{"id":"2bcadf91-6416-4481-959e-6a5dae1964a1","arxiv_id":"2608.07131","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A new Continuous Deflation method constructs ten continuous variational excited fission paths for 240Pu, overcoming the failures of two-quasiparticle excitations.","lead":"This paper introduces a new computational method, Continuous Deflation, that builds smooth excited-state paths for the Schrödinger Collective Intrinsic Model of nuclear fission, and applies it to ten excited paths of 240Pu. This matters because it is a step toward microscopically describing how intrinsic excitations and pair-breaking affect fission yields, which adiabatic models currently miss.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'SCIM-ready' claim is not yet established because Section IV.B reports 77% Hamiltonian-kernel deviations for the neutron Ω=5/2 path and adopts an overlap prescription whose accuracy is deferred to future work.","rationale":"I read the paper in good faith: the Continuous Deflation construction is a plausible variational method, the achieved average overlap with the adiabatic path (~5×10⁻⁴) is a genuine improvement over projected 2QP states, and the ¹⁶O and ²⁴⁰Pu illustrations support the proposed microscopic mechanism. My objection is not a disagreement with nuclear-structure consensus but an internally flagged gap: Sections IV.B.1–IV.B.3 state that the excited-path overlap kernels are not yet regular enough for direct SCIM extraction, that one Hamiltonian kernel deviates by 77% with an impact on inertia, and that the chosen regularization has not been validated. These are exactly the quantities SCIM consumes. The reader's formal weakest assumption (the mixed isospin-constraint strategy) is related but secondary; even if that strategy holds, the kernel-regularization issue remains unresolved. This does not justify rejection because the method may be salvageable with filtering and further validation in Part III, and the paper is honest about its limitations. I therefore leave the CONDITIONAL verdict unchanged.","tokens_in":16455,"tokens_out":9932,"duration_ms":99143,"concrete_test":"Use the Part III dynamical framework to compute the collective inertia (second moment of the Hamiltonian kernel) for the neutron Ω=5/2 path with and without the anomalous region (q̄≈270, |s|>13) included; if the inertia changes by more than about 5%, the 77% deviation is a load-bearing defect rather than a benign tail effect.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that Continuous Deflation states are continuous and regular SCIM building blocks, not merely that they are mutually orthogonal. Section IV.B.2 reports relative Hamiltonian-kernel deviations ΔĤii up to 77% for the neutron Ω=5/2 excitation around q̄≈270 and |s|>13, with an admitted 'non-negligible impact on the dynamics, in particular on the inertia tensor.' Section IV.B.3 documents residual divergences in off-diagonal Hamiltonian kernels (Figs. 25–26) and adopts the overlap prescription of Eq. (18) after noting that 'a more systematic assessment of its accuracy is deferred to future work.' Section IV.B.1 further states that the raw overlap kernels still require Savitzky–Golay filtering in Part III before V_SCIM, D_SCIM, and B_SCIM can be reliably extracted. Because the suitability of these states for SCIM dynamics is exactly the central claim, the unresolved kernel-regularity issue is more load-bearing than the isospin-mixing constraint highlighted by the reader: even if the mixed constraint works perfectly, the dynamical kernels are the actual input to the SCIM equations. The 77% anomaly concerns only one state, but the paper's own text says it affects the inertia tensor, so it cannot be dismissed as a harmless large-|s| artifact.