arXiv subjects

Jin Lei

Publications and source records attributed to Jin Lei.

At least 19 recordsLinked to original sources

arXiv2026

FUSION: a skill-based research agent for publicly obtainable nuclear-physics codes

Running an unfamiliar nuclear-physics code is rarely difficult because of the physics alone. One must find and build the program, learn its input conventions, and decide whether a plausible output is actually correct. A general-purpose coding agent helps with the first two tasks but may make the last one harder: it can write an input file that runs with the wrong physical convention. FUSION addresses this problem with code-specific skills. A skill obtains the code from its public source, starts from a verified input, runs and parses the calculation, records known failure modes, and must reproduce a stated benchmark to a stated tolerance before reporting a result. The current release covers twenty codes, spanning optical models and reactions, nuclear structure, fission and statistical models, astrophysics and R-matrix analysis, and heavy-ion transport. It also includes an offline, searchable collection of 61 167 pages derived from the nucl-th literature. User notes and credentials remain outside the public repository. FUSION is available under the MIT license at https://github.com/jinleiphys/FUSION; documentation is at https://vibeinscience.com. Here I describe the design, the checks behind the current release, and one complete calculation from input to comparison with measured data.

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arXiv2026

Integrating Out, Twice:The Open-System Case That Neural-Network Ensemble Theory Is Missing

Averaging a neural network over its random parameters and marginalizing a Gaussian sector are the same operation, the Schur complement of the eliminated block, and when that block is closed it returns a covariance and its inverse. That is all a network ensemble produces, the closed case. The open case is missing, and nuclear reaction theory has it worked out. Projecting a scattering problem onto a chosen set of channels, with the rest carrying probability irreversibly to a continuum, leaves a non-Hermitian effective generator that conserves and itemizes exactly what it loses: the nuclear optical model and its generalized optical theorem. I set the two cases side by side using only the moments of a distribution, the algebra of Gaussians, and block inversion, no field theory, and give the closed-case dictionary in full: the neural tangent kernel is the Fisher sensitivity kernel, the infinite-width Gaussian limit is the Gaussian-process emulator, and the lazy-to-feature transition is the validity boundary of a reduced-basis emulator. I then test the open export on a truncated attention map, a token-level transfer operator, and a sparse expert router, and report a mostly negative result. The conserved flux ledger ports wherever openness is genuinely present, but its distinctive content is absent, an artifact of the chosen partition, or pinned near a floor by the training objective, and the operationally useful uncertainty turns out to be epistemic, living in the closed half of the correspondence, not the open one. The negative has a structural reason this note makes precise: the open case needs an eliminated sector with a continuous spectrum and wave-like, not relaxational, dynamics, which mainstream learning's finite or dissipative objects do not supply. This is a note, not a result; its main finding is that negative one, and its value is the map that locates it.

cs.LG↗

arXiv2026

High-Dimensional Bayesian Calibration of Expensive Nuclear Models with Differentiable Emulation

Full Bayesian calibration of expensive nuclear models has been blocked not by the cost of any single solve, but by the absence of exact likelihood gradients in legacy parameter-dependent operators, which forces gradient-free samplers to spend $\mathcal{O}(10^5)$ evaluations exploring high-dimensional correlated posteriors. I introduce DREAM, a differentiable calibration strategy in which the parameter-dependent operator is sampled offline by any legacy code, compressed by singular value decomposition, and reconstructed online in a differentiable framework so that automatic differentiation delivers exact likelihood gradients through the full forward solve at the cost of one additional evaluation per Hamiltonian Monte Carlo step. The construction is operator-level and depends only on smooth, compressible parameter dependence; the underlying physics solver is treated as a black box. As a representative demonstration, DREAM is applied to a continuum-discretized coupled-channels (CDCC) analysis of $d$+$^{58}$Ni elastic scattering at $20$~MeV with eighteen optical-potential parameters, for which No-U-Turn Sampling converges on a single GPU in under ten minutes from a cold start with zero divergent transitions, yielding a full Bayesian posterior for a breakup reaction. The mean emulator error is more than an order of magnitude below the inferred model discrepancy, so the posterior is set by the reaction model rather than the surrogate. Treating the Koning-Delaroche systematics as an informative prior, the data update the well-determined parameter combinations, raising the mean deuteron surface absorption about $36\%$ above the Koning-Delaroche value, while the under-determined directions remain at the prior; this is a representative payoff that the multi-energy datasets DREAM is designed to accommodate can sharpen into a full physics interpretation.

