pith. sign in

arxiv: 2604.19576 · v2 · submitted 2026-04-21 · ⚛️ nucl-th

Shell effects and the neutron emission within the multi-dimensional Langevin model for nuclear fission

F.A. Ivanyuk , S.V. Radionov , C. Ishizuka , S. Chiba This is my paper

Pith reviewed 2026-05-10 00:44 UTC · model grok-4.3

classification ⚛️ nucl-th
keywords nuclear fissionLangevin modelneutron emissionpre-scission multiplicitypotential energy surfaceshell effectsfission fragments
0
0 comments X

The pith

Dynamically emitting neutrons during Langevin fission trajectories yields pre-scission multiplicities as the average emissions per path.

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

The paper integrates neutron emission into multi-dimensional Langevin simulations of nuclear fission by checking emission probability at every integration step. When emission occurs, the model subtracts the neutron separation energy plus average kinetic energy from the excitation energy, switches to the potential energy surface for the reduced neutron number, and continues evolving the nuclear shape. Pre-scission neutron multiplicity is obtained simply as the total neutrons emitted across all trajectories divided by the number of trajectories that reach scission. The same trajectories also produce fragment mass distributions and neutron spectra versus deformation and energy, which are then compared directly to measured data.

Core claim

We solve the Langevin equations for the time evolution of parameters that describe the shape of fissioning system. On each integration step, we calculate the probability of neutron emission and estimate whether a neutron would be emitted or not. If yes, we decrease the excitation energy of the nucleus by the neutron separation energy plus the average energy of the emitted neutron, switch to the layer of potential energy surface with a smaller number of neutrons and continue the process of integration. If the trajectory reaches the scission point, we check how many neutrons were emitted along this trajectory. The pre-scission neutron multiplicity M_pre is defined by the ratio of the total nu

What carries the argument

Multi-dimensional Langevin dynamics with on-the-fly probabilistic neutron emission and instantaneous switching between neutron-number-specific potential energy surfaces.

If this is right

  • Fragment mass distributions incorporate the energy loss and surface switching caused by neutron emission before scission.
  • Neutron emission rates vary with instantaneous deformation, producing stage-specific spectra.
  • Energy distributions of emitted neutrons follow from the excitation energy at the moment of emission along each path.
  • Shell effects in the potential surfaces remain active throughout the trajectory, influencing both emission probability and final fragment yields.

Where Pith is reading between the lines

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

  • The same dynamic switching could be extended to gamma or charged-particle emission for more complete de-excitation chains.
  • In neutron-rich fission, repeated surface switches may systematically shift the effective fission barrier and alter fragment asymmetry.
  • Static calculations that fix neutron number throughout would miss the feedback between emission and shape evolution seen in these trajectories.

Load-bearing premise

Neutron emission can be decided probabilistically from the instantaneous excitation energy without breaking the continuous shape evolution of the fissioning nucleus.

What would settle it

A measured pre-scission neutron multiplicity for a well-characterized fissioning system that lies many standard deviations outside the average obtained from the ensemble of simulated trajectories.

Figures

Figures reproduced from arXiv: 2604.19576 by C. Ishizuka, F.A. Ivanyuk, S. Chiba, S.V. Radionov.

Figure 1
Figure 1. Figure 1: FIG. 1: The average value (8) of the deformation energy of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The comparison of fission fragment mass distribution [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The energy dependence of the Fermi-function factor [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The distribution of emitted neutrons with respect to [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: The dependence of the pre-scission neutron multipli [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The calculated neutron spectra for fission of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: The pre-scission neutron multiplicity for fission of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: The demonstration for the calculation of the surface [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

We solve the Langevin equations for the time evolution of parameters that describe the shape of fissioning system. On each integration step, we calculate the probability of neutron emission and estimate whether a neutron would be emitted or not. If yes, we decrease the excitation energy of the nucleus by the neutron separation energy plus the average energy of the emitted neutron, switch to the layer of potential energy surface with a smaller number of neutrons and continue the process of integration. If the trajectory reaches the scission point, we check how many neutrons were emitted along this trajectory. The pre-scission neutron multiplicity $M_{pre}$ is defined by the ratio of the total number of emitted neutrons to the total number of fission trajectories. Besides $M_{pre}$, the mass distribution of fission fragments, the distribution of emitted neutrons with respect to the fission stage (deformation of system) and the distribution of emitted neutrons with respect to their energies are calculated. The calculated quantities are compared with the available experimental data.

