SEARCH · Engineering Papers

Results for “Fission Calculations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Progress on the reevaluation and validation of the n+233U neutron cross sections

The set of 233 U resonance parameters of the ENDF/B-VIII.0 nuclear data library was adopted from the previous ENDF/B-VII.1 evaluation using the external levels to update the thermal values. Adoption of IAEA 2017 thermal standards ( σ f = 533.0 ± 2.2 b, σ c = 44.9 ± 0.9 b, and ν ‾ tot = 2.487 ± 0.011 ) and of the IAEA-recommended thermal-neutron induced prompt fission neutron spectrum (PFNS) with average PFNS energy of 2.030 ± 0.013 MeV requires a re-evaluation of 233 U neutron cross sections in the resolved resonance region. A newly produced evaluation is being tested on benchmarks carefully selected from the Handbook of International Criticality Safety Benchmark Experiments (ICSBEP) which are highly sensitive to 233 U data. An important goal of this work was to eliminate the strong negative gradient of the calculated effective multiplication factors with respect to the epithermal fission fraction observed in the validation of the ENDF/B-VIII.0 library for those assemblies. A significant improvement in integral performance of critical 233 U solutions is observed for the newly proposed evaluation. Further work addressing the fast neutron region is needed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Godiva IV Thermal Neutron Dosimetry Modeling and Variance Reduction

The transfer of the Godiva IV experiment from the Los Alamos Critical Experiments Facility (LACEF) to the National Critical Experiments Research Center (NCERC) introduced a vastly different experiment room return to the neutron flux. The contribution of the background to the burst neutron energy spectrum is significant in the thermal and epithermal neutron energies. Target materials may be placed in various locations in the Godiva room, or outside of the room, for thermal neutron activation. Modeling of this dosimetry problem in Monte Carlo N-Particle (MCNP) presented a novel challenge compared to previous Godiva IV glory hole irradiation simulations. An advanced dosimetry modeling framework for high efficiency calculations in locations far from the Godiva IV fission source was desired. The mesh-based weight windows and point detector advanced variance reduction techniques in MCNP were implemented and tested using adaptations of the critical experiment benchmark model of the Godiva IV problem. The models were validated against measured activations of Nickel, Indium, Scandium, and Cobalt foils at locations 2 meters from the Godiva IV core. Dosimetry measurements were performed in collaboration with Sandia National Laboratory. The weight windows and point detector variance reduction coupled method resulted in the highest problem efficiency.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

TEX-Chlorine Assemblies: Highly Enriched Uranium Plates with Sodium Chloride Absorbers Using Polyethylene Moderator and Polyethylene Reflector

This evaluation documents highly enriched uranium (HEU) experimental critical configurations with polyethylene moderators and sodium chloride absorbers conducted as part of the United States Nuclear Criticality Safety Program’s Thermal/Epithermal eXperiments (TEX) program. HEU-MET-MIXED-021 provides the benchmark evaluation of five TEX experiments designed to establish baseline configurations with HEU Jemima plates moderated by high density polyethylene (HDPE). The TEX-HEU experiments were designed to cover five different fission energy regimes by varying the thickness of the interstitial HDPE moderator, with varying fractions of thermal, intermediate, and fast fissions, and to be easily modified to accommodate test materials of interest. HEU-MET-INTER-013 documents the first TEX-HEU variation, incorporating hafnium in seven different experimental configurations. This evaluation covers an additional variant that incorporates absorber plates of compacted high-purity sodium chloride salt. These experiments were motivated by a criticality safety need for validation data for uranium purification by means of electrorefining with chloride salts, especially thermal and intermediate energy configurations resulting from moderator upset conditions, and their design was optimized by matching sensitivity profiles from application cases. All three experimental configurations are judged to be acceptable as benchmark cases. The main parameter varied between the configurations is the thickness of the polyethylene moderators and the sodium chloride absorbers between the HEU plates. Varying the thickness of the polyethylene tunes the neutron energy spectrum between majority thermal (Case 1 and 2) and intermediate (Case 3). The fission fractions, presented in Table 1, are determined calculationally. Case 3 is cross listed as HEU-MET-INTER-014.

