, Shan-Gui Zhou, Xiang-Xiang Sun, Xiao Lu.

Figure 1
Figure 1. Figure 1: FIG. 1. (Color Online) Single neutron levels of [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (Color Online) Dipole strength distribution in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (Color Online) Dipole strength distribution in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (Color Online) Single neutron levels versus occupation prob [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (Color Online) Two-dimensional neutron density distributions for [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (Color Online) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. (Color Online) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (Color Online) Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
read the original abstract

We study deformed neutron halo nuclei in the mass region $40 < A < 90$ and their soft electric dipole ($E1$) excitations based on the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Three candidates, $^{43}$Si, $^{69}$Ti, and $^{75}$Cr, are selected for detailed analysis. Unique features are identified in the decoupled densities of possible $s$- and $p$-wave deformed halo nuclei in this mass region, which are influenced by large high-$l$ configurations. It is shown that the dipole response is a highly sensitive observable to detect the halo component of the single-particle wave function in deformed halo nucleus, and it helps identify the configuration and the magnitude of deformation for halo nuclei in the $40 < A < 90$ mass region. Experimental confirmation of the dipole strength in the low-energy region is highly desirable to explore possible deformed halo candidates in the medium-heavy mass region.

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 studies deformed neutron halo nuclei in the 40 < A < 90 mass region using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). It selects three candidate nuclei (^{43}Si, ^{69}Ti, ^{75}Cr) for detailed analysis of decoupled densities and soft E1 excitations, claiming that the dipole response is a highly sensitive observable for detecting the halo component of the single-particle wave function and for identifying configuration and deformation magnitude.

Significance. If the central claims hold under further validation, the work could provide a useful theoretical framework for linking low-energy dipole strength to halo properties in medium-mass deformed nuclei, an experimentally accessible observable. The identification of unique density features influenced by high-l configurations in s- and p-wave halos adds to the exploration of this mass region.

major comments (2)
  1. [Results and discussion of dipole response for ^{43}Si, ^{69}Ti, and ^{75}Cr] The claim that the dipole response is highly sensitive to the halo component of the single-particle wave function (abstract) and helps identify configuration and deformation is demonstrated exclusively within DRHBc calculations for the three nuclei. No tests of numerical convergence (energy cutoff, basis size for continuum discretization) or comparisons to alternative frameworks such as non-relativistic deformed HFB+QRPA are reported; if the soft E1 strength below ~5 MeV shifts under such changes, the observed sensitivity may be framework-specific rather than general.
  2. [Method section describing DRHBc application] The manuscript does not explicitly separate parameters fitted to known nuclei from the predicted halo and deformation properties for the selected candidates in the 40 < A < 90 region, leaving open the possibility that the reported sensitivity partly reflects model tuning rather than independent prediction.
minor comments (2)
  1. The abstract refers to 'unique features' in the decoupled densities but does not enumerate them; a concise list or table in the main text would improve clarity for readers.
  2. Consider including a summary table of deformation parameters, halo radii, and low-energy E1 strengths for the three nuclei to allow direct comparison.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions planned for the next version.

read point-by-point responses

  1. Referee: [Results and discussion of dipole response for ^{43}Si, ^{69}Ti, and ^{75}Cr] The claim that the dipole response is highly sensitive to the halo component of the single-particle wave function (abstract) and helps identify configuration and deformation is demonstrated exclusively within DRHBc calculations for the three nuclei. No tests of numerical convergence (energy cutoff, basis size for continuum discretization) or comparisons to alternative frameworks such as non-relativistic deformed HFB+QRPA are reported; if the soft E1 strength below ~5 MeV shifts under such changes, the observed sensitivity may be framework-specific rather than general.