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arXiv2026

Coulomb bridge mechanism for peripheral polarization of weakly bound projectiles

We identify the matrix elements that carry peripheral polarization of weakly bound projectiles through the Feshbach dynamical polarization potential (DPP) within the continuum-discretized coupled-channels (CDCC) framework. Splitting the two P-Q bridge couplings into nuclear and Coulomb parts, while keeping a single Q-space propagator common to every term, decomposes the DPP into a nuclear, a Coulomb, and an interference component, $\Delta U_{\rm DPP}=\Delta U_N+\Delta U_C+\Delta U_{NC}$. Applied to $d+{}^{58}$Ni, ${}^{6}$Li$+{}^{208}$Pb, ${}^{11}$Be$+{}^{64}$Zn, and ${}^{8}$B$+{}^{64}$Zn, the decomposition reveals a controlled hierarchy: a nuclear bridge in the light system, a mixed bridge with strong destructive interference in the heavy stable case, and a Coulomb-dominated bridge in both halo systems, with the proton halo showing constructive nuclear-Coulomb interference. For the halo reactions, peripheral partial waves ($L\gtrsim 35$) satisfy $\sigma_R^L\simeq\sigma_{\rm DPP}^L\simeq\sigma_{\rm BU}^L$, with the high-$L$ DPP tail dominated by $\sigma_C^L$. Two diagnostic calculations isolate the responsible matrix elements: removing the off-diagonal Coulomb propagation inside Q leaves the pattern essentially intact, whereas removing the Coulomb part of the P-Q bridge collapses both DPP-induced absorption and breakup. The peripheral polarization of halo reactions is therefore a Coulomb-bridge effect, and the high-$L$ elastic-breakup yield serves as its observable signature.

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arXiv2026

Self-consistent spectral framework for inclusive nonelastic breakup: The Trojan-horse method as its sub-Coulomb resonant limit

At the keV-scale energies of stellar nucleosynthesis, the resonant charged-particle reactions addressed by the Trojan-horse method (THM) proceed through isolated near-threshold resonances, so the low-energy cross section and the resonance strength carry the same information. The standard THM working formula is used there as a fixed extraction prescription, without a controlled reduction from the inclusive nonelastic breakup parent that would identify what it sets aside. I derive the sub-Coulomb resonant THM extraction directly from the Ichimura-Austern-Vincent inclusive nonelastic breakup cross section. A diagonal isolated-pole spectral ansatz for the absorptive participant-target potential, with four explicit validity conditions, reduces the inclusive cross section in the isolated-resonance limit to a per-pole distorted-wave Born approximation cross section on the resonance state, retaining full distortions and the postform interaction and weighted by the channel branching ratio; this is the operational quantity for resonance-strength extraction. The same one-level total-width profile follows independently from the postform transfer amplitude through the exact final states, so the extraction is route independent; a three-layer width analysis fixes its absorptive strength as half the nonelastic decay width, resolving the width and sign ambiguities of the literature. The standard factorized THM formula then follows under three dynamical approximations, plane waves, on-shell binary amplitude, and remnant neglect, together with a zero-range simplification of the projectile vertex, making explicit what it sets aside: the partial-wave coherence and the postform remnant.