42 ENGINEERING↗

DOE OSTI2023

Constraining Inputs to Realistic Kilonova Simulations through Comparison to Observed r -process Abundances

Kilonovae, one source of electromagnetic emission associated with neutron star mergers, are powered by the decay of radioactive isotopes in the neutron-rich merger ejecta. Models for kilonova emission consistent with the electromagnetic counterpart to GW170817 predict characteristic abundance patterns, determined by the relative balance of different types of material in the outflow. Assuming that the observed source is prototypical, this inferred abundance pattern in turn must match r -process abundances deduced by other means, such as what is observed in the solar system. We report on analysis comparing the input mass-weighted elemental compositions adopted in our radiative transfer simulations to the mass fractions of elements in the Sun, as a practical prototype for the potentially universal abundance signature from neutron star mergers. We characterize the extent to which our parameter inference results depend on our assumed composition for the dynamical and wind ejecta and examine how the new results compare to previous work. We find that a dynamical ejecta composition calculated using the FRDM2012 nuclear mass and FRLDM fission models with extremely neutron-rich ejecta ($Y_e$ = 0.035) along with moderately neutron-rich ($Y_e$ = 0.27) wind ejecta composition yields a wind-to-dynamical mass ratio of $M_w$/$M_d$ = 0.47, which best matches the observed AT2017gfo kilonova light curves while also producing the bestmatching abundance of neutron capture elements in the solar system, though, allowing for systematics, the ratio may be as high as of order unity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Radiation induced athermal diffusivity in uranium mononitride

Uranium mononitride (UN) is one of the ceramic nuclear fuel alternatives to oxide fuel considered for light water reactors and advanced reactor designs. Properties like self- and fission gas diffusivity need to be better understood, given that they influence key fuel performance phenomena such as fission gas swelling and release. In particular, the radiation induced athermal (D 3 ) diffusivity remains challenging to accurately predict and has only been sparsely characterized in UN, despite its importance as it likely governs diffusion at the low temperatures this high-thermal-conductivity fuel form may operate. Molecular Dynamics simulations are used to estimate the mean square displacement induced by a primary knock-on atom (PKA) with a given kinetic energy. These results are combined with the PKA energy distributions obtained from binary collision approximation calculations to obtain the displacement due to a particular fission fragment. Finally, this is combined with experimental fission fragment yields to determine the displacement due to an average fission event and, thus, express the athermal diffusivity as a function of the fission rate density. These results are in excellent agreement with available experimental data. In conclusion, a particular importance is given to the understanding and the quantification of the variability of these results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Recovery and Recycle of Irradiated Low-Enriched Uranium from the Production of 99 Mo

Technetium-99m ( 99m Tc), the daughter (decay product) of molybdenum-99 ( 99 Mo), is the most commonly used medical radioisotope in the world. 99 Mo is produced primarily from the fissioning of 235 U. A potential future producer, Eden Radioisotopes, is planning to irradiate low-enriched-uranium metal-foil targets for production of 99 Mo. Their plan is to recover, purify, and recycle the irradiated LEU in a new set of targets inside their facility. This study assesses processes to (1) purify and recycle uranium following 99 Mo recovery and (2) convert the uranium to metal for subsequent foil production and target fabrication. A UREX (uranium recovery by extraction) liquid–liquid extraction flowsheet that utilizes centrifugal contactors was developed using the Argonne model for universal solvent extraction (AMUSE) to recover and purify the uranium. The calculated flowsheet predicted high decontamination from Pu and most fission products and >99.99% recovery of uranium. Suggestions for conversion of the UREX U-product (uranyl nitrate in dilute nitric acid) to U metal were provided based on literature studies and earlier laboratory studies performed at Argonne National Laboratory.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2024

First-principles determination of the phonon-point defect scattering and thermal transport due to fission products in ThO 2