    Authors: We agree that explicit numerical convergence tests would strengthen the presentation. In the revised manuscript we will add a dedicated paragraph (or short appendix) reporting the stability of the soft E1 strength below 5 MeV with respect to both the energy cutoff and the size of the basis used for continuum discretization. We also acknowledge that a direct comparison with non-relativistic deformed HFB+QRPA calculations would be valuable for assessing framework dependence; however, such a comparison lies outside the scope of the present work, which is focused on the DRHBc approach. We will insert a brief statement in the discussion section noting this limitation and identifying it as a possible direction for future study. The sensitivity we report is therefore demonstrated within the DRHBc framework, but we maintain that the identified density features and their influence on the dipole response are robust within this well-validated method. revision: partial

  2. Referee: [Method section describing DRHBc application] The manuscript does not explicitly separate parameters fitted to known nuclei from the predicted halo and deformation properties for the selected candidates in the 40 < A < 90 region, leaving open the possibility that the reported sensitivity partly reflects model tuning rather than independent prediction.

    Authors: We thank the referee for highlighting this point. The parameters of the point-coupling effective interaction employed in DRHBc are taken from global fits to known nuclear properties performed in our earlier publications and are not readjusted for the present study. The halo structures, deformations, and dipole responses for ^{43}Si, ^{69}Ti, and ^{75}Cr are therefore genuine predictions. To remove any ambiguity, we will revise the Method section to include an explicit statement separating the fixed interaction parameters (determined from prior fits) from the predicted observables for the three candidate nuclei. revision: yes

standing simulated objections not resolved
  • Direct comparison of the soft E1 strength to results obtained with non-relativistic deformed HFB+QRPA calculations

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper applies the established DRHBc framework to compute densities and dipole responses for three specific candidate nuclei in the 40<A<90 region. The central claim that dipole response is sensitive to halo components is demonstrated via numerical results from this model rather than through any self-referential definition, fitted parameter relabeled as prediction, or load-bearing self-citation that reduces the result to unverified inputs. The method itself is treated as an external tool with prior validation outside this work, and the analysis remains exploratory without equations or steps that collapse back to the inputs by construction. This is the expected outcome for a computational exploration paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that the DRHBc model faithfully reproduces halo and continuum physics in medium-mass nuclei; no explicit free parameters or new entities are named in the abstract.

axioms (1)
  • domain assumption The deformed relativistic Hartree-Bogoliubov theory in continuum accurately describes the structure and excitations of neutron halo nuclei in the 40<A<90 region.
    Invoked as the computational foundation for selecting candidates and interpreting dipole response.

pith-pipeline@v0.9.0 · 5711 in / 1300 out tokens · 53953 ms · 2026-05-20T03:28:50.233423+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages · 2 internal anchors

  1. [1]

    shape decoupling

    43Si The nucleus 43Si is a promising candidate for a medium- heavy deformed neutron halo. Its ground state is assigned to theK π =1/2 − state with a large oblate deformation (β2 =−0.357) and Nilsson asymptotic quantum numbers [NnzΛ]Ω= [321]1/2. The one neutron separation energy is predicted to beS n =0.95 MeV . The single-neutron levels around the Fermi s...

    work page

  2. [2]

    The single-particle levels near the Fermi sur- face and their occupation probabilities for 69Ti are depicted in Fig

    69Ti Based on the DRHBc calculations, the ground state of the nucleus 69Ti is assigned to theK π =1/2 + state, character- ized by a large prolate deformation withβ 2 =0.231 and Nils- son asymptotic quantum numbers[Nn zΛ]Ω= [420]1/2 with Sn =0.62 MeV . The single-particle levels near the Fermi sur- face and their occupation probabilities for 69Ti are depic...

    work page

  3. [3]

    Similar to 69Ti, 75Cr also exhibits su- perfluid features in its ground state

    75Cr The ground state of75Cr is assigned as theKπ =1/2 + state, characterized by a prolate deformation ofβ 2 =0.311 and corresponding to the Nilsson asymptotic quantum numbers [NnzΛ]Ωπ = [411]1/2+. Similar to 69Ti, 75Cr also exhibits su- perfluid features in its ground state. The pairing gaps are eval- uated as∆ n =0.97 MeV for neutrons and∆ p =0.46 MeV f...

    work page

  4. [4]