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arXiv2026

Inclusive breakup of three-body projectiles: A unified four-body framework for pair-detected and single-particle observables

Inclusive breakup of three-body projectiles $a=i+j+k$ on a target $A$ admits two distinct inclusive observables: detection of a correlated pair $b=(ij)$ with $k+A$ unresolved, and detection of a single particle $i$ with $jk+A$ unresolved. A four-body DWBA sum-rule framework is derived for both channels from a common Hamiltonian. For the pair-detected channel, the unresolved propagator remains the two-body $k+A$ Green function and all three-body projectile effects enter through a pair-projected source built from $\Phi_a$; a reference pair-target optical interaction splits this source into a target-elastic reference part and an explicit pair-target coupling part, yielding a state-resolved semi-inclusive coincidence observable and an amplitude-level diagnostic of the two-body cluster approximation. For the single-particle channel, the unresolved propagator is the three-body $jk+A$ resolvent, whose reference-channel Feshbach reduction reproduces the Carlson-Frederico-Hussein (CFH) absorptive kernel $W_j+W_k+W_{3B}$; the additional source $V_{iA}-U_{iA}$ drives target excitations, with its direct $g_Q$ component yielding target-excited CFH-like kernels under a diagonal-intermediate-states approximation. Prior forms are derived for both partitions, with reduced post-prior identities at the single-channel level (pair-detected) and at the CFH-optical level (single-particle). For $^{6}$Li$=\alpha+n+p$, the explicit deuteron-target coupling has an E1/E2/monopole tidal structure evaluated on the full three-body wave function. The framework is validated by recovery of the two-body IAV, CFH, and detected-cluster limits, and separates exact DWBA identities from later optical and diagonal-target approximations.

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arXiv2026

Inclusive breakup reactions with non-spectator fragments: Generalization of the IAV sum rules

The Ichimura-Austern-Vincent (IAV) sum rule formalism for inclusive breakup reactions $a + A \to b + \mathrm{anything}$ treats the detected fragment $b$ as a spectator by replacing its interaction with the target by an optical potential. This assumption becomes questionable when $b$ is a loosely bound composite particle such as a deuteron. I derive a generalization that removes the spectator approximation and retains $b$'s internal degrees of freedom, providing state-resolved inclusive cross sections. Within the DWBA, all non-spectator effects enter through the source function via the operator $V_{bA} - U_{bA}$. The exact sum rule involves the full $x + A$ resolvent $(E_{x,0}^+ - H_{xA})^{-1}$, while a single-channel IAV-like expression is recovered only when the explicit target dependence of $V_{bA}$ is neglected; post-prior equivalence is preserved in both cases. A key conceptual finding is that the standard IAV result for structureless $b$ corresponds, under closure, to the \emph{total} inclusive cross section summed over all of $b$'s internal states, rather than the cross section for $b$ in a specific state. An operator-level estimate for $b = d$ on ${}^{208}\mathrm{Pb}$ shows that the non-spectator correction is not a small perturbation at the nuclear surface. The present work is purely formal: it establishes the theoretical framework and identifies the relevant operators, while quantitative assessment of the cross-section impact awaits a full numerical evaluation of the source integrals.

nucl-th↗

arXiv2026

Channel couplings redirect absorbed flux from peripheral loss to fusion in weakly bound nuclear reactions

In reactions of weakly bound nuclei, the absorption cross section mixes two physically distinct contributions: inner capture associated with compound-nucleus formation, and peripheral losses from breakup, transfer, and other direct reactions. Within a framework that combines an ingoing-wave boundary condition (IWBC) at an inner radius with a complex potential in the external region, we derive the exact flux identity $\sigma_{\rm abs}=\sigma_{\rm fusion}+\sigma_W$ from the radial continuity equation. The resulting partition is exact within the adopted CC/CDCC model space and provides a practical diagnostic of where absorbed flux is removed. Applied to $^6$Li+$^{209}$Bi, the analysis reveals that channel couplings qualitatively reorganize the absorbed flux: the dominant absorption mechanism shifts from peripheral loss at sub-barrier energies to inner capture above the barrier, whereas the single-channel baseline remains peripheral-loss dominated throughout. The resulting IWBC-defined inner-capture cross section tracks the measured complete-fusion excitation function with only a modest dependence on the chosen boundary radius. Together with the exact identity $\sigma_{\rm abs}=\sigma_{\rm fusion}+\sigma_W$, this agreement supports interpreting the peripheral term $\sigma_W$ as a major spatial contributor to the well-known CF suppression in weakly bound systems.