This work presents the first-principles calculations of the lattice thermal conductivity degradation due to point defects in thorium dioxide using an iterative solution of the Pierels-Boltzmann transport equation. We have used the non perturbative Green’s function methodology to compute the phonon- point defect scattering rates that consider the local distortion around the point defect, including the mass difference changes, interatomic force constants, and structural relaxation near the point defects. The point defects considered in this work include the vacancy of thorium ($V$ $TH$ ) and oxygen ($V$ $O$ ), substitutions of helium ($He$ $Th$ ), krypton ($Kr$ $Th$ ), zirconium ($Zr$ $Th$ ), iodine ($I$ $Th$ ) and xenon ($Xe$ $Th$ ) in the thorium site, and the three different configurations of the Schottky defects. The results of the phonon-defect scattering rate reveal that, among all the considered intrinsic defects, the thorium vacancy and helium substitution in the thorium site scatter the phonon most due to the substantial changes in the force constant and structural distortions. The scattering of phonons due to the substitutional defects unveils that the zirconium atom scatters phonons the least, followed by xenon, iodine, krypton, and helium. This is contrary to the intuition that the scattering strength follows $He$ $Th$ > $Kr$ $Th$ > $Zr$ $Th$ > $I$ $Th$ > $Xe$ $Th$ based on the mass difference. This striking difference in the zirconium phonon scattering is due to the local chemical environment changes. Zirconium is an electropositive element with valency similar to thorium and, therefore, can bond with the oxygen atoms, thus creating less force constant variance compared to iodine, an electronegative element noble gas helium, xenon, and krypton. In conclusion, these results can serve as the benchmark for the analytical models and help the engineering-scale modeling effort for nuclear design.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Examination of Legacy Metallic Fuel Pins (U-10Zr) Tested in FFTF

The MFF series of metallic fuel (U-10wt%Zr) tests performed in the Fast Fuel Test Facility (FFTF) were the beginning tests to qualify the fuel as a driver fuel for FFTF. They all performed very well, to relatively high burnup and with no pin breaches. Tests MFF-3 and MFF-5 were chosen to be destructively examined because they were run at high peak cladding temperatures, 643 and 649°C respectively, and to modest to high burnup (138 and 101 MWd/kgM respectively). They were the only sodium fast reactor (SFR) metallic tests, with long (91.4 cm) fuel columns and clad in HT9, to be operated at these high temperatures. Extensive operating condition reconstruction was performed to accompany the examination, providing detailed operating conditions axially along the pins. In addition, detailed ORIGEN calculations provided fuel burnup along the pin length. These calculations and detailed cross-section metallography allowed a PhD dissertation to be performed where the fuel/cladding chemical interaction (FCCI) was modeled using Fickian and Soret Effect driven diffusion of rare earth fission products to the cladding surface and interact with the cladding. The examination of the MFF-3 and MFF-5 pins included neutron radiography, axial profilometry including pin bow and length measurements, precision gamma scanning, plenum gas puncturing to measure fission gas release, detailed chemical/isotopic analyses of fuel samples to confirm burnup calculations, and metallography of pin cross-sections, including micro-hardness measurements of fuel and cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

NOCI-F Electronic Couplings in Assemblies of Indolonaphthyridine Molecules: From Dimers to the Full Stack

Key electronic processes related to molecular excitonic states of finite stacks of indolonaphthyridine molecules are analyzed via the non-orthogonal configuration interaction with fragments (NOCI-F) method. Indolonaphthyridine is an organic chromophore that can undergo several electronic photoexcitation-related intermolecular processes, such as exciton and electron transfer. The structures studied here are noncrystalline arrangements built as either ordered stacks of indolonaphthyridine or stacks extracted from molecular dynamics simulations including thermal disorder. Taking dimers or trimers from either model, we performed CASSCF and NOCI-F calculations to quantify the intermolecular electronic couplings governing singlet fission, excited singlet and triplet diffusion, and hole and electron diffusion processes. Also, comparing the results for the different models, we studied the effect of structural disorder and distortion on these couplings. Finally, we present a newly developed, advanced postanalysis tool. It takes the NOCI-F data as input to carry out a multifragment full Hamiltonian procedure that involves the complete stack, providing physical information not available from the dimer/trimer models, hence giving access to additional insight into the material’s properties.

