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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Evaluation of Oak Ridge National Laboratory Health Physics Research Reactor Operation Data for Critical Benchmark Creation [Abstract]

The Oak Ridge National Laboratory (ORNL) Health Physics Research Reactor (HPRR) was a research reactor designed and built at ORNL in 1961. The critical assembly was using a highly enriched uranium and molybdenum alloy as the fuel, and it could be operated in steady-state or burst modes. The reactor was used for about 25 years to produce a lot of publications related to dosimetry, radiobiology and radiation detectors testing before its decommissioning in 1987. In recent years, the idea of using legacy operation data from the to create a valuable critical accident alarm system shielding benchmark arose. Such a benchmark has been submitted to the International Criticality Safety Benchmark Experiment Project (ICSBEP) Technical Review Group for a potential inclusion in the 2022 version of the handbook. Another way to use the valuable data from the operation of the HPRR is to evaluate the feasibility of the creation of a subcritical or prompt supercritical benchmark for inclusion in the ICSBEP or the International Reactor Physics Experiments Evaluation Project (IRPhEP) handbooks. To initiate a burst, the HPRR had to be operated in a slightly subcritical state for a few minutes. Then, the insertion of the burst control rod would greatly increase the reactivity of the system and start the burst. No critical configuration of the HPRR critical assembly could be located. The only information available concerns stable subcritical and prompt supercritical states, found in a burst experiments’ logbook. In the recovered logbook pages, information about 8 different bursts is available. The information includes the rods positions before and during a burst, the recorded subcritical reactor period and reactivity, and the burst fission yield derived from the temperature elevation sulfur pellet irradiation analysis. By using the HPRR logbook information and the as-built drawings of the critical assembly, a highly detailed model of the HPRR was created with SCALE 6.2.4/KENO-VI. Eight KENO-VI models were created to replicate the sub-critical assembly configurations described in the eight bursts from the recovered logbook pages. KENO-VI calculates k eff and it can be linked to a reactivity value in cents by using the delayed neutron fraction B eff , also calculated by KENO-VI. KENO-VI can also be used to model the prompt super-critical configurations of the HPRR and to assess the similarity with the burst measurements by comparing the calculated k eff and the measured fission yields between each burst. Unfortunately, high uncertainty exist and the obtained discrepancies between experiments and calculation results are high, compromising the creation of a valuable critical benchmark from HPRR operation data. The reasons of the discrepancies and potential ways to solve them are explored.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1984

The dynamic fission instability and the origin of the Moon

A theory for the formation of the Moon which involves the dynamic fission of a rapidly rotating protoplanet, which might then result in the formation of the Earth and the Moon is discussed. The fission hypothesis was originally based on analytic, linearized models of the growth of asymmetry in homogenous bodies. The fully nonlinear evolution of the dynamic instability in inviscid, compressible bodies was calculated by numerical techniques. It was found that the dynamic instability degenerates into the ejection of a ring of matter with a substantial fraction of the mass, leaving behind a central body with most of the mass. The linearized analytical approach and the numerical approach were used to show that dynamic fission probably does not occur in rocky protoplanets. The numerical calculations are performed with a fully three dimensional hydrodynamical code, which allows the nonlinear, time evolution of the instability to be followed. Sequences of uniformly rotating equilibria were constructed and are used as the initial models for the fission calculations. An initially imposed asymmetry consisting of a 10% binary perturbation in the density was found to disappear on the rotational period time scale. No dynamic instability occurred. This result are verified by including the velocity dissipation terms in the linearized analysis of the stability of a Maclaurin spheroid: the dynamic instability disappears when the simulated viscous dissipation terms are included. It is concluded that any rocky body, even with considerable partial melt or a molten core, should be stable to dynamic fission; any rotational instability that occurs can only result in equatorial mass loss.