nucl-th↗

arXiv2026

Exact construction and uniqueness of the coupled-channel Green's function

We present a rigorous construction and uniqueness proof of the matrix Green's function for coupled radial Schrodinger equations with symmetric coupling potentials. The Green's matrix $G(R,R')$ is built from two fundamental sets of $N$ linearly independent solutions, regular and outgoing, of the coupled radial equations. We prove that the associated Wronskian matrix is diagonal with elements $W_n = -k_n$ and independent of the radial coordinate, and demonstrate through the symplectic structure of the $2N$-dimensional phase space that the resulting construction is the unique Green's matrix satisfying the defining equation with correct boundary conditions, continuity at the source point, and the prescribed derivative discontinuity. The construction applies to any system of coupled radial Schrodinger equations with symmetric coupling potentials and open channels, including coupled-channels problems arising in nuclear, atomic, and molecular scattering. As an illustrative application, we show how the Green's matrix enters the nonlocal dynamical polarization potential within the continuum-discretized coupled-channels framework, where retaining the off-diagonal elements captures multistep excitation pathways beyond the weak-coupling approximation.

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arXiv2026

Assessing continuum channel importance in continuum-discretized coupled-channels via dynamic polarization potential decomposition

A recurring question in continuum-discretized coupled-channels calculations is which continuum channels carry the breakup coupling, both to interpret the reaction and to decide which channels a model space can safely omit. The standard answer is bin deletion: remove a channel, re-solve the coupled equations, and read the change in the elastic $S$ matrix. We show that this cannot isolate an individual channel's contribution. Deleting a channel forces the surviving model space to reorganize, with the neighboring bins rerouting through the off-diagonal Green's function, so the recorded change mixes the channel's own effect with the readjustment of all the others. Working instead from the channel-resolved Feshbach dynamic polarization potential (DPP), whose full-coupling Green's function is a fixed reference shared by every channel, we define an exclusion that removes one channel while holding that reference fixed, returning its contribution to the intact system. The two operations disagree on which continuum bins matter most, for $d$+$^{58}$Ni at 21.6 MeV even sending the intrinsically leading bin to last place under deletion. The DPP further separates each channel's action into a direct path, virtual excitation and return, and a bridge path, relayed through neighboring bins, a split deletion cannot make; it shows the bins act on the elastic channel mainly as bridges, robustly across angular momentum, and that it is this bridge coupling that reorganizes under deletion. A deletion-based channel importance is therefore best read as the truncated calculation's sensitivity to a channel's removal, not as the channel's intrinsic coupling strength.

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arXiv2026

Dynamical Origin of Spectroscopic Quenching in Knockout Reactions

Nucleon-removal reactions are a primary tool for extracting single-particle structure of rare isotopes, yet the ratio $R_s=\sigma_{\exp}/\sigma_{\mathrm{th}}$ of measured to theoretical cross sections drops systematically below unity for deeply bound nucleons. I derive the exact effective three-body Hamiltonian for composite-projectile reactions using a sequential double Feshbach projection and show that the standard additive model misses two induced interactions: a non-additive term from virtual target excitations and a polarization potential from excluded projectile configurations. Their omission overestimates the stripping cross section, producing apparent quenching distinct from genuine nuclear-structure correlations. This mechanism offers a dynamical origin for the strong separation-energy dependence of the quenching ratio, a feature unique to knockout analyses. Existing four-body CDCC calculations for $^{6}$Li validate the framework: the proper Feshbach reference reproduces elastic scattering data, while a phenomenological optical potential double counts the breakup absorption and fails.

nucl-th↗

arXiv2026

Exterior complex scaling enables physics-informed neural networks for quantum scattering

