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The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)

This work describes the formalism for estimating thermonuclear reaction rates for astrophysical applications, emphasizing modern statistical approaches such as Monte Carlo sampling and Bayesian models. We discuss related topics including the calculation of resonance energies from nuclear Q values, indirect estimates of particle partial widths, and matching of reaction rates at elevated temperatures to statistical model results. We have evaluated available experimental data on cross sections, resonance energies and strengths, partial widths, lifetimes, spin-parities, and spectroscopic factors. Based on these results, we have estimated numerical values of 78 experimental charged-particle thermonuclear reaction rates for target nuclei in the A = 2–40 mass region, for temperatures ranging from 1 MK to 10 GK. For each reaction, three rate values are provided: low, median, and high, corresponding to the 16th, 50th, and 84th percentiles, respectively, of the cumulative reaction rate probability density distribution. Additionally, we present the factor uncertainty of each rate at each temperature grid point. These results enable users to sample the reaction rate probability density in nucleosynthesis calculations, facilitating uncertainty estimates of nuclidic abundances. The rates presented here refer to their laboratory values. For use in stellar model simulations, these values need to be corrected for the effects of thermal excitations of the interacting nuclei. For each reaction, we include graphs that illustrate the fractional contributions to the overall reaction rate along with the associated uncertainty. These visuals are designed to assist both stellar modelers and nuclear experimentalists by identifying the primary sources of rate uncertain=^texttx);ty at specific stellar temperatures. A graphical comparison with earlier Monte Carlo rates is also provided.

Nuclear astrophysics↗

The Trojan Horse Method: A Nuclear Physics Tool for Astrophysics

The Trojan Horse Method (THM) represents an indirect path to determine the bare nucleus astrophysical S-factor for reactions among charged particles at astrophysical energies. This is achieved by measuring the quasi-free cross section of a suitable three-body process. The method is also suited to study neutron-induced reactions, especially in the case of radioactive ion beams. A comprehensive review of the theoretical as well as experimental features behind the THM is presented here. An overview is given of some recent applications to demonstrate the method's practical use for reactions that have a great impact on selected astrophysical scenarios.

Physics↗

Investigating high-energy proton-induced reactions on spherical nuclei: Implications for the preequilibrium exciton model

A number of accelerator-based isotope production facilities utilize $100-200$ MeV proton beams due to the high production rates enabled by high-intensity beam capabilities and the greater diversity of isotope production brought on by the long range of high-energy protons. However, nuclear reaction modeling at these energies can be challenging because of the interplay between different reaction modes and a lack of existing guiding cross section data. A Tri-lab collaboration has been formed between the Lawrence Berkeley, Los Alamos, and Brookhaven National Laboratories to address these complexities by characterizing charged-particle nuclear reactions relevant to the production of established and novel radioisotopes. In the inaugural collaboration experiments, stacked-targets of niobium foils were irradiated at the Brookhaven Linac Isotope Producer ($E_p=200$ MeV) and the Los Alamos Isotope Production Facility ($E_p=100$ MeV) to measure $^{93}$Nb(p,x) cross sections between $50-200$ MeV. The results were compared with literature data as well as the default calculations of the nuclear model codes TALYS, CoH, EMPIRE, and ALICE. The default code predictions largely failed to reproduce the measurements. Therefore, we developed a standardized procedure, which determines the reaction model parameters that best reproduce the most prominent reaction channels in a physically justifiable manner. Overall, the primary focus of the procedure was to determine the best parameterization for the pre-equilibrium two-component exciton model. This modeling study revealed a trend towards a relative decrease for internal transition rates at intermediate proton energies ($E_p=20-60$ MeV) in the current exciton model as compared to the default values. The results of this work are instrumental for the planning, execution, and analysis essential to isotope production.

43 PARTICLE ACCELERATORS↗

Covariance Testing at BNL [Slides]

This presentation discusses testing implemented in FUDGE & ADVANCE in regard to proper ENDF formatting: STAN, STANEF, CHECKR, FUDGE, NJOY, convert to BOXR format, plotting, endfcovreport.py which is an overview of ENDF library’s covariance contents, and covariance Matrix class implements that are the core of all GNDS covariance. Several checks are performed, including symmetric, real, positive definite, condition # of Eigenvalues, and too big uncertainties. The presentation states that it can fix too big and/or small uncertainties and that it can plot matrices. It states that further testing is recommended by CSEWG but has not yet been implemented and suggests methods such as documentation which needs a human to execute, completeness which is partially complete, and reasonableness which has not been started. The presentation concludes by elaborating on reasonableness and states that only cross section is documented, that similar limits on CP reactions cross sections are needed, that maximum limits are needed too which is tricky since ENDF assumes Normal PDFs, and that there may be other observables.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Estimate of Lorentz force effects on charged particles