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

1 major / 2 minor

Summary. The manuscript develops a multi-dimensional Langevin model for nuclear fission that incorporates dynamical neutron emission. At each integration step the probability of neutron emission is computed from the instantaneous excitation energy; if emission occurs, the excitation energy is decremented by the neutron separation energy plus the average emitted-neutron energy, the trajectory is continued on the potential-energy surface of the (A-1) nucleus, and integration proceeds until scission. Pre-scission neutron multiplicity M_pre is obtained as the ratio of the total number of emitted neutrons to the total number of fission trajectories. The model also produces fission-fragment mass distributions and distributions of emitted neutrons versus deformation stage and neutron energy, which are compared with experimental data.

Significance. The forward-simulation character of the approach, with no free parameters fitted to the fission observables themselves, is a positive feature. If the transport coefficients remain valid after each neutron-emission switch and if the resulting M_pre and mass distributions are shown to agree quantitatively with data within stated uncertainties, the work would supply a useful dynamical treatment of neutron emission that includes shell effects. At present the absence of tabulated numerical results, error estimates, or explicit validation of the switched PES coefficients prevents a firm judgment of the magnitude of the advance.

major comments (1)
  1. [Method description] The procedure of switching mid-trajectory to the (A-1) potential-energy surface implicitly assumes that the inertia tensor, friction coefficients, and collective potential remain transferable without recomputation. Because both the time to scission and the integrated emission probability depend on these coefficients, any mismatch directly affects the counted M_pre. The manuscript gives no indication that the transport coefficients are recalculated or interpolated for the reduced-neutron system (see the description of the integration step in the abstract and the corresponding method section).
minor comments (2)
  1. [Abstract] The abstract would be strengthened by the inclusion of at least one quantitative result (e.g., a typical M_pre value and its comparison to experiment) together with an estimate of statistical uncertainty.
  2. [Method] Notation for the neutron-emission probability and the average neutron energy should be defined explicitly when first introduced.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the positive remarks on the forward-simulation character of the approach. We address the single major comment below and will revise the manuscript accordingly to improve clarity.

read point-by-point responses

  1. Referee: The procedure of switching mid-trajectory to the (A-1) potential-energy surface implicitly assumes that the inertia tensor, friction coefficients, and collective potential remain transferable without recomputation. Because both the time to scission and the integrated emission probability depend on these coefficients, any mismatch directly affects the counted M_pre. The manuscript gives no indication that the transport coefficients are recalculated or interpolated for the reduced-neutron system (see the description of the integration step in the abstract and the corresponding method section).

    Authors: We agree that the manuscript does not explicitly describe the handling of the inertia tensor and friction coefficients upon neutron emission, which is a valid point. The collective potential is switched to the PES of the (A-1) nucleus as stated in the abstract. In the numerical implementation, the inertia tensor and friction coefficients are recomputed for the new nucleus at each emission step using the same microscopic-macroscopic formalism employed for the original system; this is feasible because the change in neutron number is incremental and the computational cost is modest. We will revise the method section to state this procedure explicitly, to note that the coefficients are updated rather than held fixed, and to include a short discussion of the approximation's validity and its effect on M_pre. This revision will also supply the missing indication requested by the referee. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the Langevin fission simulation

full rationale

The paper describes a forward numerical integration of multi-dimensional Langevin equations for nuclear shape evolution. At each step the neutron emission probability is computed from the instantaneous excitation energy, the trajectory is optionally switched to a reduced-neutron PES, and M_pre is obtained simply as the ratio of total emitted neutrons to total trajectories. All other observables (mass yields, neutron spectra vs. deformation and energy) are likewise tallied from the ensemble of trajectories. The manuscript states that the computed quantities are compared with experimental data. No equation reduces to its own input by construction, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation chain. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents identification of specific free parameters, axioms, or invented entities; the model presumably relies on standard nuclear potential surfaces, friction coefficients, and shell corrections whose details are not provided here.

