{"id":"e1cea9f1-6ab4-4130-a451-e31a14bdaecd","arxiv_id":"1908.01368","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"For 236U, a GCM calculation gives a diabatic scission decay width of about 2 to 3 MeV, while pairing-mediated widths to a specific final channel are 5 keV and 60 keV.","lead":"This paper calculates how quickly a stretched uranium nucleus at the point of splitting can break into two fragments, using a many-body quantum method. It finds that decays that preserve the fragment quantum numbers can be hundreds to thousands of times faster than decays that require repartnering of nucleon pairs.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The several-MeV diabatic width and the claimed 2-3 order gap rest on extrapolated, flat-potential continuum states whose largest eigenfunction amplitudes lie on the simulated tail; no B sensitivity is reported.","rationale":"The reader's weakest_assumption targets exactly the extrapolated Hamiltonian matrix elements and the flat-bottom potential used to build the continuum. My reading of the manuscript confirms this as the load-bearing point: the diabatic decay width is extracted from a strength function over a discretized continuum whose far states are constructed with Eq. (13), and the largest amplitudes of the relevant eigenstate are on those simulated states. The pairing-mediated widths are computed with the same continuum model, so an error in B or in the flat-potential assumption could in principle move both the diabatic and pairing widths in the same direction; the paper does not quantify this. The authors themselves state that only three examples are presented and that large fluctuations are expected. My recommendation is therefore unchanged: the paper is a plausible exploratory calculation that should be accepted conditionally, pending a sensitivity check of the kind described above. I do not see an internal inconsistency severe enough to reject the manuscript, but the central claim is not fully secured without that check.","tokens_in":10498,"tokens_out":7357,"duration_ms":84347,"concrete_test":"Repeat the Section IV Glider decay with the added-block Hamiltonian modified as follows: set B to the alternative kinetic-energy estimate instead of the value fitted from the GCM H/S elements (or vary B by ±50%), and replace the flat diagonal H''_{j,j} = H_{k,k} by the Coulomb-plus-offset curve V(z) = e^2 Z_L Z_R / z + C shown in Fig. 3, re-diagonalizing the same 25-state space. If the diabatic width stays above about 1 MeV and the A/B pairing widths stay below about 0.1 MeV, the central ordering survives; if Γ_diabatic drops by more than a factor of 3 or the pairing widths move within an order of magnitude of it, the claim is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central quantitative separation (Γ_diabatic ≈ 2-3 MeV vs Γ_pairing ≈ 5-60 keV) is produced entirely inside a continuum model whose far part is not computed microscopically. The five added states in Table I and the 20 states used in Section IV are generated from Eqs. (12)-(13) with a flat diagonal H''_{j,j} = H_{k,k} and a single parameter B; no value of B or the claimed agreement between its two estimates is reported. The chosen continuum eigenstate in Table I has its largest amplitudes on the farthest simulated states (0.77 at 18.79 fm and -0.62 at 19.13 fm), so the FGR matrix elements and level spacing ΔE that determine Γ are dominated by the ad hoc entries. In the physical channel the potential is not flat: the Coulomb field changes the energy by roughly 10 MeV/fm over the extrapolated region (Fig. 3), so the asymptotic momentum and density of states differ substantially from the plane-wave model. If Eq. (13) overestimates B or the flat-bottom assumption distorts the local density of states, the 2.2 MeV FGR width and hence the two-orders-of-magnitude gap can shift. The paper provides no sensitivity analysis, and its own Discussion cautions against generalizing from just three examples.