    Tanihata, H

    I. Tanihata, H. Hamagaki, O. Hashimoto, Y . Shida, N. Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi, and N. Takahashi, Phys. Rev. Lett.55, 2676 (1985)

    work page 1985

  5. [5]

    Tanihata, T

    I. Tanihata, T. Kobayashi, O. Yamakawa, S. Shimoura, K. Ekuni, K. Sugimoto, N. Takahashi, T. Shimoda, and H. Sato, Phys. Lett. B206, 592 (1988)

    work page 1988

  6. [6]

    Fukuda, T

    M. Fukuda, T. Ichihara, N. Inabe, T. Kubo, H. Kumagai, T. Nakagawa, Y . Yano, I. Tanihata, M. Adachi, K. Asahi, M. Kouguchi, M. Ishihara, H. Sagawa, and S. Shimoura, Phys. Lett. B268, 339 (1991)

    work page 1991

  7. [7]

    Bazin, B

    D. Bazin, B. Brown, J. Brown, M. Fauerbach, M. Hellström, S. Hirzebruch, J. Kelley, R. Kryger, D. Morrissey, R. Pfaff, C. Powell, B. Sherrill, and M. Thoennessen, Phys. Rev. Lett. 74, 3569 (1995)

    work page 1995

  8. [8]

    Nakamura, N

    T. Nakamura, N. Fukuda, T. Kobayashi, N. Aoi, H. Iwasaki, T. Kubo, A. Mengoni, M. Notani, H. Otsu, H. Sakurai, S. Shi- moura, T. Teranishi, Y . X. Watanabe, K. Yoneda, and M. Ishi- hara, Phys. Rev. Lett.83, 1112 (1999)

    work page 1999

  9. [9]

    Nakamura, N

    T. Nakamura, N. Kobayashi, Y . Kondo, Y . Satou, N. Aoi, H. Baba, S. Deguchi, N. Fukuda, J. Gibelin, N. Inabe, M. Ishi- hara, D. Kameda, Y . Kawada, T. Kubo, K. Kusaka, A. Mengoni, T. Motobayashi, T. Ohnishi, M. Ohtake, N. A. Orr, H. Otsu, T. Otsuka, A. Saito, H. Sakurai, S. Shimoura, T. Sumikama, H. Takeda, E. Takeshita, M. Takechi, S. Takeuchi, K. Tanak...

    work page 2009

  10. [10]

    Nakamura, N

    T. Nakamura, N. Kobayashi, Y . Kondo, Y . Satou, J. A. Tostevin, Y . Utsuno, N. Aoi, H. Baba, N. Fukuda, J. Gibelin, N. Inabe, M. Ishihara, D. Kameda, T. Kubo, T. Motobayashi, T. Ohnishi, N. A. Orr, H. Otsu, T. Otsuka, H. Sakurai, T. Sumikama, H. Takeda, E. Takeshita, M. Takechi, S. Takeuchi, Y . Togano, and K. Yoneda, Phys. Rev. Lett.112, 142501 (2014)

    work page 2014

  11. [11]

    Kobayashi, T

    N. Kobayashi, T. Nakamura, Y . Kondo, J. A. Tostevin, Y . Ut- suno, N. Aoi, H. Baba, R. Barthelemy, M. A. Famiano, N. Fukuda, N. Inabe, M. Ishihara, R. Kanungo, S. Kim, T. Kubo, G. S. Lee, H. S. Lee, M. Matsushita, T. Motobayashi, T. Ohnishi, N. A. Orr, H. Otsu, T. Otsuka, T. Sako, H. Saku- rai, Y . Satou, T. Sumikama, H. Takeda, S. Takeuchi, R. Tanaka, Y...

    work page 2014

  12. [12]

    Takechi, S

    M. Takechi, S. Suzuki, D. Nishimura, M. Fukuda, T. Oht- subo, M. Nagashima, T. Suzuki, T. Yamaguchi, A. Ozawa, T. Moriguchi, H. Ohishi, T. Sumikama, H. Geissel, N. Aoi, R.- J. Chen, D.-Q. Fang, N. Fukuda, S. Fukuoka, H. Furuki, N. In- abe, Y . Ishibashi, T. Itoh, T. Izumikawa, D. Kameda, T. Kubo, M. Lantz, C. S. Lee, Y .-G. Ma, K. Matsuta, M. Mihara, S. M...

