Influence of the Exit Channel in $^{235}$U(n,f) and $^{239}$Pu(n,f) Reactions in Time-Dependent Density Functional Theory

Aurel Bulgac; Ibrahim Abdurrahman; Ionel Stetcu; Matthew Kafker

REVIEW 4 major objections 4 minor 46 references

Influence of the Exit Channel in $^{235}$U(n,f) and $^{239}$Pu(n,f) Reactions in Time-Dependent Density Functional Theory

T0 review · 4 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Fission trajectories from the outer saddle fall into three classes set by the initial octupole moment; near-symmetric fission's elongated neck lowers fragment kinetic energy by about 25 MeV and sends the extra excitation into a deformed hea

desk verdict Useful TDSLDA study of rare fission modes; the long-neck/TKE mechanism is credible for the sampled trajectories, but the jump to neutron-energy trends needs an ensemble weighting that the paper doesn't have. read the letter →

arxiv 2607.18511 v1 pith:YGJRDPVQ submitted 2026-07-20 nucl-th

Ibrahim Abdurrahman , Matthew Kafker , Aurel Bulgac , Ionel Stetcu This is my paper

classification nucl-th PACS 25.85.-w21.60.Jz

keywords nuclearfissiontime-dependentdensityfunctionaltheorysuperfluidlocalapproximationsaddle-to-scissiondynamicsoctupoledeformationtotalkineticenergyneckrupturescissionneutrons

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper simulates neutron-induced fission of 235U and 239Pu from the outer saddle to scission, showing that the initial octupole deformation of the nucleus sorts the descent into three distinct channels: asymmetric, near-symmetric, and highly-asymmetric. Near-symmetric fission produces a long, thin neck, so when the neck snaps the proto-fragments are farther apart, giving about 25 MeV less Coulomb energy to the fragments. That deficit appears as extra excitation of the heavy fragment, which becomes strongly deformed. These results offer a microscopic explanation for the measured decrease of average total kinetic energy as the incident neutron energy increases, and they show that rarer fission channels have distinctive scission-neutron angular distributions.

What carries the argument

The engine of the argument is the initial octupole moment Q30 at the outer saddle, together with the neck rupture distance d_rupt. Q30 chooses the fission valley: small (near-symmetric), moderate (asymmetric), large (highly-asymmetric). The rupture distance then converts that initial choice into observable energy partition through the Coulomb formula TKE ≈ e² Z_L Z_H / d_rupt + K_rupt. The superfluid time-dependent density functional theory provides the non-adiabatic many-body dynamics that carries the nucleus from saddle to scission and allows neck densities, rupture times, and fragment excitation energies to be read off directly.

What would settle it

Measure the total kinetic energy and mass asymmetry of fission fragments from 235U under neutron energies where near-symmetric fission is enhanced (e.g., a few MeV). If the TKE of near-symmetric mass splits is not ~25 MeV below that of asymmetric mass splits, or if the angular distribution of scission neutrons shows no excess perpendicular component, the proposed neck-length mechanism would be contradicted.

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Extended reading notes

Core claim

On its own terms, the paper's central finding is that a memory of the outer-saddle shape survives all the way to scission: the initial octupole moment Q30 selects which of three fission modes a nucleus follows, and each mode has its own scission geometry. The near-symmetric mode stretches into an elongated neck and ruptures when the proto-fragments are separated by about 23 fm instead of 20 fm, lowering the total kinetic energy by roughly 25 MeV relative to typical asymmetric fission. The energy balance is re-routed: nearly all of the missing kinetic energy shows up as extra excitation of the heavy fragment, which inflates its quadrupole deformation. The highly-asymmetric mode, when it forms

Load-bearing premise

The division into three non-communicating fission modes presupposes that the nucleus starts on the outer-saddle surface with axial symmetry and without stochastic fluctuations; if triaxial or fluctuating paths connect the valleys, the identity and memory of a given mode could fade before scission.