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a Generator Coordinate Method (GCM) treatment of the final stage of nuclear fission, focusing on 236U and the pre-scission configuration labeled Glider. The authors construct a discretized continuum channel from GCM configurations along the relative-fragment coordinate and compute decay widths by Fermi’s Golden Rule and by the width of the Lanczos strength function. For the diabatic case (Glider decaying into the Glider continuum) they obtain Γ_FWHM ≈ 3 MeV and Γ_FGR = 2.2 MeV. For two pairing-mediated transitions from intermediate configurations A and B into the Glider channel they obtain 5 keV and 60 keV, from which they conclude that non-diabatic widths to a specific channel are 2–3 orders of magnitude smaller than diabatic widths. The continuum is partly built by extrapolating overlap and Hamiltonian matrix elements via Eqs. (12)–(13), introducing a parameter B, and the external potential is approximated as flat beyond the last computed GCM configuration.","tokens_in":10778,"tokens_out":5221,"duration_ms":59949,"significance":"If the order-of-magnitude separation between diabatic and pairing-mediated decay widths is robust, this is an important step toward a fully microscopic, quantum-mechanical description of scission dynamics. The paper provides a concrete framework for estimating partial widths in a realistic Gogny-D1S mean-field basis, and it connects the widths to independent physics: the TDHFB scission delay of order 10000 fm/c corresponds to Γ ≈ 20 keV, bracketed by the two pairing-mediated widths. The manuscript is also exemplary in stating its approximations openly and in giving enough detail to reproduce the construction. However, the central quantitative claim rests on an extrapolated, flat-potential continuum whose controlling parameter B is not reported and for which no sensitivity study is given; at present the several-MeV versus tens-of-keV separation is a plausible estimate rather than a firmly established result.","major_comments":[{"comment":"The central claim (Γ_diabatic ≈ 2–3 MeV vs Γ_pairing ≈ 5–60 keV) is controlled by the extrapolated part of the continuum. The selected eigenstate has its largest weights on the two farthest added states (a_n = 0.77 at 18.79 fm and −0.62 at 19.13 fm), so both the FGR matrix element and the level spacing ΔE are dominated by entries generated from Eq. (13). The parameter B is introduced without reporting its value or the promised comparison between its two estimates, and no sensitivity study is given. Because the two-order-of-magnitude separation is the central result, the manuscript should show how Γ_diabatic and Γ_pairing change when B is varied over a plausible range and when the number or spacing of added states is changed. Without such a study, the abstract's 'several MeV' and '2–3 orders of magnitude' statements rest on an unquantified modeling choice.","section":"III, Eq. (13), Table I"},{"comment":"Fig. 3 shows that the HF energy beyond scission follows the Coulomb law with a slope of order 10 MeV/fm, yet the continuum is constructed with H''_{j,j} = H_{k,k}, i.e., a flat potential beyond zrel ≈ 17.44 fm. For a repulsive Coulomb field the local momentum and density of states at the initial-state energy differ substantially from plane-wave values, so the wave function in Fig. 5 and the ΔE used in Eq. (26) are model-dependent precisely in the region that determines the width. The authors should either justify that the flat-bottom approximation preserves the relevant density of states to within the claimed factor, or repeat the calculation with the Coulomb tail included, for example by matching to Coulomb wave functions or using WKB normalization.","section":"III, flat-potential assumption"},{"comment":"The abstract asserts that 'typical widths to a specific final state channel are 2–3 orders of magnitude smaller,' but only two pairing-mediated channels are computed (5 keV and 60 keV), and the paper's own Discussion cautions against drawing general conclusions from just three examples. The FGR estimates in Table II also use a single nearest-neighbor matrix element and a local spacing in a small discretized space (Appendix), so the 'typical' claim is not strongly supported. The abstract should either be softened to match the exploratory status of the calculation or additional examples and/or averaged widths should be provided to justify the word 'typical.'","section":"Abstract and IV, Table II"}],"minor_comments":[{"comment":"The text says '20 configurations constructed with Eq. (14,15)'; the correct references are Eqs. (12)–(13), which define the extrapolated overlaps and Hamiltonian matrix elements, not the normalization condition and energy offset.","section":"IV, paragraph after Eq. (18)"},{"comment":"The phrase 'the estimated decay with is' should read 'the estimated decay width is'.","section":"IV, text before Eq. (19)"},{"comment":"The Breit-Wigner expression appears malformed: the form given by 'P ∼ 1/((E−E_i)^2+(Γ/2)^2)^2' is not a standard Lorentzian and likely contains a typographical error; please correct it.","section":"Appendix, Eq. (20)"},{"comment":"The repeated ' ' entries for the added states are ambiguous; please state explicitly that the diagonal energies and H/S ratios are set