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving differential equations, yet their application to nuclear scattering has been hindered by the oscillatory, non-decaying nature of scattering wave functions. In this work, I demonstrate that exterior complex scaling (ECS) transforms scattering boundary conditions into exponentially decaying waves suitable for neural network solutions, enabling PINNs to solve nuclear reaction problems for the first time. I develop a driven-equation formulation where the source term is confined to the real axis, avoiding the need to analytically continue nuclear potentials into the complex plane. The method is validated on nucleon-nucleus scattering (n+$^{40}$Ca at $E_{\text{lab}}=20$~MeV) with 21 partial waves, achieving phase shift accuracy of $\Delta\delta \lesssim 0.1^\circ$ for the strongly absorbed channels ($\ell \leq 4$) and $\Delta\delta \leq 0.60^\circ$ for all channels up to $\ell = 10$, when compared to conventional solvers. I further demonstrate the approach on heavy-ion scattering ($^6$Li+$^{208}$Pb at 40~MeV) with 41 partial waves and strong Coulomb effects, where an auto-adaptive anchor warm-down for weak-source channels yields a mean S-matrix accuracy of $|\Delta|S_\ell|| \approx 3 \times 10^{-3}$ across the full angular momentum range, including the absorption-to-transparency transition region. This work establishes the foundation for extending PINNs to inverse problems where end-to-end differentiability enables direct fitting of optical potential parameters, coupled-channel reactions, and few-body scattering where traditional grid methods face exponential scaling.

nucl-th↗

arXiv2026

Coherent Absorption Dynamics: The Dual Role of Off-Diagonal Couplings in Weakly Bound Nuclei

Disentangling reaction mechanisms in weakly bound nuclei remains a long-standing challenge, complicated by the common practice of treating absorption as an incoherent sum of channel contributions. Within the continuum-discretized coupled-channels (CDCC) framework, we apply the generalized optical theorem [Nucl. Phys. A 842, 48 (2010)] and show that the total absorption cross section, $\sigma_A \propto -\langle\Psi|W|\Psi\rangle$, decomposes as $\sigma_A = \sigma_D + \sigma_B + \sigma_{int}$, where $\sigma_{int}$ is a coherent interference term between channel components. For the systems and complex fragment-target optical potentials considered, $\sigma_{int}$ is negative and comparable in magnitude to the direct absorption terms. The off-diagonal imaginary couplings play a dual role: they redistribute flux among channels and generate $\sigma_{int}$, which is required for flux-balance consistency. In calculations for $d+^{93}$Nb and $^6$Li$+^{59}$Co/$^{208}$Pb, retaining the full non-diagonal coupling matrix nearly doubles the breakup-channel absorption for the heavy target, while reducing the total absorption through $\sigma_{int}$. Neglecting the off-diagonal imaginary couplings $W_{ij}$ ($i \neq j$) is not merely an approximation but leads to a systematically biased physical picture: the total absorption is overestimated while the breakup absorption component is severely underestimated. Experimental analyses that employ incoherent-sum models to extract direct and breakup cross sections from data will inherit this bias. The full coupling matrix is therefore essential for mechanism-resolved cross-section extraction, and we advocate that experimentalists adopt full-coupling CDCC calculations as the standard for consistent interpretation of absorption data in weakly bound systems.

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arXiv2025

Bidirectional Neural Networks for Global Nucleon-Nucleus Optical Model Calculations

Modern nuclear data evaluation increasingly requires not only accurate scattering calculations, but also efficient methods for uncertainty quantification and parameter optimization, tasks that benefit from differentiable solvers amenable to gradient-based algorithms. I present a neural network emulator based on Bidirectional Liquid Neural Networks (BiLNN) that provides a fully differentiable mapping from optical potential parameters to scattering wave functions. The key innovation enabling generalization across the parameter space is the use of phase-space coordinates $\rho = kr$ that normalize the oscillation wavelength regardless of projectile energy, allowing a single network to span 1 to 200~MeV. Trained on Numerov solutions for twelve target nuclei (\nuc{12}{C} to \nuc{208}{Pb}), both protons and neutrons, and partial waves up to $l=30$, the network achieves an overall relative error of 1.2\%. The predicted wave functions yield accurate $S$-matrix elements and elastic scattering cross sections, reproducing diffraction patterns spanning four orders of magnitude. Importantly, the model extrapolates successfully to nuclei not included in training (\nuc{24}{Mg}, \nuc{63}{Cu}, \nuc{184}{W}) with comparable accuracy, demonstrating that it has learned the physics of the optical model rather than memorizing specific targets. The differentiable nature of the trained model opens the door to gradient-based optimization of optical model parameters and efficient uncertainty quantification.