coupling reactions↗

DOE OSTI2022

Fission Product Evaluation (Quarterly Report)

The LLNL team has developed a theoretical framework to compute the fission fragment charge and mass distributions of odd-mass nuclei, which can be formed in neutron-induced reactions on even-even nuclei. For example, n+ 238 U leads to the compound nucleus 239 U which has 147 neutrons. Odd-mass and odd-odd nuclei are spin-polarized: the spin of the nucleus is not equal to 0 as in even-even nuclei (a consequence of pairing correlations) but is in fact set by a single particle. In practice, that single particle can occupy different quantum-mechanical configurations, each with different spin. This affects the deformation properties of the nucleus and, as a result, the distribution of fission fragments. These distributions require two inputs for the calculation: a potential energy surface (= the total energy of the nucleus as a function of the deformation of the nuclear shape, often parametrized with 2 degrees of freedom) and the collective inertia tensor associated with each point of the PES. In an odd-mass or odd-odd nucleus, each quantity depends on the configuration of the single particle. We computed of the order of 20 to 30 different such configurations to extract the PES for spins K=1/2, 3/2, 5/2, 7/2, and 9/2 of 239 U. We then computed the primary yields for each such PES, as shown in Fig. 1 below. These yields were weighed with the spin distribution associated with the reaction 238 U+n and the resulting distribution used as input to FREYA to compute the independent yields shown in Fig. 2. These yields are then used as inputs to the FIER code to extract the cumulative yields and compare with LLNL-LANL measurements at TUNL.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Shell effects in quasi-fission: Reactions forming actinide and superheavy compound nuclei

Quasi-fission occurs in fully damped heavy-ion collisions following a significant mass transfer between the fragments, without formation of a compound nucleus. As in fission, quasi-fission is expected to be affected by quantum effects leading to asymmetric mass splits. Quantum shells stabilising fission fragments with octupole shapes have been invoked as a factor determining the distribution of nucleons between the fragments at scission, explaining the fact that the centroid of the heavy fragment charge distribution is found around Z = 54 protons in fission and quasi-fission of actinides. These shell effects are studied in microscopic studies of quasi-fission. In particular, time-dependent Hartree-Fock (TDHF) calculations have been performed for reactions forming actinides.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Determining the 9 $\mathrm{Be}$($n, γ$) 10 $\mathrm{Be}$ integral cross section at fission neutron energies

The 9 B neutron capture cross section has significant implications for Be materials in the nuclear industry as well as the α process in stellar nucleosynthesis. While the cross section is well constrained at thermal neutron energies, there is a lack of experimental data at higher neutron energies, and the evaluated nuclear data libraries can differ by up to two orders of magnitude. We calculate the 9 Be(n, γ) 10 Be integral cross section at fission neutron energies in an effort to resolve disagreements amongst the nuclear data libraries. Foil irradiation experiments were performed using the Flattop critical assembly at the National Criticality Experiments Research Center with either the highly enriched U or Pu cores, with target foil stacks placed at multiple locations to exploit different neutron energy profiles. Accelerator mass spectrometry was used to measure the 10 Be/ 9 Be ratio in irradiated Be foils, while all other activation products were quantified through gamma spectrometry. The experiments were simulated using the Monte Carlo N-Particle radiation transport code and combined with experimental results to determine the total neutron fluence, while the staysl-pnnl suite and fispact-ii code were used to validate the model and assess the systematic uncertainty. The new 9 Be(n, γ) 10 Be integral cross sections calculated in this work are 26.5 ± 2.2µb at 0.59 ± 0.07 MeV, 24 ± 3 µb at 0.98 ± 0.14 MeV, 21.7 ± 1.3 µb at 1.26 ± 0.11 MeV, 21.8 ± 1.4 µb at 1.32 ± 0.11 MeV, and 18.6 ± 1.1 µb at 1.46 ± 0.13 MeV. These results do not agree with integral cross sections from any of the nuclear data library evaluations. Discrepancies between the new integral cross sections reported here and the nuclear data libraries suggest a more complex cross-section structure in the MeV range which allows for more resonance contributions, and more work is needed to further constrain the evaluated cross sections.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2026