Editorial extensions

If this is right

As incident neutron energy rises, more near-symmetric fission occurs, reducing the average TKE—a long-known experimental trend that this mechanism explains.
In near-symmetric fission the heavy fragment carries most of the extra excitation energy and emerges strongly deformed, implying harder gamma-ray and neutron emission from heavy fragments at higher incident energies.
The longer neck and slower rupture in near-symmetric fission produce a distinctive angular distribution of scission neutrons (more perpendicular than parallel), a signature that could be sought in experiments.
The observed memory of the initial octupole moment at scission implies that the neck rupture position is not random, and that the widths of fragment mass distributions in TDDFT may be broadened simply by sampling more initial saddle configurations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the three-class division is real, the TKE distribution of fission at high excitation may be multi-modal; sorting measured TKE by fragment mass asymmetry might reveal sub-structure that current data analyses average over.
Pre-saddle fluctuations could be used as a control knob: tuning how much octupole deformation is populated at the outer saddle would directly steer the relative yields of the three modes, which is relevant for applications relying on fission product spectra.
A testable extension of the paper's logic is to verify whether the ~25 MeV TKE deficit of near-symmetric modes persists across other actinides; if it does, the neck-length effect is generic, not merely a feature of 236U and 240Pu.
The near-symmetric elongated neck and its two-stage decay might offer a window into non-equilibrium neck dynamics that could be further probed by computing angular correlations of charged particles emitted near scission.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know this paper is worth engaging with, but read it as a mechanism study, not a quantitative prediction. The central observation—near-symmetric trajectories develop a long neck, rupture at larger separation, and come out with ~25 MeV less TKE than asymmetric ones—is well supported inside the model. Eq. (2) is a clean decomposition and Table I/Fig. 6 back the correlation.

What is actually new: a systematic TDSLDA comparison of asymmetric, near-symmetric, and highly-asymmetric exit channels for 236U and 240Pu, plus the first microscopic look at scission-neutron directionality in near-symmetric fission. The authors also report heavy-fragment excitation sharing, a second neck-rupture timescale, and a useful analysis of fragment deformations. They are transparent about limitations: they flag the missing fluctuation/triaxiality effects, the lack of a weighting prescription, and the TKE bias of the method. That honesty earns credit.

The soft spots are real. Per-class statistics are tiny (4–6 trajectories; one exactly-symmetric run; one near-symmetric scission-neutron run). All initial states are hand-picked, axially symmetric saddle configurations. One 240Pu trajectory with small initial Q30 ends up in the asymmetric valley, and exactly symmetric fission is unstable—so the 'memory of initial octupole moment' is not absolute. The stress-test concern about fluctuations coupling the valleys is legitimate: if triaxiality or stochastic dynamics mixes the modes, the clean three-class picture could blur. But that does not break the mechanism for the trajectories actually computed; it limits the generality of the classification. The larger issue is the paper's own point: without a weighting prescription for initial configurations, the claim that this explains the experimental decrease of TKE with incident neutron energy is a plausible hypothesis, not an established trend. The authors say so themselves, but the abstract's causal phrasing is stronger than the evidence.

For fission theorists and nuclear data people, this is a worthwhile read and a fair candidate for peer review. I would send it to a good referee, expecting a request for more trajectories or at least a sharply reduced scope in the conclusions.

Referee Report

4 major / 4 minor

Summary. This manuscript uses the superfluid local density approximation (TDSLDA) with the SeaLL1 functional to follow 236U and 240Pu fission from the outer saddle to scission and beyond. The authors classify initial states by their octupole moment Q30 on the potential-energy surface into asymmetric, near-symmetric, and—for 236U—highly-asymmetric modes. The central result is that near-symmetric trajectories develop a highly elongated neck, rupture at a larger fragment separation distance, and emerge with roughly 25 MeV lower total kinetic energy (TKE) and correspondingly higher excitation energy, most of which goes to the heavy fragment. The paper also analyzes neck-rupture dynamics and, for one near-symmetric trajectory, scission-neutron emission. The key observable link is Eq. (2), TKE ≈ e^2 Z_L Z_H / d_rupt + K_rupt, with d_rupt and K_rupt taken from the simulations.

Significance. If the mode-dependent neck dynamics is robust, the paper offers a microscopic mechanism for rare fission modes and a plausible explanation for the experimentally observed decrease of average TKE with increasing excitation energy. A clear strength is that Eq. (2) is a decomposition rather than a fit: the TKE differences are traced to simulated d_rupt and K_rupt, not adjusted to any target observable. The paper is also candid about its approximations. However, the central claim rests on very small samples and on axially symmetric, fluctuation-free initial conditions, and the paper itself states that including fluctuations may alter the conclusions. The result is therefore best read as a well-posed mechanism hypothesis rather than a quantitatively established prediction.

major comments (4)