Boss, A. P.↗
DOE OSTI2022

Accelerated coupled Monte Carlo-Thermal hydraulic calculations using a hybrid GTF-diffusion-based prediction block: first results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections' variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint Eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Accelerated Coupled Monte Carlo-Thermal Hydraulic Calculations using a Hybrid GTF-Diffusion-based Prediction Block: First Results

Accurate predictions of spatial power and temperature distributions require the coupling of a neutron transport solver with a thermal-hydraulic (TH) feedback. Nowadays, Monte Carlo (MC) codes are widely coupled to TH solvers, typically via a Picard iteration (PI) method, due to the higher fidelity that such frameworks can produce. To speed up a PI, a prediction step can produce an improved initial guess for a source distribution and feed it to the MC code. Recent work [1, 2] investigated a prediction step that uses generalized transfer functions (GTFs) to predict the macroscopic cross sections’ variations following a perturbation in TH properties, such as coolant density. The previous method also relied on first order perturbation (FOP) theory to predict perturbed power profiles, rather than using an expensive MC iterate. The implemented FOP method relied on generating a fission matrix from which the forward and adjoint eigenmodes were extracted and later used to for power calculations. The generation of the fission matrix can introduce a significant computational overhead, therefore undermining the performance of the proposed hybrid technique when applied to high-dimensional problems, e.g., full core calculations. This work attempts to improve the GTF-FOP prediction step by replacing the FOP solver with a nodal diffusion solver, thus eliminating the need to calculate a fission matrix. The GTF-diffusion step was tested for various moderator density perturbations. In each case, the predicted power distribution showed good agreement with the reference case. The latter is attributed to the generally good prediction of most spatially distributed macroscopic cross sections, except the transport cross section, which will become the focus of future work.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1992

Relativistic Coulomb Fission

Nuclear fission reactions induced by the electromagnetic field of relativistic nuclei are studied for energies relevant to present and future relativistic heavy ion accelerators. Cross sections are calculated for U-238 and Pu-239 fission induced by C-12, Si-28, Au-197, and U-238 projectiles. It is found that some of the cross sections can exceed 10 b.

Norbury, John W.↗
DOE OSTI2022

Impact of fission yield covariance matrices on decay heat uncertainty quantification with the DARWIN2 package

Although fission yields are strongly correlated, correlations between them are usually not taken into account when performing decay heat uncertainty calculations with the CEA DARWIN2 package due to the lack of reference covariance matrices associated to the JEFF-3.1.1 evaluation. However, covariance matrices for {sup 235}U and {sup 239}Pu thermal fission yields have been produced recently by the subgroup 37 of OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation (WPEC). The study presented in this paper evaluates the effect of those covariances on the decay heat uncertainty calculation, both on fission burst experiments and on integral decay heat measurements that are part of the DARWIN2 experimental validation database. Although some differences are observed, partly due to the variety of models used to produce the matrices, the propagation of fission yield covariances always leads to a reduction of the decay heat uncertainty for cooling time above 10 seconds, indicating that not taking them into account is a conservative hypothesis from a safety point of view. Nevertheless, the strong impact of those covariances on the decay heat uncertainty also highlights the need of documented and consistent fission yield uncertainties and correlation data. On top of that, all the covariance matrices used for this study represent the correlation between the physical model parameters, but none of them includes the experimental correlations. An evaluation of the experimental correlations would also be of strong interest for decay heat uncertainty calculations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Towards the Development of Molten Salt Reactor Multiphysics Modeling Capabilities: Depletion, Thermochemistry, Reactor Dynamics, and Species Tracking