according to H''_{j,j}=H_{k,k} and Eq. (13).","section":"Table I"},{"comment":"The sinusoidal fit is shown only over zrel = 17.5–18.5 fm, while the largest eigenfunction amplitudes are at 18.79 and 19.13 fm; fitting the full asymptotic region would be more persuasive evidence for the plane-wave representation.","section":"Fig. 5"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a serious exploratory calculation with transparently stated approximations, and the requested sensitivity study is well within scope. The main concern is not internal inconsistency but robustness: the abstract's headline numbers are not yet sufficiently supported without reporting B and testing sensitivity to the extrapolation and flat-potential assumptions. I would not reject; a careful revision with the sensitivity analysis and a tempered abstract would make the paper publishable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nWhat is actually new here: the first attempt I know of to put a many-body GCM number on scission decay widths—a diabatically connected channel at roughly 2–3 MeV, and two pairing-mediated channels at 5 and 60 keV. The qualitative ordering is the paper's real contribution, and I think it is plausible.\n\nWhat the paper does well: it works with the full Gogny-based HFB+GCM framework, it is explicit about the non-orthogonality problem and how the Lanczos-based strength function deals with it, and it gives a sanity check on the discretized continuum wave function by fitting it to a sine wave with a reasonable effective mass. The Discussion is honest about the limitations: three examples, no quasiparticle excitations, no collective flow, only pairing residual interactions.\n\nThe soft spots are the ones your stress-test note identifies. The continuum beyond about 17.4 fm is extrapolated via Eq. (13), with a free parameter B, and no value of B or comparison between the two claimed estimates is reported. The flat-bottom potential ignores the Coulomb slope that their own Fig. 3 shows is roughly 10 MeV/fm over that region. The FGR width, and hence the two-orders-of-magnitude separation, is dominated by the simulated tail: the fifth eigenstate in Table I has its largest amplitudes on the two farthest added states. So the central numbers are model-dependent in a way the paper does not quantify. This is a real limitation, but it is not fatal—the authors repeatedly call the estimates rough, and they avoid claiming more than the ordering. A referee should require a sensitivity study over B, the flat-bottom assumption, and chain length, plus a few more channels before the 2–3 order gap is treated as a general result.\n\nThe math and the citation pattern look solid. The GCM equations, orthogonalization, and FGR estimate are internally consistent; the heavy reliance on their own prior work is natural since this is a continuation. I would accept this for peer review: it deserves a serious referee, not a desk reject. It is a methods paper that could be tightened. I would cite it, with the caveat about the extrapolated tail, as the first GCM estimate of scission widths.\n\nRecommendation: send it to a competent referee and ask explicitly for sensitivity analysis of B and the external potential before publication.","headline":"A plausible first GCM estimate of scission decay widths, but the headline 2–3 MeV vs 5–60 keV gap rests partly on an unquantified extrapolated continuum tail.","tokens_in":11279,"tokens_out":2671,"would_cite":true,"duration_ms":28830,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For 236U, the decay width of a pre-scission configuration into a diabatically connected continuum channel is about 2–3 MeV, while pairing-mediated decays to a specific channel are 5–60 keV.","keywords":["nuclear fission","scission point","decay width","Generator Coordinate Method","diabatic dynamics","pairing interaction","uranium-236","strength function"],"falsifier":"Recompute the 236U Glider decay chain with explicit constraints on the relative momentum of the fragments, so that the kinetic energy beyond the scission point is treated exactly instead of through the Gaussian ansatz; if the diabatic golden-rule width drops from the MeV range into the keV range, the reported hierarchy would be an artifact of the extrapolation.","tokens_in":10294,"feed_emoji":"⚛️","tokens_out":13782,"duration_ms":131910,"temperature":0.7,"pith_summary":"The paper asks how a fissioning nucleus takes the final step of fission—the rupture of the neck that turns a single bound, highly elongated nucleus into two separate fragments—and it provides the first Generator Coordinate Method (GCM) estimates of