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Determination of Molecular Structure and Dynamics of Molten Salts by Advanced Neutron and X-ray Scattering Measurements and Computer Modeling

The design and development of fully functional Molten-Salt Reactors (MSR) require detailed knowledge of the molten salt properties in order to understand and predict the salt’s behavior. Fundamental properties of interest include molecular structure, speciation, and dynamics (such as diffusion coefficients) of salt components and dissolved corrosion and fission products. Computer modeling is necessary to predict changes in physical and chemical properties due to irradiation, burning of dissolved fuel, and corrosion. The modeling requires experimental data, and advanced neutron and x-ray scattering and spectroscopy provide the most reliable and direct determination of the structure (Pair-Distribution Functions, PDF), and dynamics of ions in the melt. This project dealt with both fluoride and chloride salts. The PDFs have been measured by a combination of neutron and x-ray diffraction. We utilized the techniques of isotope substitutions, a very powerful tool available for neutron-scattering, to extract the details of the liquid structure. Although similar measurements have been done before, modern advanced neutron and x-ray-scattering techniques allow collecting the data at much higher resolution and in a wider range of temperatures. Importantly, we were among the first to study fluoride salts by neutron scattering. The importance of impurities and their effects on salt properties have become apparent recently and so new methods of salt purification were developed. We took advantage of these developments to produce reliable data, which have been used for computer simulations of both clean salts and those with added fission and corrosion products most relevant for MSRs. Ab initio molecular dynamics simulations have been performed to understand the multi-component liquid solution, in particular solubility of impurities and thermodynamic interactions in relation to the ionic-cluster structure of the fluid. We applied machine learning to regress from the simulation and experimental data in order to develop a fast-acting model that can handle molten salt with an arbitrary (≥ 10) number of chemical elements and be able to predict chemical potential as a function of composition and temperature. This project resulted in a number of experimental and computer-simulation publications, a patent application, and numerous conference presentations (American Physical Society, American Chemical Society, and The Electrochemical Society among others). Multiple students and postdocs participated and collaborated on aspects of this project. This project seeded new collaborations between MIT and other institutions, such as the University of Massachusetts Lowell, the University of Illinois Urbana-Champaign, the University of California Berkeley, and Oak Ridge and Los Alamos National Labs. As such, this project has had a broad and lasting impact beyond its original scientific scope.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Electromagnetic radii of light nuclei from variational Monte Carlo calculations

We present variational Monte Carlo calculations of charge and magnetic radii in 𝐴 ≤ 10 nuclei. The calculations are based on the Norfolk two- and three-nucleon interactions, and associated one- and two-nucleon electromagnetic charge and current operators derived up to next-to-next-to-next-to-leading order in the chiral expansion. The charge and magnetic radii are extracted from the respective form factors. We find that the charge radii are within 5% of the experimental values for the nuclei considered. For the magnetic radii, a comparison is available only with 3 H and 3 ⁢He electron scattering data that are affected by large error bars. We hope that our predictions foster an interest in precisely measuring magnetic radii of heavier systems.