    work page 2014

  13. [13]

    Suzuki, Y

    T. Suzuki, Y . Ogawa, M. Chiba, M. Fukuda, N. Iwasa, T. Izu- mikawa, R. Kanungo, Y . Kawamura, A. Ozawa, T. Suda, I. Tanihata, S. Watanabe, T. Yamaguchi, and Y . Yamaguchi, Phys. Rev. Lett.89, 012501 (2002)

    work page 2002

  14. [14]

    Z. H. Yang, Y . Kubota, A. Corsi, K. Yoshida, X.-X. Sun, J. G. Li, M. Kimura, N. Michel, K. Ogata, C. X. Yuan, Q. Yuan, G. Authelet, H. Baba, C. Caesar, D. Cal- vet, A. Delbart, M. Dozono, J. Feng, F. Flavigny, J.-M. Gheller, J. Gibelin, A. Giganon, A. Gillibert, K. Hasegawa, T. Isobe, Y . Kanaya, S. Kawakami, D. Kim, Y . Kiyokawa, M. Kobayashi, N. Kobaya...

    work page 2021

  15. [15]

    K. J. Cook, T. Nakamura, Y . Kondo, K. Hagino, K. Ogata, A. T. Saito, N. L. Achouri, T. Aumann, H. Baba, F. Delau- nay, Q. Deshayes, P. Doornenbal, N. Fukuda, J. Gibelin, J. W. Hwang, N. Inabe, T. Isobe, D. Kameda, D. Kanno, S. Kim, N. Kobayashi, T. Kobayashi, T. Kubo, S. Leblond, J. Lee, F. M. Marqués, R. Minakata, T. Motobayashi, K. Muto, T. Mu- rakami,...

    work page 2020

  16. [16]

    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. Motobayashi, T. Nakabayashi, S. Nakajima, T. Nakamura, H. Sakurai, R. Shinoda, M. Shin...

    work page 2010

  17. [17]

    Bagchi, R

    S. Bagchi, R. Kanungo, Y . K. Tanaka, H. Geissel, P. Door- nenbal, W. Horiuchi, G. Hagen, T. Suzuki, N. Tsunoda, D. S. Ahn, H. Baba, K. Behr, F. Browne, S. Chen, M. L. Cortés, A. Estradé, N. Fukuda, M. Holl, K. Itahashi, N. Iwasa, G. R. Jansen, W. G. Jiang, S. Kaur, A. O. Macchiavelli, S. Y . Mat- sumoto, S. Momiyama, I. Murray, T. Nakamura, S. J. Novario...

    work page 2020

  18. [18]

    Minamisono, T

    T. Minamisono, T. Ohtsubo, I. Minami, S. Fukuda, A. Kita- gawa, M. Fukuda, K. Matsuta, Y . Nojiri, S. Takeda, H. Sagawa, and H. Kitagawa, Phys. Rev. Lett.69, 2058 (1992)

    work page 2058

  19. [19]

    Warner, H

    R. Warner, H. Thirumurthy, J. Woodroffe, F. Becchetti, J. Brown, B. Davids, A. Galonsky, J. Kolata, J. Kruse, M. Lee, A. Nadasen, T. O’Donnell, D. Roberts, R. Ronningen, C. Samanta, P. Schwandt, J. von Schwarzenberg, M. Steiner, K. Subotic, J. Wang, and J. Zimmerman, Nucl. Phys. A635, 292 (1998)

    work page 1998

  20. [20]

    Sagawa, Phys

    H. Sagawa, Phys. Lett. B286, 7 (1992)

    work page 1992

  21. [21]

    Riisager, A

    K. Riisager, A. Jensen, and P. Møller, Nucl. Phys. A548, 393 (1992)

    work page 1992

  22. [22]