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript presents the \"Continuous Deflation\" method for constructing excited intrinsic states, expressed as HFB vacua, along a fission path, with the aim of providing building blocks for the Schrödinger Collective-Intrinsic Model (SCIM). The authors first argue that conventional 2QP excitations, even with particle-number projection, fail because of particle-number fluctuations and level repulsions. They then construct ten excited paths on top of the asymmetric 240Pu fission path, analyze their quasiparticle content, overlap and Hamiltonian kernel regularity, and study scission-region fragment properties such as chemical potentials, neutron necking, and fragment number distributions. The central claim is that the resulting states provide a sufficiently clear separation from the adiabatic states and satisfy the continuity and regularity requirements of SCIM.","tokens_in":16748,"tokens_out":6642,"duration_ms":56367,"significance":"If fully established, the method would address a recognized difficulty in collective fission modeling, namely the inclusion of pair-breaking excitations in a formalism that is compatible with the GCM/SCIM framework. The paper provides a transparent demonstration of the failures of 2QP excitations, a detailed microscopic characterization of the new excited states, and a systematic comparison of fragment observables. The reported computational cost (about 10 hours for a 700-state path on one core) is useful for practical assessment. However, the central suitability claim is weakened by the manuscript's own admissions about kernel regularity, as detailed in the major comments.","major_comments":[{"comment":"The reported 77% relative deviation in the Hamiltonian kernel for the neutron Ω=5/2 excitation at q̄≈270 and |s|>13, which the authors state has a non-negligible impact on the inertia tensor, is a direct counterexample to the abstract's claim that Continuous Deflation generates 'regular' excited paths. Because the inertia tensor is a central input to the SCIM dynamical equations, this exception cannot be dismissed as a harmless large-|s| artifact; the paper must either resolve the anomaly or explicitly qualify the claim of regularity.","section":"IV.B.2, Fig. 23"},{"comment":"The statement that the overlap kernels still require Savitzky–Golay low-pass filtering in Part III before V_SCIM, D_SCIM, and B_SCIM can be reliably extracted means that the raw kernels are not sufficiently regular for SCIM as constructed. This is an internal admission that contradicts the abstract's characterization of the excited paths as regular. The paper should either demonstrate that the filtering is a benign numerical step whose effect on the dynamics is negligible, or revise the central claim.","section":"IV.B.1"},{"comment":"The overlap prescription, which replaces off-diagonal Hamiltonian kernels by a weighted overlap, is adopted after testing on only two cases, and the authors explicitly defer a systematic accuracy assessment to future work. Since these kernels enter the SCIM generator-coordinate equations, a prescription whose accuracy is unquantified leaves the suitability claim insufficiently supported. A quantitative validation, for example by comparing the corrected kernels with a high-precision evaluation in non-divergent regions, is needed.","section":"IV.B.3, Eq. (18)"},{"comment":"The mixed constraint strategy, which imposes orthogonality in one isospin subspace and constrains the complementary-isospin overlap to unity, is justified by the assumed uniformity of the neutron-to-proton ratio and is only illustrated for one neutron excitation (Fig. 7). The paper should show, for all ten excited paths and in particular for the proton excitations, that the multipole moments track the adiabatic path; otherwise the existence of the shared collective coordinate required by SCIM is not guaranteed.","section":"III.B"},{"comment":"The claim of a 'sufficiently clear separation' between adiabatic and excited states is based on average overlaps of about 5×10^-4, but individual overlaps reach about 10^-2 for the Ω=1/2, 3/2, and 5/2 excitations. The paper provides no quantitative criterion for how small these overlaps must be for SCIM to avoid double counting; without such a criterion, the assertion is not fully supported.","section":"III.B"}],"minor_comments":[{"comment":"Typo: 'Extensions of the algorithm are planed' should read 'planned'.","section":"III.B"},{"comment":"Typo: 'we detail le behavior' should read 'we detail the behavior'.","section":"V"},{"comment":"The notation δs≠0 and δs=0 in Eqs. (19) and (20) is ambiguous; please specify that these are Kronecker deltas on the discretized relative coordinate.","section":"IV.B.3, Eqs. (19)-(20)"},{"comment":"The definitions of σ(2) and σ(4) depend on quasiparticle operators ξ+ and ξ̄+, but the relationship between the HFB vacuum of the excited state and the quasiparticle vacuum of the adiabatic state is not explicitly stated; a brief sentence would improve reproducibility.","section":"IV.A.1, Eqs. (10)-(11)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is part of a trilogy, and several key validations (the filtering procedure, the dynamical impact of the 77% kernel anomaly, and the accuracy of the overlap prescription) are deferred to Part III. While a series structure is legitimate, the present paper's central claim of constructing SCIM-ready states should be self-contained enough for a reader to assess. The anomalies documented in Sections IV.B.2 and IV.B.3 should be addressed directly rather than only deferred."