the quantum decay widths for that step in 236U. The authors build a two-fragment continuum channel out of a chain of mean-field configurations that keep the same K-partition, the same set of occupied single-particle states, and they find that a configuration decaying along this diabatic path has a width of roughly 2–3 MeV. When the decay instead requires the residual pairing interaction to change the configuration, the width to a specific final channel is 5 keV and 60 keV in the two examples, two to three orders of magnitude smaller. The result matters because this hierarchy determines whether a pre-scission state disintegrates almost immediately or lingers long enough to shape fragment yields, total kinetic energies, and the odd-even staggering observed in fragment charge distributions.","feed_headline":"Diabatic fission decays reach MeV; pairing decays stay keV","feed_subtitle":"GCM estimates for 236U show scission favors diabatic channels by two to three orders of magnitude.","key_machinery":"The load-bearing object is the Generator Coordinate Method (GCM) representation of the two-fragment continuum as a chain of constrained mean-field configurations labeled by the relative fragment coordinate $z_{\\mathrm{rel}}$ and by a conserved K-partition, the set of occupied single-particle states in an axially symmetric mean field. Overlap and Hamiltonian matrix elements between neighboring configurations are computed from the energy density functional; beyond the last explicitly calculated configuration, the authors extrapolate them using a Gaussian overlap ansatz and a quadratic intrinsic term with a fitted parameter $B$, effectively placing the separated fragments in a flat potential. Decay widths are then extracted from the strength function of the chosen initial configuration in the eigenstates of this finite space, either as the full width at half maximum of the smoothed strength function or from the golden rule applied to the off-diagonal matrix elements after an orthogonalization step based on tridiagonalization. The chain construction and the extrapolation together supply the final-state wave function that is needed to define a two-fragment decay in a many-body Hamiltonian framework.","core_discovery":"The central numerical discovery is a hierarchy of decay widths at the scission point of 236U. The authors construct a continuum channel, labeled Glider, from five GCM configurations near scission plus five extrapolated states at larger fragment separations, and take the pre-scission Glider configuration at $z_{\\mathrm{rel}} = 16.71$ fm as the decaying state. For the diabatic decay, in which the K-partition is preserved along the whole chain, the smoothed strength function gives $\\Gamma_{\\mathrm{FWHM}} \\approx 3$ MeV and the golden-rule estimate gives 2.2 MeV. For two non-diabatic decays that first require a pair jump—configurations A and B connecting the bound configuration Buenavista to Glider—the widths are 5 keV and 60 keV. The paper concludes that diabatically allowed transitions can have widths up to several MeV, while non-diabatic decays through the pairing interaction to a specific final channel are two to three orders of magnitude smaller.","pith_inferences":["If the same calculation is repeated in other actinides, a natural expectation is that the MeV-versus-keV separation holds whenever a diabatic channel exists, making diabatic paths the generic doorway for fast scission.","A momentum-constrained version of the chain would provide a sharper test: the paper's effective-mass ratio $M^*/M = 0.87$ puts the Gaussian kinetic energy off by roughly 13 percent, far too small to erase the hierarchy unless the correction is strongly channel-dependent.","Because the current GCM space contains no quasiparticle excitations, real pre-scission states carrying internal excitation could reach the continuum through additional pairing channels; whether those extra paths close the order-of-magnitude gap is left open by the paper."],"forward_implications":["When a diabatic channel is open, the scission step is fast: the computed 2–3 MeV widths imply decay times of order $10^{-22}$ seconds, so there is no significant pause at the rupture point.","Pairing-mediated decay into a specific final channel is slow by comparison, with widths of 5–60 keV, so such channels can only matter through the cumulative effect of many open channels or through large fluctuations in their matrix elements.","The roughly 20 keV width implied by the approximately $10^4$ fm/c scission delay seen in time-dependent Hartree-Fock-Bogoliubov calculations lies between the two pairing widths, which the paper