    Meng and P

    J. Meng and P. Ring, Phys. Rev. Lett.77, 3963 (1996)

    work page 1996

  23. [23]

    J. Meng, H. Toki, S. Zhou, S. Zhang, W. Long, and L. Geng, Prog. Part. Nucl. Phys.57, 470 (2006), arXiv:nucl-th/0508020

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  24. [24]

    Tanihata, H

    I. Tanihata, H. Savajols, and R. Kanungo, Prog. Part. Nucl. Phys.68, 215 (2013)

    work page 2013

  25. [25]

    Meng and S

    J. Meng and S. G. Zhou, J. Phys. G: Nucl. Part. Phys.42, 12 093101 (2015)

    work page 2015

  26. [26]

    J. Meng, H. Toki, J. Y . Zeng, S. Q. Zhang, and S. G. Zhou, Phys. Rev. C65, 041302 (2002)

    work page 2002

  27. [27]

    Terasaki, S

    J. Terasaki, S. Q. Zhang, S. G. Zhou, and J. Meng, Phys. Rev. C74, 054318 (2006)

    work page 2006

  28. [28]

    T. Misu, W. Nazarewicz, and S. Åberg, Nucl. Phys. A614, 44 (1997)

    work page 1997

  29. [29]

    S.-G. Zhou, J. Meng, P. Ring, and E.-G. Zhao, Phys. Rev. C82, 011301 (2010)

    work page 2010

  30. [30]

    Hamamoto, Phys

    I. Hamamoto, Phys. Rev. C85, 064329 (2012)

    work page 2012

  31. [31]

    Nakamura, T

    T. Nakamura, T. Motobayashi, Y . Ando, A. Mengoni, T. Nishio, H. Sakurai, S. Shimoura, T. Teranishi, Y . Yanagisawa, and M. Ishihara, Phys. Lett. B394, 11 (1997)

    work page 1997

  32. [32]

    Nakamura, A

    T. Nakamura, A. M. Vinodkumar, T. Sugimoto, N. Aoi, H. Baba, D. Bazin, N. Fukuda, T. Gomi, H. Hasegawa, N. Imai, M. Ishihara, T. Kobayashi, Y . Kondo, T. Kubo, M. Miura, T. Motobayashi, H. Otsu, A. Saito, H. Sakurai, S. Shimoura, K. Watanabe, Y . X. Watanabe, T. Yakushiji, Y . Yanagisawa, and K. Yoneda, Phys. Rev. Lett.96, 252502 (2006)

    work page 2006

  33. [33]

    Hamamoto, Phys

    I. Hamamoto, Phys. Rev. C72, 024301 (2005)

    work page 2005

  34. [34]

    Hamamoto, Phys

    I. Hamamoto, Phys. Rev. C81, 021304 (2010)

    work page 2010

  35. [35]

    Hamamoto, Phys

    I. Hamamoto, Phys. Rev. C95, 044325 (2017)

    work page 2017

  36. [36]

    Urata, K

    Y . Urata, K. Hagino, and H. Sagawa, Phys. Rev. C83, 041303 (2011)

    work page 2011

  37. [37]

    Urata, K

    Y . Urata, K. Hagino, and H. Sagawa, Phys. Rev. C86, 044613 (2012)

    work page 2012

  38. [38]

    Urata, K

    Y . Urata, K. Hagino, and H. Sagawa, Phys. Rev. C96, 064311 (2017)

    work page 2017

  39. [39]

    Otsuka, N

    T. Otsuka, N. Fukunishi, and H. Sagawa, Phys. Rev. Lett.70, 1385 (1993)

    work page 1993

  40. [40]

    T. T. S. Kuo, F. Krmpoti ´c, and Y . Tzeng, Phys. Rev. Lett.78, 2708 (1997)

    work page 1997

  41. [41]

    Descouvemont, Nucl

    P. Descouvemont, Nucl. Phys. A655, 440 (1999)

    work page 1999

  42. [42]