This report documents the simulation and modeling work performed under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, utilizing the tools and codes developed under the program. The focus in this Fiscal Year (FY) is on the depletion, thermochemistry, reactor dynamics, and species transport in MSRs. The fission products travelling in the entire primary loop is unique in MSRs. There are many physical/chemical mechanisms that can significantly affect the fission products concentration in the fuel salt, e.g., diffusion into gas bubbles, diffusion in the core moderators, deposition on the surface of structures/pipes, etc. The fission product concentration in the fuel salt can potentially affect the neutronics, system dynamics, chemical potentials, etc., so accurately predicting the fission products distribution in the primary loop is important. Under the main objective, different activities are pursued to assess the NEAMS tools applicability for a variety of areas on species transport, including the depletion analyses using Griffin (fission product source), the redox potential assessment at different depletion points, the assessment of xenon transport effect on the neutronics and reactor dynamics, a survey of correlations for calculating the mass transfer coefficient of different fission products, etc.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Neural network emulation of spontaneous fission

Large-scale computations of fission properties are an important ingredient for nuclear reaction network calculations simulating rapid neutron-capture process (the 𝑟 process) nucleosynthesis. Due to the large number of fissioning nuclei potentially contributing to the 𝑟 process, a microscopic description of fission based on nuclear density functional theory (DFT) is computationally challenging. Here, we explore the use of neural networks (NNs) to construct DFT emulators capable of predicting potential energy surfaces and collective inertia tensors across the whole nuclear chart, starting from a minimal set of DFT calculations. We use constrained Hartree-Fock-Bogoliubov (HFB) calculations to predict the potential energy and collective inertia tensor in the axial quadrupole and octupole collective coordinates, for a set of nuclei in the 𝑟-process region. We then employ NNs to emulate the HFB energy and collective inertia tensor across the considered region of the nuclear chart. Least-action pathways characterizing spontaneous fission half-lives and fragment yields are then obtained by means of the nudged elastic band method. The potential energy predicted by NNs agrees with the DFT value to within a root-mean-square error of 500 keV, and the collective inertia components agree to within an order of magnitude. These results are largely independent of the NN architecture. The exit points on the outer turning line are found to be well emulated. For the spontaneous fission half-lives the NN emulation provides values that are found to agree with the DFT predictions within a factor of 10 3 across more than 70 orders of magnitude. Neural networks are able to emulate the potential energy and collective inertia well enough to reasonably predict physical observables. Future directions of study, such as the inclusion of additional collective degrees of freedom and active learning, will improve the predictive power of microscopic theory and further enable large-scale fission studies.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

SCALE Analyses of Scenarios in the Molten Salt Reactor Fuel Cycle

In support of the US Nuclear Regulatory Commission non-light-water reactor fuel cycle demonstration project, the capabilities of SCALE 6.3.1 for radionuclide characterization, criticality, and shielding were demonstrated through several scenarios in a molten salt reactor (MSR) nuclear fuel cycle. Three scenarios were selected for this study, with the molten salt breeder reactor (MSBR) serving as the reference design. The original thorium-based fuel salt used in MSBR was replaced with a 235 U-enriched fuel salt to better reflect anticipated future MSR concepts. The first scenario focused on the fuel salt preparation stage. Criticality analyses, using SCALE/CSAS-Shift and SCALE/SAMPLER, examined potential critical configurations in the fresh fuel salt container based on variables such as 235 U enrichment, UF 4 molar fraction, temperature, and container geometry. The second scenario explored the release of fission products during reactor operation in which the tritium buildup in the primary fuel salt was quantified through depletion calculations using SCALE/TRITON with continuous fuel makeup and fractional fission product removal. This scenario also assessed radioactivity levels in the off-gas system (OGS), quantifying radiotoxic nuclides that could be released into the environment. SCALE/SAMPLER was employed to perform uncertainty quantification to identify key operating parameters influencing the buildup of radiotoxic nuclides in the OGS. Additionally, radiation dose rates were calculated using SCALE/MAVRIC to estimate the maximum exposure levels within the reactor cell complex during operation. The final scenario evaluated the decay heat and radioactivity of the primary fuel salt collected in the drain tank, as well as the radiation dose rate outside the building from the presence of the drain tank. Overall, the application of SCALE’s various capabilities for radionuclide inventory generation, criticality analysis, and shielding in MSR fuel cycles was successfully demonstrated across these scenarios.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Measurement of the U 235 ( n , f ) prompt fission neutron spectrum from 10 keV to 10 MeV induced by neutrons of energy from 1 MeV to 20 MeV