[Sec. II, Table I and Fig. 1] The three-mode classification and the near-symmetric vs. asymmetric TKE difference are based on only 4–6 trajectories per class: n=6 (236U A), n=4 (236U S and H), n=5 (240Pu A and S), and n=1 each for the exactly symmetric and intermediate trajectories. The quoted standard deviations are trajectory-to-trajectory scatters, not uncertainties of the mean, and no significance test is reported. Because the ~25 MeV TKE deficit is the central quantitative claim, the authors should report standard errors or confidence intervals and ideally add trajectories for the rare modes. As listed, the error bars are easy to misread as statistical precision. In addition, highly-asymmetric fission is studied only for 236U, so the abstract's two-reaction framing is only partially realized.
[Sec. II, Fig. 1 and end of Sec. II] The manuscript states that the 'forbidden zone' separating fission modes exists 'at least in the absence of triaxial deformations or fluctuations [31]' and later notes that fluctuations are ignored and 'may alter this conclusion in the future.' This is not a peripheral caveat: the causal chain 'initial Q30 -> valley choice -> long neck -> lower TKE' depends on the initial octupole moment deterministically selecting a valley. If triaxial or fluctuating paths mix the valleys, the memory of the initial octupole moment could weaken or disappear. The authors should either provide a concrete sensitivity test—e.g., small triaxial components or a stochastic ensemble of initial states—or explicitly frame the central conclusion as conditional on the axial, fluctuation-free approximation.
[Sec. IV, Figs. 10–11] The scission-neutron conclusion that near-symmetric fission emits 'significantly more' neutrons perpendicular to the fission axis is based on exactly one near-symmetric trajectory on a 48x48x96 lattice, while the asymmetric reference is an average over several trajectories from Ref. [11]. With n=1, the difference in anisotropy cannot be distinguished from sensitivity to the particular initial condition or numerical parameters. Please provide additional near-symmetric runs or explicitly downgrade this result to a single-trajectory observation with no claim of generality.
[Sec. III, paragraph after Fig. 7] The paper acknowledges that TDDFT in its current implementation 'underestimates the TKE of the rarer fission modes, and, consequentially, overestimates their FF excitation energies when compared to experiment,' citing similar behavior in Ref. [19]. Since the ~25 MeV TKE difference between modes is a central quantitative output, a mode-dependent systematic bias could change the magnitude of the effect even if Eq. (2) is algebraically correct. The authors should quantify this sensitivity—for example by examining an alternate EDF or varying the scission threshold n_neck < 0.1 fm^-1—or explicitly present 25 MeV as a model-dependent estimate rather than a quantitative prediction.

minor comments (4)

[Table I, 236U (H) row] The light-fragment charge is listed as 33.93 (85); the standard deviation is presumably 0.85, not 85. Please correct the typo.
[Ref. [5]] 'in three dimentions' should be 'in three dimensions.'
[Sec. IV] 'there are a few exception to this rule' should be 'there are a few exceptions to this rule.'
[Sec. II, exact-symmetry discussion] The statement that exactly symmetric fission is highly unlikely for thermal-neutron fission is based on one successful symmetric trajectory for 236U and two non-symmetric outcomes for 240Pu. This is suggestive but statistically thin; consider wording it as inferential rather than a firm conclusion.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the neck-length/TKE relation is a direct TDSLDA output, not a fitted or definitional relation; only a minor self-citation for the asymmetric scission-neutron baseline is present.

full rationale

The derivation chain is self-contained. The central observables (neck length, d_rupt, TKE, E*) are computed from TDSLDA trajectories; no quantity in Table I or Fig. 6 is fitted to reproduce the claimed ~25 MeV TKE deficit. Eq. (2) is a decomposition (Coulomb repulsion plus collective kinetic energy), and the paper separately reports d_rupt and K_rupt, so the longer-neck/lower-TKE correlation is a dynamical consequence rather than a construction. Mode classes are defined by the initial PES location (Q20, Q30), and the final mass asymmetry/TKE are independent outputs; the paper even shows an intermediate 240Pu trajectory that begins near-symmetric but fissions asymmetrically, and an exactly symmetric trajectory, so the Q30-to-final-properties mapping is not definitional. The main caveat is acknowledged: axial symmetry and absence of fluctuations [31] may alter the valley separation ('fluctuations [31] are ignored, which may alter this conclusion in the future'), but that is a robustness/correctness limitation, not circularity. The only self-citation of note is use of Abdurrahman et al. [11] for the asymmetric scission-neutron baseline and 'universal' first rupture time; this is comparative/supporting and partially independently corroborated by ref. [43] with a different EDF, so it is not load-bearing for the main claim.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new fitted constants or entities. Its results depend on EDF parameters from SeaLL1 [30] (input from prior literature), hand-set initial deformations, an arbitrary class boundary, and the chosen scission definition. The most consequential unvalidated input is the assumption that axial, fluctuation-free initial conditions on the outer saddle are representative.

free parameters (3)