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Continuous Deflation is a genuine step forward for the SCIM program, and the paper is admirably honest about where the validation stops. The excited paths are continuous, orthogonal to the adiabatic reference, and microscopically well-characterized; but \"suitable SCIM building blocks\" is demonstrated in the orthogonality sense, not yet in the dynamical-kernel sense, and the paper says so itself.\n\nThe strongest part is the demolition of the obvious alternatives. The 2QP and projected-2QP cases are documented carefully: particle-number drift, loss of orthogonality after PAV, and level repulsion all genuinely break the shared-collective-coordinate requirement. That justifies the detour into constrained variational states. The Continuous Deflation construction itself is clean - fixed consecutive overlap x0, orthogonality in a single (tau, Omega) subspace, mixed isospin constraint to track the shape - and it works on a realistic nucleus: ten excited paths, average adiabatic-excited overlap around 5e-4, smooth Q20/Q30/Q40 evolution. The 16O example is a nice microscopic illustration. The fragment-property analysis near scission is careful, and I credit the authors for not fitting anything to data; the empirical relation (Eq. 15) is observed, not imposed, so the circularity burden stays low.\n\nThe soft spot is exactly where the stress-test note puts it. Section IV.B says the raw overlap kernels still need Savitzky-Golay filtering before V, D, B can be extracted, and the neutron Omega=5/2 path shows up to 77% relative deviation in the Hamiltonian kernel with admitted non-negligible impact on the inertia tensor. These are acknowledged limitations, not hidden ones, but together with the overlap prescription (Eq. 18) whose accuracy is deferred to future work, they mean \"SCIM-ready\" is a promise for Part III, not a result established here. The mixed N/Z-ratio assumption is plausible but untested beyond this one nucleus, and no code or data are released; those are minor by comparison.\n\nThis is a methods paper for fission and GCM/SCIM practitioners, and it deserves a serious referee. I would send it to review, and I would review Parts I-III as a set, with Part III required to show that the filtered kernels give stable dynamics. The \"SCIM-ready\" language in the central claim should be softened until that lands.","headline":"Continuous Deflation is a genuine methodological advance honestly presented, but 'SCIM-ready' remains a promise for Part III: the paper's own kernels need smoothing and one state shows a 77% Hamiltonian-kernel deviation affecting the inertia tensor.","tokens_in":17282,"tokens_out":4935,"would_cite":true,"duration_ms":41421,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Continuous Deflation gives the SCIM excited paths that replace failing two-quasiparticle states.","keywords":["nuclear fission","Schrodinger Collective Intrinsic Model","Continuous Deflation","HFB excited states","two-quasiparticle excitations","240Pu","particle-number projection","fragment distributions"],"falsifier":"Run the same Continuous Deflation construction in a nucleus with a strongly non-uniform neutron-to-proton ratio and check whether the quadrupole, octupole, and hexadecapole moments of the excited path stay locked to the adiabatic ones; if they drift, the mixed constraint strategy fails and the shared collective coordinate is lost.","tokens_in":16267,"feed_emoji":"⚛️","tokens_out":10939,"duration_ms":93229,"temperature":0.7,"pith_summary":"Standard two-quasiparticle (2QP) excitations, the usual way to put intrinsic excitations into the Schrödinger Collective Intrinsic Model (SCIM), fail for fission: their average particle number drifts along the deformation path, particle-number projection smooths their energies but destroys orthogonality to the adiabatic reference, and level