nucl-th↗

arXiv2025

Reduced basis emulator for elastic scattering in continuum-discretized coupled-channels calculations

I develop a reduced basis emulator for continuum-discretized coupled-channel (CDCC) calculations that achieves speedups of $\approx 10^2$ while maintaining sub-percent accuracy. The emulator is constructed using the proper orthogonal decomposition (POD) method applied to snapshots of CDCC solutions computed at sampled points in the optical potential parameter space. The prediction is performed via Galerkin projection onto the reduced basis. I demonstrate the method using deuteron scattering on $^{58}$Ni at 21.6 MeV as a test case, emulating 18 optical potential parameters simultaneously. The emulator reproduces elastic scattering cross sections with errors below 0.1% across a wide parameter range. This development enables efficient uncertainty quantification and Bayesian parameter estimation for nuclear reaction calculations that were previously computationally prohibitive.

nucl-th↗

arXiv2025

HPRMAT: A high-performance R-matrix solver with GPU acceleration for coupled-channel problems in nuclear physics

I present HPRMAT, a self-contained, high-performance R-matrix solver framework for coupled-channel scattering calculations in nuclear physics. It provides the full R-matrix propagation machinery with the same user-supplied-potential interface as standard R-matrix packages, and is additionally a drop-in replacement for the linear algebra routines of Descouvemont's package. It employs direct linear equation solving with optimized libraries instead of traditional matrix inversion, achieving significant performance improvements. The package provides four solver backends: (1) double-precision LU factorization, (2) mixed-precision arithmetic with iterative refinement, (3) a Woodbury formula approach exploiting the kinetic-coupling matrix structure, and (4) GPU acceleration. Benchmark calculations demonstrate that the GPU solver achieves about 15x speedup over the optimized CPU direct solver, and 41x over the legacy inversion-based code, at N=25600. The mixed-precision strategy is particularly effective on consumer GPUs (e.g., NVIDIA RTX 3090/4090), where single-precision throughput exceeds double-precision by a factor of 64:1; by performing the factorization in single precision, with iterative refinement available to recover full double-precision accuracy where needed, HPRMAT overcomes the poor FP64 performance of consumer hardware while retaining the accuracy required for cross-section calculations. This makes large-scale continuum-discretized coupled-channels (CDCC) and coupled-channel calculations accessible to researchers using standard desktop workstations, without requiring expensive data-center GPUs.

physics.comp-ph↗

arXiv2025

Direct Boundary Matching: A Bound-State Technique for Nuclear Scattering with Lagrange-Legendre Functions

I present a direct boundary matching method (DBMM) for solving nuclear scattering problems using Lagrange-Legendre basis functions. This approach belongs to the family of bound-state techniques for the continuum, reformulating scattering problems into a localized, square-integrable ($L^2$) representation. The key feature is the direct incorporation of the outgoing wave boundary condition into the last row of the matrix equation, eliminating the need for Bloch operators and two-step matching procedures required in traditional R-matrix methods. Unlike the complex scaling method that rotates coordinates into the complex plane, DBMM operates entirely in real coordinate space. The formalism is extended to coupled-channel problems, where the wave function decomposition naturally leads to an effective source potential that distinguishes between the entrance channel and other channels. Benchmark calculations for p~+~$^{12}$C scattering demonstrate excellent agreement with the Numerov integration method.

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arXiv2025

Paths to Superheavy Nuclei

This document summarizes the discussions and outcomes of the Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program "The path to Superheavy Isotopes" held in June 2024 at FRIB. Its content is non-exhaustive, reflecting topics chosen and discussed by the participants. The program aimed to assess the current status of theory in superheavy nuclei (SHN) research and identify necessary theoretical developments to guide experimental programs and determine fruitful production mechanisms. This report details the intersection of SHN research with other fields, provides an overview of production mechanisms and theoretical models, discusses future needs in theory and experiment, explores other potential avenues for SHN synthesis, and highlights the importance of building a strong theory community in this area.

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