lepton induced nuclear reactions↗

RELAP5-3D validation studies based on the High Temperature Test facility

In the spring and summer of 2019, experiments were conducted at the High Temperature Test Facility (HTTF) that form the basis of an upcoming high-temperature gas-cooled reactor (HTGR) thermal hydraulics (T/H) benchmark. HTTF is an integral effects test facility for HTGR T/H modeling validation. This paper presents RELAP5-3D models of two of those experiments: PG-27, a pressurized conduction cooldown (PCC); and PG-29, a depressurized conduction cooldown (DCC). These models used the RELAP5-3D model of HTTF originally developed by Paul Bayless as a starting point. The sensitivity analysis and uncertainty quantification code, RAVEN was used to perform calibration studies for the steady-state portion of PG-27. Here we developed four PG-27 calibrations based on steady-state conditions. These calibrations all used an effective thermal conductivity equal to 36 % of the measured thermal conductivity, but they differed with respect to the frictional pressure drops and radial conduction models. These models all captured the trends in steady-state temperature distributions and transient temperature behavior well. All four calibrations show room for improvement in predicting the transient temperature rise. The smallest error in temperature rise during the transient was a 21 % underprediction, and the largest was a 48 % underprediction. The errors in transient temperature rise are largely a result of a mismatch in power density between the RELAP5-3D model and the experiment due to the location of active heater rods along the boundary between heat structures in the model. The best of these calibrations was applied to PG-29 to model the DCC. Once again, temperatures during the transient were underpredicted but trends in temperature were captured. The RELAP5-3D model captured trends in the data but could not reproduce measured temperatures exactly. This result is not attributed to deficiencies in the experimental data or to RELAP5–3D itself. Rather, this result likely arises due to the some of the assumptions and decisions made when the RELAP5-3D model was first developed, prior to the execution of HTTF experiments. An agreement in prediction of temperature trends but challenges reproducing HTTF temperatures within measurement uncertainty is consistent with previous analyses of HTTF in the literature. Future RELAP5-3D validation activities centered around HTTF may be able to provide greater insight into the code’s capabilities for HTGR modeling with a more finely nodalized model.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Small Reactors in Microgrids: Technology Modeling and Selection (Net-Zero Microgrid Program Project Report)

This report demonstrates the capabilities of the net-zero microgrid (NZM) Xendee platform for modeling an SR module with electricity, heat extraction and thermal storage in microgrids configurations. The model effectively captures the most important technical and economic considerations for SR technology specific analysis: cost and operational characteristics of SR technology and financial costs and incentives. The model can analyze multiple scenarios to establish metrics for cost-competitive and zero-carbon microgrids connected to the grid or completely isolated. The model is fully integrated within the Xendee platform for modeling and analysis of clean energy microgrids with storage and generation from renewable energy sources. The model captures the capabilities, constraints, and nuances of SR by incorporating parameters related to plant economics, design efficiency and performance, plant operation and component and fuel lifespan. The cost and operational parameters modeled in the SR module are specific to the technology selected for integration in the microgrid. Cost parameters recognize advanced nuclear technology for modular production and installation based on economies of scale from factory manufacture and related commissioning, and cost reduction through technology maturation—first-of-a-kind (FOAK) and nth-of-a-Kind (NOAK). The cost parameters include installation, operations and maintenance (O&M), fuel refueling cycle, and reactor life. Installation cost reflects economies of scale due to unit sizing at scale and colocation. O&M economies of scale for both fixed- and variable-cost fuel life-cycle costs are incurred at every refueling interval, with separate front- and back-end fuel costs, as well as waste-handling and disposition costs. This report investigates key characteristics of different SR technologies suitable for microgrid applications, including design principles, sizing, coolant properties, temperature ratings, fuel structures, and life-cycle considerations. This also includes fuel technologies applicable to these SR systems, alongside strategies for nuclear-waste and spent-fuel management and approaches to address safety, security, and proliferation challenges. Four primary groups of SR technologies are examined: water-cooled, liquid-metal-cooled, high-temperature gas-cooled, and molten-salt-cooled systems. In this report, an initial guideline for technology selection is established, aligning the characteristics of the technologies with the requirements of microgrids. The selection of technology in a microgrid is influenced by various factors, including financial capacity, location and accessibility, demand type and characteristics, reliability and resilience requirements, area constraints, and the lifespan of the microgrid. The types of electrical and non-electrical applications within the microgrid also play a significant role in technology selection. The characteristics of SRs, such as their smaller size, modularity, transportability, long refueling interval, improved safety features, ability to operate in autonomous or semi-autonomous mode, and provision of high-grade heat, are particularly appealing for microgrids. Furthermore, a list of considerations for implementing SRs in microgrids is outlined. The SR model is created to be continuously improved with the acquisition of actual data on investment and operational costs, experience with supply chains, production at scale, and field deployments. In the near term, performance data on applications in microgrids will become available from lessons learned from laboratory tests, such as those planned for the Microreactor Applications Research Validation and Evaluation Project (MARVEL), led by Idaho National Laboratory (INL). The SR model incorporates scenario data and known SR design specifications, enabling technoeconomic analysis for SR deployment in microgrids. It specifically considers the distinctive attributes of SRs as generators in technoeconomic studies. SRs can be modeled and analyzed with generation from renewable-energy sources, energy storage, and flexible loads over a range of functionality and applications. This offers a comprehensive tool for feasibility studies, scenario development, and sensitivity analysis for “what-if” consideration of any range of assumptions about SRs in microgrids and other aggregations of distributed-energy resources, including virtual power plants.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Neutron occupancies and single-particle energies across the stable tin isotopes