    L. Li, J. Meng, P. Ring, E.-G. Zhao, and S.-G. Zhou, Phys. Rev. C85, 024312 (2012)

    work page 2012

  43. [43]

    L. Li, J. Meng, P. Ring, E.-G. Zhao, and S.-G. Zhou, Chin. Phys. Lett.29, 042101 (2012), arXiv:1203.1363 [nucl-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  44. [44]

    X.-X. Sun, J. Zhao, and S.-G. Zhou, Phys. Lett. B785, 530 (2018)

    work page 2018

  45. [45]

    K. Y . Zhang, D. Y . Wang, and S. Q. Zhang, Phys. Rev. C100, 034312 (2019)

    work page 2019

  46. [46]

    X.-X. Sun, J. Zhao, and S.-G. Zhou, Nucl. Phys. A1003, 122011 (2020)

    work page 2020

  47. [47]

    Sun, Phys

    X.-X. Sun, Phys. Rev. C103, 054315 (2021)

    work page 2021

  48. [48]

    Sun and S.-G

    X.-X. Sun and S.-G. Zhou, Sci. Bull.66, 2072 (2021)

    work page 2072

  49. [49]

    Sun and S.-G

    X.-X. Sun and S.-G. Zhou, Phys. Rev. C104, 064319 (2021), arXiv:2107.05925 [nucl-th]

    work page arXiv 2021

  50. [50]

    Zhong, S.-S

    S.-Y . Zhong, S.-S. Zhang, X.-X. Sun, and M. S. Smith, Sci. China-Phys. Mech. Astron.65, 262011 (2022)

    work page 2022

  51. [51]

    K. Y . Zhang, P. Papakonstantinou, M.-H. Mun, Y . Kim, H. Yan, and X.-X. Sun, Phys. Rev. C107, L041303 (2023)

    work page 2023

  52. [52]

    Zhang, S

    K. Zhang, S. Yang, J. An, S. Zhang, P. Papakonstantinou, M.- H. Mun, Y . Kim, and H. Yan, Phys. Lett. B844, 138112 (2023), arXiv:2306.16011 [nucl-th]

    work page arXiv 2023

  53. [53]

    An, K.-Y

    J.-L. An, K.-Y . Zhang, Q. Lu, S.-Y . Zhong, and S.-S. Zhang, Phys. Lett. B849, 138422 (2024)

    work page 2024

  54. [54]

    C. Pan, K. Zhang, and S. Zhang, Phys. Lett. B855, 138792 (2024), arXiv:2403.03713 [nucl-th]

    work page arXiv 2024

  55. [55]

    K. Y . Zhang, C. Pan, and S. Wang, Phys. Rev. C110, 014320 (2024)

    work page 2024

  56. [56]

    Papakonstantinou, M

    P. Papakonstantinou, M. Mun, C. Pan, and K. Zhang, Phys. Rev. C112, 044301 (2025)

    work page 2025

  57. [57]

    Zhang and X

    K. Zhang and X. Lu, Phys. Lett. B871, 139989 (2025)

    work page 2025

  58. [58]

    C. Pan, J. An, P. Ring, X. Wu, P. Papakonstantinou, M.-H. Mun, Y . Kim, S. Zhang, and K. Zhang, Phys. Lett. B877, 140487 (2026)

    work page 2026

  59. [59]

    Y . N. Zhang, J. C. Pei, and F. R. Xu, Phys. Rev. C88, 054305 (2013)

    work page 2013

  60. [60]

    J. C. Pei, Y . N. Zhang, and F. R. Xu, Phys. Rev. C87, 051302 (2013)

    work page 2013

  61. [61]

    Nakada and K

    H. Nakada and K. Takayama, Phys. Rev. C98, 011301 (2018)

    work page 2018

  62. [62]

    Kasuya and K

    H. Kasuya and K. Yoshida, Prog. Theor. Exp. Phys.2021, 013D01 (2020)

    work page 2021

  63. [63]

    Q. Chai, H. Chen, M. Zha, J. Pei, and F. Xu, Symmetry14, 215 (2022)

    work page 2022

  64. [64]