repulsions make the excitation's identity ambiguous. This paper introduces a third protocol, Continuous Deflation, that instead builds excited states as Hartree-Fock-Bogoliubov (HFB) vacua by minimizing energy under orthogonality and continuity overlap constraints. Applied along the asymmetric fission path of $^{240}$Pu, it generates ten continuous excited paths with an average overlap of about $5\\times10^{-4}$ with the adiabatic reference, a separation the authors take as sufficient to avoid double counting in SCIM dynamics. The paper's point is that a microscopic, pair-breaking description of fission can be carried by these deflated variational states rather than by quasiparticle configurations.","feed_headline":"Ten continuous excited paths now built for 240Pu fission","feed_subtitle":"Continuous Deflation keeps excited intrinsic states nearly orthogonal and regular enough for SCIM dynamics.","key_machinery":"The central object is the Continuous Deflation algorithm, an iterative constrained HFB minimization. It augments the energy functional with orthogonality penalty terms and two constraints: a vanishing overlap between the excited state and the adiabatic reference in a selected $(\\tau,\\Omega)$ subspace, and a fixed overlap $x_0=0.995$ between consecutive excited states so that the excited path shares the adiabatic path's collective coordinate. A mixed constraint strategy imposes orthogonality in one isospin subspace while constraining the complementary isospin overlap to unity, which indirectly locks the excited state's shape to the adiabatic deformation. This machinery produces ten continuous paths whose overlaps with the adiabatic reference average about $5\\times10^{-4}$.","core_discovery":"The central claim is that Continuous Deflation provides the class of excited intrinsic states the SCIM framework needs: continuous, regular HFB vacua that stay nearly orthogonal to the adiabatic path while preserving collective deformation. The paper first argues that 2QP states cannot do this job, even after particle-number projection, because projection leaves a large, oscillating overlap with the adiabatic state and because avoided crossings reshuffle quasiparticle content. It then constructs ten deflated paths for $^{240}$Pu, one per $(\\tau,\\Omega)$ block with $\\Omega$ from $1/2$ to $9/2$, seeded at the saddle point and propagated through scission, enforcing a fixed overlap $x_0=0.995$ between neighboring states. The resulting excited states are dominated by low-order quasiparticle content, show kernel regularity comparable to the adiabatic set, and yield fragment distributions that are broader than the adiabatic ones, with reduced proton odd-even staggering.","pith_inferences":["Inference: the same mixed-constraint construction could be stress-tested in a very neutron-rich isotope; this would reveal whether the uniform neutron-to-proton ratio assumption is a general basis for the method or a $^{240}$Pu-specific convenience.","Inference: the empirical lower bound $\\sigma^{(4)} \\ge \\sqrt{\\sigma^{(2)}(1-\\sigma^{(2)})}$ reported here may be a structural identity of deflated HFB vacua; testing it on a second nucleus would show whether it is a useful invariant or a numerical coincidence.","Inference: the division of excitations into neck-coupled and pre-fragment-localized classes suggests a practical selection rule for dynamics: states with stable $\\sigma^{(2)}$ and $\\sigma^{(4)}$ through scission may be the ones to retain in reduced dynamical models.","Inference: one could use the fragment particle-number distributions of the excited paths as direct inputs to a statistical scission model, turning the observed broadening into a quantitative prediction for measured yield widths."],"forward_implications":["The ten $^{240}$Pu excited paths are ready to serve as SCIM building blocks, adding pair-breaking intrinsic excitations to fission dynamics without double counting the adiabatic state.","Fragment neutron distributions from the excited paths are broader than the adiabatic TDGCM ones and carry odd components, correcting the known overly narrow adiabatic yields.","Proton variational excitations suppress the adiabatic odd-even staggering in charge yields, bringing calculated fragment distributions closer to experimental charge yields.","Neutron variational excitations systematically delay fragment separation near scission, which is expected to affect