The characterization of fission-driven nuclear systems primarily relies on calculations of neutron-induced chain reactions, and these calculations require evaluated nuclear data as input. Calculation accuracy heavily depends on input nuclear data evaluation accuracy, and thus high precision on the experimental input to the nuclear data evaluation is essential for fundamental quantities like the energy spectrum of neutrons emitted from neutron-induced fission (i.e., the prompt fission neutron spectrum, PFNS). Despite decades of measurement efforts, prior to the measurements described in this work there were only three literature data sets for the 235 U(n,f) PFNS at incident neutron energies above 1.0 MeV considered reliable for inclusion in nuclear data evaluations and no reliable data sets above 3.0 MeV incident neutron energy. In this work we report on new measurements of the 235 U(n,f) PFNS spanning a grid of 1.0–20.0 MeV in incident neutron energy and 0.01–10.0 MeV in outgoing (PFNS) neutron energy. These measurements were carried out at the Weapons Neutron Research facility at the Los Alamos Neutron Science Center and used a multifoil parallel-plate avalanche counter target with both a Li-glass and a liquid scintillator detector array in separate experiments to span the quoted outgoing neutron energy ranges. The PFNS results are shown in terms of the energy spectra themselves as well as the average PFNS energy $(\langle{E}\rangle)$ and ratios of $\langle{E}\rangle$ at forward and backward angles. Here, the results are compared with literature data and selected nuclear data evaluations. Generally, the data agree with the ENDF/B-VIII.0 evaluation below 5.0-MeV incident neutron energy and more closely with the JEFF-3.3 evaluation above 5.0 MeV, though no evaluations considered for comparison in this work agree with the data across all of the incident and outgoing neutron energies shown, especially in regions where the third-chance fission process becomes available. Additionally, we show a ratio of the present PFNS results for 235 U(n, f) with a recent and highly correlated experiment to measure the 239 Pu(n, f) PFNS at the same experimental facility and with nearly identical equipment and analysis procedures. Many observations reported in this work are the first of their kind and represent significant advancements for knowledge of the 235 U(n, f) PFNS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Earth Filter Mathematica Toolbox V4 User’s Guide: Simplifying, Visualizing and Quick Modeling of All Fission Products from 60 Nuclear Sources

The Earth Filter Mathematica toolbox is a set of user-friendly routines that accurately calculate the ingrowth and decay of any of the 908 fission products for an infinite combination of sources over a large dynamic range and large time scales. This toolbox was developed by Dr. W. P. Brug at Los Alamos National Laboratory and eliminates the need for the user to define and solve differential equations by automatically scanning the ENDF-349 dataset and creating a complete set of differential equations (including delayed neutron branches to both the ground and metastable states) for every fission product. Additionally, this code allows the user to choose the data source for half-lives from several key references (i.e., TORI, IAEA, ENDF or NUDAT.) The complete set of ENDF-349 independent and cumulative fission yields for all 60 isotopic targets and 4 different neutron spectrums are included. This allows nearly any nuclear fission source to be accurately modeled as a linear combination of endpoint sources. The Earth Filter Toolbox has no limit as to the length of split list, and split lists of 5 or more endpoint sources can be quite common.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Angular momentum of fission fragments from microscopic theory