Initial saddle deformations (Q20, Q30) of each trajectory = See Table I; e.g., 236U (A): Q20 about 161 b, Q30 about 17 b^(3/2)
Hand-selected starting points on PES ridges define the fission-mode classes and largely determine final fragment masses and TKE; no probability weighting is assigned.
Octupole-mode class boundary = Q30 about 35 b^(3/2)
Used to separate asymmetric from highly-asymmetric trajectories; changes pooling and averages in Table I and Figs. 5–7.
Neck-density scission threshold = 0.1 fm^-1
Defines rupture time and d_rupt used in Eq. (2) and thus the TKE decomposition; a convention chosen by the authors.

assumptions (5)

domain assumption The TDSLDA equation set with the SeaLL1 energy density functional is an adequate microscopic description of the saddle-to-scission stage; missing beyond-mean-field correlations alter quantitative values but not the qualitative mode dependence.
Invoked throughout Secs. II–V; the paper concedes in Sec. III that TDDFT underestimates TKE and overestimates E* for rare modes, so quantitative accuracy is assumed not to change trends.
domain assumption The fissioning nucleus can be initialized as a generalized Slater determinant at the outer saddle with specified Q20 and Q30; the history from ground state to the outer saddle (dissipation, barrier passage, triaxiality) can be neglected.
Intro footnote 1 and Sec. II; footnote 2 criticizes other TDDFT starts 7–8 MeV below the barrier, but this paper also starts at the outer saddle without simulating the approach.
domain assumption The initial configurations are effectively axial and fluctuations are negligible; the 'forbidden zones' separating fission modes exist in the absence of triaxial deformations and fluctuations.
Sec. II, Fig. 1 discussion: 'at least in the absence of triaxial deformations or fluctuations'; 'fluctuations [31] are ignored, which may alter this conclusion in the future.'
domain assumption Total kinetic energy at scission is approximately the point-charge Coulomb energy plus collective kinetic energy, Eq. (2), with minor corrections from deformations and particle emission.
Sec. III, Eq. (2); this decomposition is the basis for attributing the TKE reduction to larger rupture distance.
ad hoc to paper The scission time and fragment properties can be defined by the criterion min integral(n_n + n_p) dx dy < 0.1 fm^-1.
Sec. III, Table I caption; this threshold sets d_rupt, t_rupt, and the TKE decomposition; a different threshold would shift quantitative results.

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Cite this review

Pith. "Pith review of Influence of the Exit Channel in $^{235}$U(n,f) and $^{239}$Pu(n,f) Reactions in Time-Dependent Density Functional Theory." pith.science (2026). https://pith.science/paper/YGJRDPVQ

@misc{pith2026260718511,
  author       = {Pith},
  title        = {Pith review of: Influence of the Exit Channel in $^235$U(n,f) and $^239$Pu(n,f) Reactions in Time-Dependent Density Functional Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YGJRDPVQ}},
  note         = {Machine review of arXiv:2607.18511}
}

read the original abstract

This study investigates the consequences of the intrinsic deformation of the fissioning nuclear system near the outer saddle point on the shape evolution of the nucleus from saddle to scission and on the properties of the fission fragments. It is found that trajectories generally split into at least three classes, asymmetric, near-symmetric, and highly-asymmetric fission, that are roughly determined by the initial magnitude of the octupole moment, and each of which exhibits different scission dynamics and fragment properties. Near-symmetric modes result in a highly elongated neck at scission, leading to the neck rupture occurring when the proto-fragments are further apart than is the case for typical asymmetric fission, which in turn leads to a lower total kinetic energy and higher total excitation energy. The majority of this additional excitation energy goes into the heavy fission fragment, that develops a substantial quadrupole deformation. A similar trend is observed for the total kinetic energy of highly-asymmetric fission events, and the opposite trend for the excitation energy of the fission fragments as the majority of the additional excitation energy goes into the light fission fragment instead. The study also characterizes the neck rupture, including its effect on the emission of scission neutrons in near-symmetric fission.

Figures

Figures reproduced from arXiv: 2607.18511 by the authors.

**Figure 3.** FIG. 3. Panels (a) and (b) show the evolution of the [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** FIG. 4. Slices of the neutron and proton number densities for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (7 more)

**Figure 5.** Figure 5: FIG. 5. The separation distance between the proto-fission [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: FIG. 6. Panel (a) shows the TKE vs. the initial octupole [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: FIG. 7. Panels (a) and (b) show the excitation energies of the light and heavy FFs vs. the initial octupole moment of the FNS [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: FIG. 8. In panel (a) the integrated neck density is shown [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: FIG. 9. Panel (a) shows the rupture time for the neutron [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 11.** Figure 11: FIG. 11. Panel (a) shows the number of scission neutrons re [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]

**Figure 10.** Figure 10: FIG. 10. Time series of slices of the neutron number density [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]

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