    Takatsu, Y

    R. Takatsu, Y . Suzuki, W. Horiuchi, and M. Kimura, Phys. Rev. C107, 024314 (2023)

    work page 2023

  65. [65]

    S. Shen, S. Elhatisari, D. Lee, U.-G. Meißner, and Z. Ren, Phys. Rev. Lett.134, 162503 (2025), arXiv:2411.14935 [nucl-th]

    work page arXiv 2025

  66. [66]

    Sun and S.-G

    X.-X. Sun and S.-G. Zhou, Nucl. Phys. Rev.41, 75 (2024)

    work page 2024

  67. [67]

    Zhang, C

    K. Zhang, C. Pan, S. Chen, Q. Luo, K. Wu, and Y . Xiang, Nucl. Phys. Rev.41, 191 (2024)

    work page 2024

  68. [68]

    K. Y . Zhang, C. Pan, X. H. Wu, X. Y . Qu, X. X. Lu, and G. A. Sun, AAPPS Bull.35, 13 (2025)

    work page 2025

  69. [69]

    P. Guo, X. Cao, K. Chen, Z. Chen, M.-K. Cheoun, Y .-B. Choi, P. Lam, W. Deng, J. Dong, P. Du, X. Du, K. Duan, X. Fan, W. Gao, L. Geng, E. Ha, X.-T. He, J. Hu, J. Huang, and L. Zou, At. Data Nucl. Data Tables158, 101661 (2024)

    work page 2024

  70. [70]

    Zhang, M.-K

    K. Zhang, M.-K. Cheoun, Y .-B. Choi, P. S. Chong, J. Dong, L. Geng, E. Ha, X. He, C. Heo, M. C. Ho, E. J. In, S. Kim, Y . Kim, C.-H. Lee, J. Lee, Z. Li, T. Luo, J. Meng, M.-H. Mun, Z. Niu, C. Pan, P. Papakonstantinou, X. Shang, C. Shen, G. Shen, W. Sun, X.-X. Sun, C. K. Tam, Thaivayongnou, C. Wang, S. H. Wong, X. Xia, Y . Yan, R. W.-Y . Yeung, T. C. Yiu, ...

    work page 2020

  71. [71]

    Pan, M.-K

    C. Pan, M.-K. Cheoun, Y .-B. Choi, J. Dong, X. Du, X.-H. Fan, W. Gao, L. Geng, E. Ha, X.-T. He, J. Huang, K. Huang, S. Kim, Y . Kim, C.-H. Lee, J. Lee, Z. Li, Z.-R. Liu, Y . Ma, J. Meng, M.-H. Mun, Z. Niu, P. Papakonstantinou, X. Shang, C. Shen, G. Shen, W. Sun, X.-X. Sun, J. Wu, X. Wu, X. Xia, Y . Yan, T. C. Yiu, K. Zhang, S. Zhang, W. Zhang, X. Zhang, Q...

    work page 2022

  72. [72]

    Ring and P

    P. Ring and P. Schuck,The Nuclear Many-Body Problem (Springer-Verlag, 1980)

    work page 1980

  73. [73]

    S.-G. Zhou, J. Meng, and P. Ring, Phys. Rev. C68, 034323 (2003)

    work page 2003

  74. [74]

    Hamamoto, Phys

    I. Hamamoto, Phys. Rev. C99, 024319 (2019)

    work page 2019

  75. [75]

    Bohr and B

    A. Bohr and B. R. Mottelson,Nuclear Struture V ol. I(World Scientific, 1975)

    work page 1975

  76. [76]

    Möller, A

    P. Möller, A. Sierk, T. Ichikawa, and H. Sagawa, At. Data Nucl. Data Tables109-110, 1 (2016)

    work page 2016

  77. [77]

    P. W. Zhao, Z. P. Li, J. M. Yao, and J. Meng, Phys. Rev. C82, 054319 (2010)

    work page 2010

  78. [78]

    Hamamoto, Phys

    I. Hamamoto, Phys. Rev. C100, 014324 (2019)

    work page 2019