FPMS_XPeRT_INL_Poster

As nuclear energy expands and experimental programs increasingly rely on the facilities at Idaho National Laboratory (INL) for reactor and fuel testing, research capabilities must also expand to meet these demands. A new Fission Product Monitoring System (FPMS) has been deployed at the Advanced Test Reactor (ATR) at the Auxiliary Lead-out Experiment (ALE) House to support this expanding fuel testing mission. By tracking gaseous fission products releases from test fuel in near real-time, release rates, calculated from FPMS data, can be used to characterize the effectiveness of fuel cladding, especially for Tri-structural Isotropic (TRISO) fuel concepts. The new iteration of the FPMS supports up to 14 fission product monitors for online fission-product tracking via gamma-ray spectroscopy of the experiment’s effluent gas. Each monitor consists of a nominally 10% HPGe detector housed in a copper-lined lead shield with a warm gas trap. The new system features gamma-ray count rate information with a five-second temporal resolution and provides isotopic activity every five minutes, capable of resolving multiple overlapping fission product releases over a broad range of activities in near real-time. This work includes data from ATR cycle 175D data to demonstrate these capabilities. The hourly resolution data shows general trends and significant releases over the cycle, while the 5-minute resolution data allows for a more detailed examination of events due to unexpected particle releases.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

DOE OSTI2023

Development of Mechanistic Fission Gas Release and Swelling Models for UN Fuels in BISON

This report describes the work in NEAMS (Nuclear Energy Advanced Modeling and Simulation) to develop a mechanistic fission gas model for uranium nitride fuels in BISON. The existing Sifgrs (Simple integrated fission gas release and swelling) model tracks the average properties of two bubble populations in the bulk and at the grain boundaries. It was recognized that dislocations play a crucial role in the fission gas swelling of UN, and an irradiation-induced dislocation density model was needed, as well as a model describing how fission gas interacts with dislocations creating a third population of bubbles along dislocations. A mechanistic model that tracks dislocation bubbles was implemented in Sifgrs. This model was used to simulate fission gas swelling and release in UN. Lower-length-scale calculations and experimental observations from carbide fuel were leveraged to help populate the model with essential parameters. As a placeholder, an empirical function was formulated for the evolution of the dislocation network. Because of the difference in evolution of this network at different temperatures, the dislocation bubbles are able to capture behavior that the bulk intragranular bubbles cannot. It was found that the bulk bubbles dominate microscopic swelling at low temperatures, and the dislocation bubbles dominate at higher temperatures. Based on this model, the transition between the two bubble types is the main factor behind the breakaway swelling phenomenon in UN. In order to test the model, a couple of assessments were run. For the lower temperature JOYO pins, the model produces reasonable fission gas release and swelling values. For the higher temperature SP1 pin, the model dramatically underestimates the fission gas release. This issue is attributed to the gas being trapped inside dislocation bubbles, unable to escape to grain boundaries to cause fission gas release, and could be remedied by a mechanistic dislocation model that allows the dislocation density to decrease at very high temperatures. A preliminary mechanistic dislocation model was developed supported by first-principle calculations. These calculations provided valuable insight into how interstitial defects cluster in UN in the {110} orientation, and may eventually form dislocation loops, leading to the conclusion that dislocation loops may nucleate from these clusters. An estimate of the dislocation line energy in UN was obtained and will be improved in future work. The free-energy cluster dynamics code Centipede was used to track interstitial and vacancy absorption at dislocation loops and calculate their growth. In addition, improvements to Centipede were made including new convergence criteria for transient simulations and sink driving force updates.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Kiwi-TNT Simulation Model [Slides]