reads as confirmation of the microscopic estimates.","If a representative sample of final channels can be constructed, the same machinery would give branching ratios among exit channels and thus predictions for fluctuations in mass yields and total kinetic energies."],"supporting_citations":[{"why":"Supplies the 236U Glider scission path, overlap data, and the assessment that the configurations are well described by Gaussian overlaps.","marker":"[2]"},{"why":"Derives the GCM Hamiltonian dynamics for separated subsystems and the energy-offset formula used to interpret the continuum wave function.","marker":"[5]"},{"why":"Identifies the pair jumps from Buenavista through intermediate configurations A and B into Glider, providing the initial states for the non-diabatic width calculations.","marker":"[13]"},{"why":"Supplies the strength-function and orthogonalization procedure used to extract decay widths in the GCM basis.","marker":"[6]"},{"why":"Provides the density-dependent functional prescription for computing Hamiltonian matrix elements in the GCM.","marker":"[4]"},{"why":"Gives the contraction formula used to compute Hamiltonian matrix elements between the HFB configurations.","marker":"[11]"},{"why":"Supplies the experimental observation of no 1 keV fluctuations in fission cross sections, used to argue that the widths are consistent with large average decay rates.","marker":"[16]"}],"fun_headline_variants":["MeV diabatic fission decay, keV pairing decay","Fission scission decay widths: MeV vs keV","Scission decay: diabatic MeV, pairing keV","U-236 scission: diabatic decays dominate","Diabatic fission decays exceed pairing by 1000x"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation's weakest point is the extrapolation that replaces the real potential between separated fragments with a flat potential and a simple Gaussian overlap model controlled by one fitted parameter; if that extrapolation is wrong, the computed widths could shift by more than the reported two-to-three-order-of-magnitude separation.","fun_headline_variants_meta":{"raw":{"variants":["MeV diabatic fission decay, keV pairing decay","Fission scission decay widths: MeV vs keV","Scission decay: diabatic MeV, pairing keV","U-236 scission: diabatic decays dominate","Diabatic fission decays exceed pairing by 1000x"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000609,"raw_usage":{"total_tokens":2775,"prompt_tokens":824,"completion_tokens":1951,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":440,"completion_tokens_details":{"reasoning_tokens":1873}},"tokens_in":440,"tokens_out":1951,"duration_ms":14131,"temperature":1.0,"reasoning_tokens":1873,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:14:19.345547+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the 236U Glider decay chain with explicit constraints on the relative momentum of the fragments, so that the kinetic energy beyond the scission point is treated exactly instead of through the Gaussian ansatz; if the diabatic golden-rule width drops from the MeV range into the keV range, the reported hierarchy would be an artifact of the extrapolation.","supporting_citations":[{"cited_title":"Diabatic scission paths","cited_arxiv_id":"1904.06751","evidence_quote":"Supplies the 236U Glider scission path, overlap data, and the assessment that the configurations are well described by Gaussian overlaps."},{"cited_title":"Bertsch and W","cited_arxiv_id":null,"evidence_quote":"Derives the GCM Hamiltonian dynamics for separated subsystems and the energy-offset formula used to interpret the continuum wave function."},{"cited_title":"A\" and “B","cited_arxiv_id":null,"evidence_quote":"Identifies the pair jumps from Buenavista through intermediate configurations A and B into Glider, providing the initial states for the non-diabatic width calculations."},{"cited_title":"Caurier, G","cited_arxiv_id":null,"evidence_quote":"Supplies the strength-function and orthogonalization procedure used to extract decay widths in the GCM basis."},{"cited_title":"Robledo, T","cited_arxiv_id":null,"evidence_quote":"Provides the density-dependent functional prescription for computing Hamiltonian matrix elements in the GCM."},{"cited_title":"Balian and E","cited_arxiv_id":null,"evidence_quote":"Gives the contraction formula used to compute Hamiltonian matrix elements between the HFB configurations."},{"cited_title":"Peierls and D","cited_arxiv_id":null,"evidence_quote":"Supplies the experimental observation of no 1 keV fluctuations in fission cross sections, used to argue that the widths are consistent with large average decay rates."}],"review_version":1}