pith-pipeline@v0.9.0 · 5484 in / 1139 out tokens · 32018 ms · 2026-05-10T00:44:05.130593+00:00 · methodology

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

52 extracted references · 52 canonical work pages

  1. [1]

    In the present model, we consider a nucleus as a piece of infinite matter of volume V put into the potential well of depth U0

    Note that for prolate shapes the surface area becomes larger, but the surface integral Eqs.(26, 39) - smaller. In the present model, we consider a nucleus as a piece of infinite matter of volume V put into the potential well of depth U0. In this case, only particles with the kinetic energy larger than U0 can escape from nucleus, see [43] and Eqs. B1, B35 i...

    work page 2000

  2. [2]

    Acknowledgments Acknowledgments

    Note that for prolate shapes the surface area becomes larger, but the surface integral Eqs.(26, 39) - smaller. Acknowledgments Acknowledgments. The authors would like to ex- press their gratitude to Prof. K. Pomorski and Dr. C. Schmitt for valuable comments and suggestions, and Dr. K. Nishio for sharing the experimental data on the fission fragment mass di...

    work page

  3. [3]

    Langevin, C.R

    P. Langevin, C.R. Acad. Sci. (Paris), 146, 530 (1908)

    work page 1908

  4. [4]

    K. T. R. Davies, A. T. Sierk, and J. R. Nix. Phys. Rev. C 13, 2385 (1976)

    work page 1976

  5. [5]

    T. Wada, Y. Abe and N. Carjan, Phys. Rev. Lett. 70, 3538 (1993)

    work page 1993

  6. [6]

    Fr¨ obrich and I

    P. Fr¨ obrich and I. I. Gontchar, Phys. Rep. 282, 131 (1998)

    work page 1998

  7. [7]

    Pomorski, J

    K. Pomorski, J. Bartel, J. Richert, and K. Dietrich, Nucl . Phys. A 605, 87 (1996)

    work page 1996

  8. [8]

    Karpov, P.N

    A.V. Karpov, P.N. Nadtochy, D.V. Vanin, and G.D. 9 Adeev, Phys. Rev. C 63, 054610 (2001)

    work page 2001

  9. [9]

    Asano, T

    T. Asano, T. Wada, M. Ohta, T. Ichikawa, S. Yamaji, H. Nakahara. J. Nucl. Radiochem. Sci. 5, 15 (2004)

    work page 2004

  10. [10]

    Adeev, A.V

    G.D. Adeev, A.V. Karpov, P.N. Nadtochy, D.V. Vanin, Fiz. Elem. Chastits At. Yadra 36, 732 (2005) [Phys. Part. Nucl. 36, 378 (2005)]

    work page 2005

  11. [11]

    Aritomo, S

    Y. Aritomo, S. Chiba, and F. A. Ivanyuk, Phys. Rev. C 90, 054609 (2014)

    work page 2014

  12. [12]

    Mazurek, P

    K. Mazurek, P. N. Nadtochy, E. G. Ryabov, and G. D. Adeev, Eur. Phys. J. A 53, 79 (2017)

    work page 2017

  13. [13]

    M. D. Usang, F. A. Ivanyuk, C. Ishizuka, and S. Chiba, Phys. Rev. C 96, 064617 (2017)

    work page 2017

  14. [14]

    Usang, F.A

    M.D. Usang, F.A. Ivanyuk, C. Ishizuka, and S. Chiba, Scientific Reports 9, 1525 (2019)

    work page 2019

  15. [15]

    Kostryukov, A

    P.V. Kostryukov, A. Dobrowolski, B. Nerlo-Pomorska, M. Warda, Z.G. Xiao, Y.J. Chen, L.L. Liu, J.L. Tian, and K. Pomorski, Chin. Phys. C 45, 124108 (2021)

    work page 2021

  16. [16]