The occupancies and vacancies of the valence neutron orbitals across the stable tin isotopic chain from 112 ≤ A ≤ 124 have been determined. These were inferred from the cross sections of neutron adding and -removing reactions. In each case, the reactions were chosen to have good angular momentum matching for transfer to the low- and high-` orbitals present in this valence space. Here, these new data are compared to older systematic studies. The effective single-neutron energies are determined by combining information from energy centroids determined from the adding and removing reactions. Two of the five orbitals are nearly degenerate, below N = 64, and approximately two MeV more bound than the other three, which are also degenerate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Extended range X-ray pair distribution functions

Here we describe a dual detector system for high-energy X-ray, simultaneous, small and wide-angle X-ray scattering (SAXS and WAXS), designed to extract extended-range pair distribution functions (ER-PDF) for disordered materials. The hardware and software provides continuous reciprocal space coverage over atomic to nanometer length-scales. Details of the varying resolution, splicing of data and normalization on an absolute scale are outlined. In addition, the combination of SAXS and WAXS theory is considered with a view to enabling a direct Fourier transformation of the structure factor spanning multiple length-scales into real space. Important distinctions between the ER-PDF and the pair distance distribution function (PDDF) representations are demonstrated. It is shown that when the SAXS intensity in the structure factor, S(Q), is similar to the WAXS intensity, the contributions to the ER-PDF are minimal. However, when the SAXS S(Q) intensities are substantially stronger than the WAXS, the ER-PDF can provide important structural information on the local, intermediate and nanometer length-scales. Notably, the ER-PDF method provides direct information on particle sizes and their density distributions, overcoming the limitations of PDDF analysis for densely packed systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Structure of 43 P and 42 Si in a two-level shape-coexistence model

Exclusive cross sections for the 43 P(-1p) 42 Si reaction to the lowest 0 + and 2 + states, measured at NSCL with GRETINA and the S800, are interpreted in terms of a two-level mixing (collective) model of oblate and prolate co-existing shapes. Here, using the formalism developed for deformed nuclei we calculate the spectroscopic amplitudes and exclusive cross-sections in the strong coupling limit, where for 43 P the schematic wavefunction includes the coupling of the Nilsson [211] 1/2 proton orbit. Good agreement with the experimental data is obtained when the amplitude of the oblate configuration is larger or equal than 80%, suggesting that both nuclei are predominantly oblate, in line with theoretical expectations. Model predictions for excitation energies and electromagnetic observables, that could motivate further studies of both nuclei, are also presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Observation of Exotic 𝐽/𝜓⁢𝜙 Resonant Structure in Diffractive Processes in Proton-Proton Collisions

The first study of 𝐽/𝜓⁢𝜙 production in diffractive processes in proton-proton collisions is presented. The study is based on an LHCb dataset recorded at center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5 fb −1 . The data disfavor a nonresonant 𝐽/𝜓⁢𝜙 production but are consistent with a resonant model including several resonant states observed previously only in 𝐵 + →𝐽/𝜓⁢𝜙⁢𝐾 + decays. The 𝜒 𝑐⁢0⁡ (4500) state is observed with a significance over 6⁢𝜎 and the 𝜒 𝑐⁢1 ⁡(4274) is confirmed with a significance of more than 4⁢𝜎.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Learning Management System User Requirements for the National Nuclear Security Administration's International Nuclear Safeguards Engagement Program