Thermonuclear (TN) fusion reaction between deutrons are D + D → T + P D + D → 3 He + n where P is the proton, D is the deuteron, T is the triton, n is the neutron, and 3 He is the helion. They are born with high energies (0.82 MeV for 3 He, 1.01 MeV for T, 3.02 MeV for P, and 2.45 MeV for n). The charged particles slow down due to the drag force (stopping power). While slowing down, the charged particles deposit their energy, which may affect the TN burn characteristics. When magnetic field is present, the velocity of the charged particle would be affected due to the Lorentz force, which can affect the stopping of the charged particle. As a consequence, TN burn characteristics may change, Our purpose is to asses the importance of the Lorentz force in stopping of the charged particle, based on a simple comparison between the Lorentz force and stopping power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Trojan horse method as an indirect approach to study resonant reactions in nuclear astrophysics

The primary goal of the Trojan horse method (THM) is to analyze resonant rearrangement reactions when the density of the resonance levels is low and statistical models cannot be applied. The main difficulty of the analysis is related with the facts that in the final state the THM reaction involves three particles and that the intermediate particle, which is transferred from the Trojan horse particle to the target nucleus to form a resonance state, is virtual. Another difficulty is associated with the Coulomb interaction between the particles, especially, taking into account that the goal of the THM is to study resonant rearrangement reactions at very low energies important for nuclear astrophysics. The exact theory of such reactions with three charged particles is very complicated and is not available. This is why different approximations are used to analyze THM reactions. In this review paper we describe a new approach based on a few-body formalism that provides a solid basis for deriving the THM reaction amplitude taking into account rescattering of the particles in the initial, intermediate and final states of the THM reaction. Since the THM uses a two-step reaction in which the first step is the transfer reaction populating a resonance state, we address the theory of the transfer reactions. The theory is based on the surface-integral approach and R-matrix formalism. We also discuss application of the THM to resonant reactions populating both resonances located on the second energy sheet and subthreshold resonances, which are subthreshold bound states located at negative energies close to thresholds. We consider the application of the THM to determine the astrophysical factors of resonant radiative-capture reactions at energies so low that direct measurements can hardly be performed due to the negligibly small penetrability factor in the entry channel of the reaction. Here, we elucidated the main ideas of the THM and outline necessary conditions to perform the THM experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Dust in magnetised plasmas - Basic theory and some applications

In this paper the theory of charged test particle motion in magnetic fields is reviewed. This theory is then extended to charged dust particles, for which gravity and charge fluctuations play an important role. It is shown that systematic drifts perpendicular to the magnetic field and stochastic transport effects may then have to be considered none of which occur in the case of atomic particles (with the exception of charge exchange reactions). Some applications of charged dust particle transport theory to planetary rings are then briefly discussed.

Northrop, T. G.↗

Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to the Noether procedure. However, the canonical energy-momentum tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure to symmetrize the EMTs, which also renders them gauge symmetric for first-order field theories. High-order electromagnetic field theories appear in the study of gyrokinetic systems for magnetized plasmas and the Podolsky system for the radiation reaction of classical charged particles. For these high-order field theories, gauge-symmetric EMTs are not necessarily symmetric and vice versa. In the present study, we develop a new gauge-symmetrization method for EMTs in high-order electromagnetic field theories. The Noether procedure is carried out using the Faraday tensor $F_{μν}$, instead of the 4-potential $A_{μ}$, to derive a canonical EMT $T^{μν}_{N}$. We show that the gauge-dependent part of $T^{μν}_{N}$ can be removed using the displacement-potential tensor $F^{σμν}$ ≡ $D^{σμ}A^{ν}/4π$, where $D^{σμ}$ is the antisymmetric electric displacement tensor. This method gauge-symmetrizes the EMT without necessarily making it symmetric, which is adequate for applications not involving general relativity. For first-order electromagnetic field theories, such as the standard Maxwell system, $F^{σμν}$ reduces to the familiar BR superpotential $S^{σμν}$, and the method developed can be used as a simpler procedure to calculate $S^{σμν}$ without employing the angular momentum tensor in 4D spacetime. When the electromagnetic system is coupled to classical charged particles, the gauge-symmetrization method for EMTs is shown to be effective as well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Energy Distribution of Electrons in Radiation Induced-Helium Plasmas

Energy distribution of high energy electrons as they slow down and thermalize in a gaseous medium is studied. The energy distribution in the entire energy range from source energies down is studied analytically. A helium medium in which primary electrons are created by the passage of heavy-charged particles from nuclear reactions is emphasized. A radiation-induced plasma is of interest in a variety of applications, such as radiation pumped lasers and gaseous core nuclear reactors.