    V. L. Litnevsky, F. A. Ivanyuk, G. I. Kosenko, and S. Chiba, Phys. Rev. C 101, 064616 (2020)

    work page 2020

  17. [17]

    Pomorski, B

    K. Pomorski, B. Nerlo-Pomorska, J. Bartel, C. Schmitt, Z.G. Xiao, Y.J. Chen, and L. L. Liu, Phys. Rev. C 110, 034607 (2024)

    work page 2024

  18. [18]

    Takagi, S

    S. Takagi, S. Harada, Y. Aritomo, K. Hirose, and K. Nishio, Phys. Rev. C 112, 044607 (2025)

    work page 2025

  19. [19]

    Song, C.-H

    C.-h. Song, C.-H. Lee, Y. Aritomo, S. Takagi, K. Naka- jima, I.J. Shin, and Y. Kim, Phys. Rev. C 113, 024616 (2026)

    work page 2026

  20. [20]

    Davies, A.J

    K.T.R. Davies, A.J. Sierk, J.R. Nix, Phys. Rev. C 13, 2385 (1976)

    work page 1976

  21. [21]

    Blocki, Y

    J. Blocki, Y. Boneh, J.R. Nix, J. Randrup, M. Robel, A.J. Sierk, and W. J. Swiatecki, Ann. Phys. 113, 330 (1978)

    work page 1978

  22. [22]

    Randrup and W.J

    J. Randrup and W.J. Swiatecki, Nucl. Phys. A 429, 105 (1984)

    work page 1984

  23. [23]

    Hofmann, Phys

    H. Hofmann, Phys. Rep. 284 (4&5), 137 (1997)

    work page 1997

  24. [24]

    Hofmann, The Physics of Warm Nuclei

    H. Hofmann, The Physics of Warm Nuclei

    work page

  25. [25]

    Hofmann, Nucl

    F.A.Ivanyuk, H. Hofmann, Nucl. Phys. A 657, 19 (1999)

    work page 1999

  26. [26]

    Sierk, Phys

    A.J. Sierk, Phys. Rev. C 96, 034603 (2017)

    work page 2017

  27. [27]

    Ivanyuk, C

    F.A. Ivanyuk, C. Ishizuka, and S. Chiba, Phys. Rev. C 109, 034602 (2024)

    work page 2024

  28. [28]

    Ivanyuk, C

    F.A. Ivanyuk, C. Ishizuka, C. Schmitt, and S. Chiba, Phys. Rev. C 111, 054620 (2025)

    work page 2025

  29. [29]

    Pomorski, B

    K. Pomorski, B. Nerlo-Pomorska, A. Surowiec, M. Kowal, J. Bartel, K. Dietrich, J. Richert, C. Schmitt, B. Benoit, E. de Goes Brennand, L. Donadille, C. Badimon, Nucl. Phys. A 670, 25 (2000)

    work page 2000

  30. [30]

    Delagrange, C

    H. Delagrange, C. Gregoire, F. Scheuter, Y. Abe, Z. Phys. A 323, 437 (1986)

    work page 1986

  31. [31]

    Dietrich, K

    K. Dietrich, K. Pomorski, J. Richert, Z. Phys. A 351, 397 (1995)

    work page 1995

  32. [32]

    Surowiec, K

    A. Surowiec, K. Pomorski, C. Schmitt, J. Bartel, APPB 33, 479 (2002)

    work page 2002

  33. [33]

    Maruhn and W

    J. Maruhn and W. Greiner, Zeit. f. Phys. 251, 431 (1972)

    work page 1972

  34. [34]

    Suekane, A

    S. Suekane, A. Iwamoto, S. Yamaji, and K. Harada, JAERI-memo 5918, (1974)

    work page 1974

  35. [35]

    Iwamoto, S

    A. Iwamoto, S. Yamaji, S. Suekane, and K. Harada, Prog. Theor. Phys. 55, 115 (1976)

    work page 1976

  36. [36]