The National Nuclear Security Administration's (NNSA) International Nuclear Safeguards Engagement Program (INSEP) is considering investing in new tools that would allow the program to support its partner states from a distance. At the same time, the program is considering approaches that would allow several organizations, including NNSA, IAEA, national laboratories and contractor staff, to collaborate in the development and maintenance of instructional content. Software systems known as Learning Management Systems (LMSs) might represent a mechanism through which INSEP could accomplish these goals (collaborative development and remote support). To assess the usefulness of an LMS, INSEP has specified its needs for delivering online training and compared those needs to the capability of a range of LMSs. This comparison will allow INSEP to determine whether an LMS would be a useful tool and may set the stage for a "make-buy" decision in the future. The study team concluded that INSEP's content development and delivery needs align well with the capabilities of the leading LMSs on the market today and that that INSEP performance requirements allow for a customized approach using existing training portals that are already available to NNSA. Additional work would be required to specify the desired processes for developing online training and outreach materials, structuring the databases, specifying the data that should be collected, and detailing the desired system reports and documentation.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

Primary track recovery in high-definition gas time projection chambers

Abstract We develop and validate a new algorithm called primary track recovery () that effectively deconvolves known physics and detector effects from nuclear recoil tracks in gas time projection chambers (TPCs) with high-resolution readout. This gives access to the primary track charge, length, and vector direction (helping to resolve the “head-tail” ambiguity). Additionally, provides a measurement of the transverse and longitudinal diffusion widths, which can be used to determine the absolute position of tracks in the drift direction for detector fiducialization. Using simulated helium recoils in an atmospheric pressure TPC with a 70:30 mixture of $$\hbox {He:CO}_2$$ He:CO 2 we compare the performance of to traditional methods for all key track variables. We find that the algorithm reduces reconstruction errors, including those caused by charge integration, for tracks with mean length-to-width ratios 1.4 and above, corresponding to recoil energies of 20 keV and above in the studied TPCs. We show that improves on existing methods for head-tail disambiguation, particularly for highly inclined tracks, and improves the determination of the absolute position of recoils on the drift axis via transverse diffusion. We find that can partially recover charge structure integrated out by the detector in the z direction, but that its determination of energy and length have worse resolution compared to existing methods. We use experimental data to qualitatively verify these findings and discuss implications for future directional detectors at the low-energy frontier.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Mitochondrial Genomes of the United States Distribution of Gray Fox (Urocyon cinereoargenteus) Reveal a Major Phylogeographic Break at the Great Plains Suture Zone

We examined phylogeographic structure in gray fox (Urocyon cinereoargenteus) across the United States to identify the location of secondary contact zone(s) between eastern and western lineages and investigate the possibility of additional cryptic intraspecific divergences. We generated and analyzed complete mitochondrial genome sequence data from 75 samples and partial control region mitochondrial DNA sequences from 378 samples to investigate levels of genetic diversity and structure through population- and individual-based analyses including estimates of divergence (FST and SAMOVA), median joining networks, and phylogenies. We used complete mitochondrial genomes to infer phylogenetic relationships and date divergence times of major lineages of Urocyon in the United States. Despite broad-scale sampling, we did not recover additional major lineages of Urocyon within the United States, but identified a deep east-west split (~0.8 million years) with secondary contact at the Great Plains Suture Zone and confirmed the Channel Island fox (Urocyon littoralis) is nested within U. cinereoargenteus. Genetic diversity declined at northern latitudes in the eastern United States, a pattern concordant with post-glacial recolonization and range expansion. Beyond the east-west divergence, morphologically-based subspecies did not form monophyletic groups, though unique haplotypes were often geographically limited. Gray foxes in the United States displayed a deep, cryptic divergence suggesting taxonomic revision is needed. Secondary contact at a common phylogeographic break, the Great Plains Suture Zone, where environmental variables show a sharp cline, suggests ongoing evolutionary processes may reinforce this divergence. Follow-up study with nuclear markers should investigate whether hybridization is occurring along the suture zone and characterize contemporary population structure to help identify conservation units. Comparative work on other wide-ranging carnivores in the region should test whether similar evolutionary patterns and processes are occurring.