Lo, R. H.↗

H-2, H-3, He-3 production in solar flares

The production of deuterium, tritium, and helium-3 from nuclear reactions of accelerated charged particles is evaluated with the ambient solar atmosphere. Updated cross sections and kinematics are used, calculations are extended to very low energies (approximates 0.1 MeV/nucleon), and the angular distribution of the secondary particles is calculated. The calculations are compared with data on accelerated isotopes from solar flares. In particular, the August 1972 events are considered for which both He-3 and nuclear gamma rays were observed. An explanation for He-3-rich events is provided in terms of the angular distributions of secondary isotopes, and the flux of 2.2 MeV gamma rays from such flares are also predicted.

Ramaty, R.↗

Atmospheric Physics

The possibility of extending the atmospheric observation from space is discussed. Observations of the earth's limb from GEO at microwave frequencies, global mapping of ozone, charged particle precipitation, photochemical reactions, spectral emissions from the atmosphere, microwave measurements, and radio probing of the atmosphere and ionosphere, which were not feasible prior to the availability of the shuttle because of the antenna limitations, may be readily carried out from the space stations.

Source record↗

Computational chemistry and aeroassisted orbital transfer vehicles

An analysis of the radiative heating phenomena encountered during a typical aeroassisted orbital transfer vehicle (AOTV) trajectory was made to determine the potential impact of computational chemistry on AOTV design technology. Both equilibrium and nonequilibrium radiation mechanisms were considered. This analysis showed that computational chemistry can be used to predict (1) radiative intensity factors and spectroscopic data; (2) the excitation rates of both atoms and molecules; (3) high-temperature reaction rate constants for metathesis and charge exchange reactions; (4) particle ionization and neutralization rates and cross sections; and (5) spectral line widths.

Cooper, D. M.↗

Antimatter Driven P-B11 Fusion Propulsion System

One of the major advantages of using P-B11 fusion fuel is that the reaction produces only charged particles in the form of three alpha particles and no neutrons. A fusion concept that lends itself to this fuel cycle is the Magnetically Insulated Inertial Confinement Fusion (MICF) reactor whose distinct advantage lies in the very strong magnetic field that is created when an incident particle (or laser) beam strikes the inner wall of the target pellet. This field serves to thermally insulate the hot plasma from the metal wall thereby allowing thc plasma to burn for a long time and produce a large energy magnification. If used as a propulsion device, we propose using antiprotons to drive the system which we show to be capable of producing very large specific impulse and thrust. By way of validating the confinement propenies of MICF we will address a proposed experiment in which pellets coated with P-B11 fuel at the appropriate ratio will be zapped by a beam of antiprotons that enter the target through a hole. Calculations showing the density and temperature of the generated plasma along with the strength of the magnetic field and other properties of the system will be presented and discussed.

Kammash, Terry↗

Kinematics reconstruction in solenoidal spectrometers operated in active target mode

Here, we discuss the reconstruction of low-energy nuclear reaction kinematics from charged-particle tracks in solenoidal spectrometers working in Active Target Time Projection Chamber mode. In this operation mode, reaction products are tracked within the active gas medium of the Active Target with a three dimensional space point cloud. We have inferred the reaction kinematics from the point cloud using an algorithm based on a linear quadratic estimator (Kalman filter). The performance of this algorithm has been evaluated using experimental data from nuclear reactions measured with the Active Target Time Projection Chamber (AT-TPC) detector.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Advancements in nuclear data evaluations in the unresolved resonance region [Slides]

Minimal updates to current capabilities (SAMMY/AMPX) and to the ENDF format are proposed to include threshold reaction for outgoing charged-particle channels in the URR formalism. If average resonance parameters are reported, probability tables for newly defined reactions channels may be needed, implemented, and tested. Nuclear data evaluation of n+ 35 Cl reactions can be considered the best case to apply the proposed updates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Determination of boron and lithium by recording the products from (n, alpha) reactions

Irradiation with thermal neutrons in the VVR-S reactor provides a nondestructive method for determining the presence of boron and lithium in solids. The charged particles produced in the reactions Li-6(n,alpha)H-3 and B-10(n,alpha)Li-7 were detected using CsI single crystal. For alpha-particle spectrometry in the boron determination, an ionization chamber (W and Sn electrodes, 99% Ar + 1% H2) was developed allowing both absolute and relative measurements. In determining boron in lithium-containing samples, both scintillation and ionization chambers are used. In determining lithium in minerals, the error was 1.5%, and the sensitivity 0.00005 wt.%. In the determination of boron in SiC with a concentration of boron approximately (3 plus or minus 2) the error given by the alpha-range uncertainty was 15%.

Lobanov, Y. M.↗

Towards modelling AR Sco: generalized particle dynamics and strong radiation-reaction regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realized the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time-step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform E- and B-fields and a static dipole B-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time-steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand–Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytical Aristotelian Electrodynamics expectations.

79 ASTRONOMY AND ASTROPHYSICS↗