    K. Sato, S. Yamaji, K. Harada, and S. Yoshida, Z. Phys. A 290, 149 (1979)

    work page 1979

  37. [37]

    V. M. Strutinsky, Nucl. Phys. A 95, 420 (1967); A 122, 1 (1968)

    work page 1967

  38. [38]

    Brack, J

    M. Brack, J. Damgaard, A. S. Jensen, H. C. Pauli, V. M. Strutinsky, and C. Y. Wong, Rev. Mod. Phys. 44, 320 (1972)

    work page 1972

  39. [39]

    Ivanyuk, C

    F.A. Ivanyuk, C. Ishizuka, M.D. Usang, and S. Chiba, Phys. Rev. C 97, 054331 (2018)

    work page 2018

  40. [40]

    Pomorski and H

    K. Pomorski and H. Hofmann, J. Physique, 42, 381 (1981)

    work page 1981

  41. [41]

    Hofmann, D

    H. Hofmann, D. Kiderlen, Int. Jour. Mod. Phys. E 7, 243 (1998)

    work page 1998

  42. [42]

    P.C.Martin, J.Schwinger, Phys. Rev. 115, 1342 (1959)

    work page 1959

  43. [43]

    A.K.Kerman, S.E.Koonin, Ann. Phys. 100, 332 (1976)

    work page 1976

  44. [44]

    D.M.Brink, M.Di Toro, Nucl. Phys. A 372, 151 (1981)

    work page 1981

  45. [45]

    Friedman, W.G

    W.A. Friedman, W.G. Lynch, Phys. Rev. C 28, 16 (1968)

    work page 1968

  46. [46]

    Zeynalov, V

    S. Zeynalov, V. Furman, F.-J. Hambsch, M. Florec, V. Yu. Konovalov, V. A. Khryachkov, and Yu. S. Zamyat- nin, in Proceedings of the 13th International Seminar on Interaction of Neutrons with Nuclei (ISINN-13), Dubna, Russia, May 25-28 , 2005 (Joint Institute for Nuclear Re- search, Dubna, 2006), p. 351

    work page 2005

  47. [47]

    Shibata, O

    K. Shibata, O. Iwamoto, T. Nakagawa, N. Iwamoto, A. Ichihara, S. Kunieda, S. Chiba, K. Furutaka, N. Otuka, T. Ohasawa, T. Murata, H. Matsunobu, A. Zukeran, S. Kamada, and J.-i. Katakura, J. Nucl. Sci. Technol. 48, 1 (2011)

    work page 2011

  48. [48]

    M. J. Vermeulen, K. Nishio, K. Hirose, K.R. Kean, H. Makii, R. Orlandi, K. Tsukada, I. Tsekhanovich, A.N. Andreyev, S. Ishizaki, M. Okubayashi, S. Tanaka, and Y. Aritomo, Phys. Rev. C 102, 054610 (2020)

    work page 2020

  49. [49]

    M¨ oller, J.R

    P. M¨ oller, J.R. Nix, and K.-L. Kratz, Atomic Data and Nuclear Data Tables 66, 131 (1997)

    work page 1997

  50. [50]

    Watt, Phys

    B.E. Watt, Phys. Rev. 87, 1037 (1952)

    work page 1952

  51. [51]

    Santra, K

    Kavita Rani, R. Santra, K. Banerjee, T.K. Ghosh, A. Sen, Pratap Roy, R.Shil, A. S. Roy, S.S. Nayak, S. Manna, D. Paul, K. Atreya, P. Pant, A. Sultana, T.K. Rana, S. Kundu, P. Karmakar, R. Pandey, S. Mukhopad- hyay, D. Pandit, D. Mondal, G. Mukherjee, and J. Sad- hukhan, Proceedings of the DAE Symp. on Nucl. Phys. 68 (2024)

    work page 2024

  52. [52]

    Strecker, R

    M. Strecker, R. Wien, P. Plischke, and W. Scobel, Phys. Rev. C 41, 2172 (1990)

    work page 1990