54 ENVIRONMENTAL SCIENCES↗

Long-lived axionlike particles from tau decays

Axionlike particles (ALPs) are well-motivated examples of light, weakly coupled particles in theories beyond the Standard Model. In this work, we study long-lived ALPs coupled exclusively to leptons in the mass range between 2⁢𝑚 𝑒 and 𝑚 𝜏 − 𝑚 𝑒 . For anarchic flavor structure the leptophilic ALP production in tau decays or from ALP-tau bremsstrahlung is enhanced thanks to derivative couplings of the ALP and can surpass production from electron and muon channels, especially for ALPs heavier than 𝑚 𝜇 . Using past data from high-energy fixed-target experiments such as CHARM and BEBC we place new constraints on the ALP decay constant 𝑓 𝑎 , reaching scales as high as 𝒪⁡(10 8 ) GeV in lepton-flavor-violating channels and 𝑓 𝑎 ∼ 𝒪⁡(10 2 ) GeV in lepton-flavor-conserving ones. We also present projections for the event-rate sensitivity of current and future detectors to ALPs produced at the Fermilab Main Injector, the CERN SPS, and in the forward direction of the LHC. We show that SHiP will be sensitive to 𝑓 𝑎 values that are over an order of magnitude above the existing constraints.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Comparison of short-range order in irradiated dysprosium titanates

Abstract The structural response of Dy 2 TiO 5 oxide under swift heavy ion irradiation (2.2 GeV Au ions) was studied over a range of structural length scales utilizing neutron total scattering experiments. Refinement of diffraction data confirms that the long-range orthorhombic structure is susceptible to ion beam-induced amorphization with limited crystalline fraction remaining after irradiation to 8 × 10 12 ions/cm 2 . In contrast, the local atomic arrangement, examined through pair distribution function analysis, shows only subtle changes after irradiation and is still described best by the original orthorhombic structural model. A comparison to Dy 2 Ti 2 O 7 pyrochlore oxide under the same irradiation conditions reveals a different behavior: while the dysprosium titanate pyrochlore is more radiation resistant over the long-range with smaller degree of amorphization as compared to Dy 2 TiO 5 , the former involves more local atomic rearrangements, best described by a pyrochlore-to-weberite-type transformation. These results highlight the importance of short-range and medium-range order analysis for a comprehensive description of radiation behavior.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Ultrafast Molecular Frame Quantum Tomography

Here, we develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH 3 ). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH 3 , we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

74 ATOMIC AND MOLECULAR PHYSICS↗

Providing Experimental Infrastructure for Accelerating Advanced Reactor Demonstrations through the National Reactor Innovation Center

A suite of experimental infrastructure projects has been developed by the National Reactor Innovation Center to accelerate advanced reactor demonstrations and facilitate their development, addressing crucial gaps in data, materials characterization, and modeling. First, the Molten Salt Thermophysical Examination Capability (MSTEC) provides a specialized platform for post-irradiation characterization of molten salt reactor fuel, coolant salts, and structural materials, essential for supporting the design and operation of advanced reactors and future commercial molten salt reactor development and licensing. The Virtual Test Bed (VTB) complements these efforts by leveraging advanced modeling and simulation tools to evaluate reactor performance and safety. Serving as a library of reference models, the VTB offers a database of multiphysics reactor models, facilitating rapid safety evaluations and includes continuous software quality assurance, crucial for accelerating deployment while maintaining reliability. Additionally, the Helium Component Test Facility (HeCTF) addresses the need for high-temperature helium-cooled reactor component testing. As the first-of-its-kind facility in the United States, HeCTF emulates high-temperature gas reactor conditions, reducing time and cost associated with component validation, thereby accelerating reactor development. Finally, In-cell Thermal Creep Frames provide a unique solution for obtaining thermal creep data from irradiated materials, critical for materials qualification and licensing. Developed by the National Reactor Innovation Center, these compact frames enable the examination of previously irradiated materials, overcoming traditional limitations and enhancing the understanding of mechanical properties crucial for reactor development. Collectively, these experimental infrastructure projects form a comprehensive framework aimed at expediting advanced reactor demonstrations, fostering innovation, and ensuring the viability of next-generation nuclear energy solutions.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling support for the development of material surveillance specimens and procedures