the predicted total kinetic energy and pre-scission neutron emission.","The adopted overlap prescription for singular Hamiltonian kernels needs only diagonal matrix elements, lowering the cost of multi-excitation SCIM calculations."],"supporting_citations":[{"why":"Defines the adiabatic $^{240}$Pu path and the continuity, regularity, and overlap-kernel requirements the new method must satisfy.","marker":"[1]"},{"why":"Introduces the Link and Drop overlap-constraint protocols that Continuous Deflation complements.","marker":"[4]"},{"why":"Supplies the numerical implementation details for overlap evaluation and basis handling along the path.","marker":"[5]"},{"why":"Brings the original SCIM 2QP excited-state construction that this paper shows is unsuitable.","marker":"[6]"},{"why":"Provides the particle-number projection formalism whose loss of orthogonality motivates the deflation construction.","marker":"[7]"},{"why":"Supplies the regularization scheme for vanishing Hamiltonian kernel denominators that the overlap prescription adapts.","marker":"[11]"},{"why":"Provides the particle-number projection technique used to compute fragment particle-number distributions.","marker":"[13]"},{"why":"Supplies experimental neutron yields used to compare the computed fragment distributions.","marker":"[14]"}],"fun_headline_variants":["Continuous Deflation builds 10 excited fission paths for 240Pu","New method yields continuous excited states for 240Pu fission","Overcoming 2QP limits: Continuous Deflation for fission paths","Ten regular excited paths in 240Pu via Continuous Deflation","Continuous Deflation enables 240Pu excited fission paths"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method banks on the assumption that the excited state's shape will follow the adiabatic path if the unconstrained proton/neutron part is pinned to match the reference state, an indirect shortcut that only works because neutrons and protons are distributed fairly uniformly relative to each other in nuclei.","fun_headline_variants_meta":{"raw":{"variants":["Continuous Deflation builds 10 excited fission paths for 240Pu","New method yields continuous excited states for 240Pu fission","Overcoming 2QP limits: Continuous Deflation for fission paths","Ten regular excited paths in 240Pu via Continuous Deflation","Continuous Deflation enables 240Pu excited fission paths"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000395,"raw_usage":{"total_tokens":2084,"prompt_tokens":969,"completion_tokens":1115,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":585,"completion_tokens_details":{"reasoning_tokens":1030}},"tokens_in":585,"tokens_out":1115,"duration_ms":7013,"temperature":1.0,"reasoning_tokens":1030,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:13:49.009367+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same Continuous Deflation construction in a nucleus with a strongly non-uniform neutron-to-proton ratio and check whether the quadrupole, octupole, and hexadecapole moments of the excited path stay locked to the adiabatic ones; if they drift, the mixed constraint strategy fails and the shared collective coordinate is lost.","supporting_citations":[{"cited_title":"Deflation","cited_arxiv_id":null,"evidence_quote":"Defines the adiabatic $^{240}$Pu path and the continuity, regularity, and overlap-kernel requirements the new method must satisfy."},{"cited_title":"Continuous Deflation","cited_arxiv_id":null,"evidence_quote":"Introduces the Link and Drop overlap-constraint protocols that Continuous Deflation complements."},{"cited_title":"Continuous Deflation","cited_arxiv_id":null,"evidence_quote":"Supplies the numerical implementation details for overlap evaluation and basis handling along the path."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Brings the original SCIM 2QP excited-state construction that this paper shows is unsuitable."},{"cited_title":"This choice is motivated by the fact that the relevant property for dynamical applications is ultimately the regularity of the ratio between the Hamiltonian and overlap kernels","cited_arxiv_id":null,"evidence_quote":"Provides the particle-number projection formalism whose loss of orthogonality motivates the deflation construction."},{"cited_title":"Bernard, H","cited_arxiv_id":null,"evidence_quote":"Supplies experimental neutron yields used to compare the computed fragment distributions."}],"review_version":1}