The Kiwi-TNT Test (Toonerville Trolley) was performed on January 12, 1965. LANL has the objective: "LANL will develop a defensible methodology for establishing the maximum number of fissions for postulated inadvertent criticality events. The methodology may include several methods, such as hand calculations, sophisticated modeling, and the use of historical data.” The historic test, Kiwi TNT, posed a starting point for predictive simulations to determine the number of fissions and excursion understanding. This presentation gives results of that effort.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Impact of Increased Monte Carlo Parameters on Sensitivity Calculations with SCALE [Slides]

For both models and tests, NPG and NSK parameters have only small effects on calculated sensitivity coefficients. Outside of NPG=100, only differences in CFP affected sensitivity coefficient values. Fission reactions ( 235 U) require more NPG values than scattering ( 238 U) reactions – more particles are needed to locate fission sources in the model more accurately. This work confirms the previous results with the IFP method where the CFP parameter has the greatest impact on calculated sensitivity coefficients. While immediate work focuses on fast systems, other model specifications may require a different set of MC parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Radiological Safety Analysis Computer (RSAC) Program Version 7.4 Users’ Manual

The Radiological Safety Analysis Computer (RSAC) Program Version 7.4 (RSAC-7) is the newest version of the RSAC legacy code. RSAC-7 calculates the consequences of a release of radionuclides to the atmosphere. Users generates a fission product inventory from either reactor operating history or a nuclear criticality event. RSAC-7 models the effects of high-efficiency particulate air filters or other cleanup systems and calculates the decay and ingrowth during transport through processes, facilities, and the environment. Doses are calculated for inhalation, air immersion, ground surface, ingestion, and cloud gamma pathways. RSAC-7 is used as a tool to evaluate accident conditions in emergency response scenarios, radiological sabotage events, and safety basis accident consequences. This users’ manual contains the mathematical models and operating instructions for RSAC-7. Instructions, screens, and examples are provided to guide the user through the functions provided by RSAC-7. This program is designed for users who are familiar with radiological dose assessment methods.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Sensitivity Calculations for Systems with Polyethylene Reflector Materials Using CLUTCH

The SCALE 6.2.4 code package contains four sequences for calculating $k_{eff}$ sensitivity coefficients. Two of these sequences use deterministic transport solvers: a one-dimensional (1D) capability based on XSDRN, and a two-dimensional (2D) capability based on NEWT. These sequences are restricted to the multigroup (MG) treatment of neutron energy. The three-dimensional (3D) sequences use the KENO V.a or KENO-VI Monte Carlo transport codes and can be used to calculate sensitivity coefficients with either MG or continuous-energy (CE) transport. The 3D sensitivities are ultimately reported in an MG structure, regardless of the method used in the transport calculations. If desired, the sensitivity coefficients can be reported with very fine energy resolution from a CE calculation, but they are calculated only in the MG library structure in the MG mode. CE TSUNAMI methods are available in SCALE starting in SCALE version 6.2. Sensitivity coefficients were generated using the 3D sequences as part of the generation of the SCALE 6.2.2 Validation Report; difficulties encountered when using the CLUTCH method for thick, fissionable-material reflectors were discussed and investigated as documented in a previous paper. This paper discusses the difficulties encountered in generating accurate sensitivity coefficients using the CLUTCH technique for polyethylene reflectors for two fast spectrum benchmarks. Direct perturbation (DP) calculations were performed to confirm the accuracy of the total sensitivity coefficient for important isotopes with large sensitivities in the system. Discrepancies were detected for CLUTCH-calculated sensitivity coefficients in the reflector of a critical experiment with a radial polyethylene reflector. A simple polyethylene-reflected plutonium sphere was then used to further investigate the discrepancy. Calculations performed using the iterated fission probability (IFP) method generated accurate sensitivity coefficients in both cases. The results of this study emphasize the need to confirm CLUTCH sensitivity results with DP calculations. IFP calculations are generally less efficient but more reliable than CLUTCH calculations. Improvements to the CLUTCH methodology that retain the greater efficiency but address identified difficulties are therefore potentially useful to analysts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