This report describes modeling and simulation activities performed at Argonne National Laboratory supporting the development of passively actuated mechanical test articles for material surveillance in Molten Salt Reactors (MSRs). These test articles are a critical technology in formulating material surveillance programs for future MSRs to monitor the degradation in the structural properties of the materials in critical plant components. The main activity described in this report is the development of a method for inferring the amount of mechanical damage a test article has experienced during some duration of exposure to plant thermal and environmental conditions, using only mechanical test data collected from the test articles before and after exposure. The basic approach is to develop a model of the test article, including a description of mechanical degradation through continuum damage mechanics, and then use this model to cast the problem of inferring mechanical degradation in the test article materials into a shooting problem for a set of ordinary differential equations. We can then solve the shooting problem to determine the amount of damage accumulated in the sample. The report also details a few miscellaneous simulation studies completed at Argonne to support the development of the test articles themselves at Idaho National Laboratory.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Production of neutron-rich isotopes for 𝑍 ≥ 98 in the 238 U + 248 Cm reaction

Multinucleon transfer (MNT) reactions in actinide systems are a promising method to synthesize transuranium neutron-rich elements. Appropriate theoretical approaches are needed to understand the mechanisms behind MNT. We employ a microscopic approach to calculate neutron-rich isotope production in the reaction 238 U + 248 Cm system. Here, the stochastic mean-field (SMF) approach is used to calculate the primary cross sections in MNT reactions based on the quasifission and inverse quasifission processes, and a statistical de-excitation model with GEMINI ++ code to calculate the secondary fragment cross sections. The calculated cross sections using SMF and GEMINI ++ explain available experimental results for the 238 U + 248 Cm system at 𝐸 c.m. = 898.7 MeV energy. This shows the effectiveness and applicability of the quantal diffusion approach, based on the SMF theory, in heavy-ion collisions. Production of transuranium neutron-rich elements with a proton number up to 𝑍=101 is obtained with sizable cross sections. Theoretical results calculated for the 𝑍=102–105 region, for which there are no experimental data, show that the cross-section values would be lower than the microbarn level. SMF theory does not contain any adjustable parameters other than the standard parameters of the energy density functional used in the TDHF theory and is an important approach for the microscopic understanding of reaction mechanisms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Measurement of fifth- and sixth-order fluctuations of (net-)proton number in Au + Au collisions from phase II of the beam energy scan program at RHIC

We report high-statistics measurements of fifth- and sixth-order factorial cumulants and cumulant ratios of (net-)proton multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7–27GeV, using data from the STAR experiment collected during the Beam Energy Scan Phase II at RHIC. Protons and antiprotons are identified at midrapidity (|𝑦| < 0.5) with transverse momentum 0.4 < 𝑝 𝑇 < 2.0GeV/𝑐. The proton factorial cumulants 𝜅 4 , 𝜅 5 , and 𝜅 6 increase with order but exhibit no sign alternation within current uncertainties, offering no evidence for a two-component structure in the proton multiplicity distribution, as might be expected near a first-order phase transition. The cumulant ratios 𝐶 5 /𝐶 1 and 𝐶 6 /𝐶 2 fluctuate around zero in collisions at 0–40% centrality. The results are consistent with both the negative predictions from lattice QCD and the positive trends obtained from the ultrarelativistic quantum molecular dynamics (UrQMD) model. At $\sqrt{s_{NN}}$ ≳ 27GeV, the 𝐶 4 /𝐶 2 and 𝐶 5 /𝐶 1 results are compatible with predictions from lattice QCD, functional renormalization group (FRG), and hadron resonance gas (HRG) models, while UrQMD describes the data better at lower energies. Here, these measurements place constraints on baryon number fluctuations and offer valuable insights into the QCD phase structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