During nuclear fission, a heavy nucleus splits into two rotating fragments. The associated angular momentum is large, yet the mechanism of its generation and its dependence on the mass of fragments remain poorly understood. In this Letter, we provide the first microscopic calculations of angular-momentum distributions in fission fragments for a wide range of fragment masses. For the benchmark case of 239 Pu(n th ,f), we find that the angular momentum of the fragments is largely determined by the nuclear shell structure and deformation, and that the heavy fragments therefore typically carry less angular momentum than their light partners. We use the fission model freya to simulate the emission of neutrons and photons from the fragments. The dependence of the angular momenta on fragment mass after the emission of neutrons and statistical photons is linear for the heavy fragments and either constant or weakly linear for the light fragments, consistent with the universal sawtooth pattern suggested by recent experimental data. Finally, we observe that using microscopic angular-momentum distributions modifies the number of emitted photons significantly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Assessment of tritium effluent from Prototype Generation IV Sodium-cooled Fast Reactor

We report a tritium transport model for a pool-type sodium cooled fast reactor was developed for estimation of tritium effluents from the Prototype Generation IV Sodium-cooled Fast Reactor (PGSFR). For this purpose, the transport model developed for Experimental Breeder Reactor II and Fast Flux Test Facility was updated and validated. The tritium production rate from ternary fission and activations in PGSFR were calculated by the Argonne Reactor Computation (ARC) code suite for fast reactor analysis, and due to the potential uncertainties in source terms and variations of cold trap performance and material permeability during reactor operation, the tritium distributions and tritium effluents were estimated for several bounding cases. The upper bounding gaseous and liquid tritium release rates from PGSFR are similar to ~440.7 Ci/year and 14.7 Ci/year, respectively. The gaseous tritium effluent is about few orders of magnitude smaller than the regulatory constraint of the tritium concentration in the air. The peak tritium concentration in the steam-generator feedwater is similar to ~1.1x10 -3 mu Ci/g, which is required to be diluted prior to releasing as tritiated water. The accumulated tritium in the cold trap after five cycle operations is ~ 52,000 Ci. Because of significant conservatism in these upper bounding estimations, it is expected that the tritium effluent at the nominal case with plausible source terms would be about 2 orders of magnitude smaller than that of the upper bounding case.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Statistical uncertainty of fission matrix eigenvalues using perturbation theory

Eigenvalue search of high dominance ratio systems may be slow to converge. The fission matrix element is defined by its element (FM){sub ij}, which are the probability for a neutron born in cell i to create a fission in cell j for a spatial mesh of n{sub i}*n{sub j} elements. Fission matrices are used in Monte Carlo criticality simulations to enhance computing speed, but also to find higher order eigenvalues. However, few studies have been made on the link between statistical uncertainties of fission matrix elements and eigenvalues uncertainties. Thus, dominance ratio statistical uncertainties remain unknown. This paper uses a new generalized perturbation theory (GPT) method to estimate sensitivities of eigenvalues to fission matrix elements and then to calculate dominance ratio uncertainties.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Flowsheet Design for the Purification of Mo-99 and Uranium Target Recovery by Solvent Extraction

New production and purification methods are sought to meet the increasing demand of 99 Mo but without the use of highly enriched uranium (HEU). To this end, larger quantities of low-enriched uranium (LEU) or even natural uranium (NU) are being leveraged to maintain high production capacities of 99 Mo. Solvent extraction is widely used to treat bulk quantities of uranium and to separate out trace quantities of fission products. This report describes the calculation of AMUSE-generated flowsheets to process irradiated uranium targets to recover 99 Mo by solvent extraction. Flowsheets are presented and discussed along with a number of advantages and disadvantages.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Consistent $\overline{ν}$ evaluation for minor U isotopes with $\tt{CGMF}$

Following several successful prompt $\overline{ν}$ evaluations using $\tt{CGMF}$, including consistent evaluations for minor Pu isotopes, we detail in this report our efforts to perform a consistent $\overline{ν}$ evaluation for minor U isotopes during FY25. Although we have not yet produced a finalized evaluation, we present the progress that we have made towards such an evaluation for 232,233,234,236,237,239 U prompt $\overline{ν}$. Our milestone explicitly calls out evaluations for 233 U, 234 U, and 236 U, however, to better constrain the model with reliable experimental $\overline{ν}$ data, we also include 235 U and 238 U in the evaluation procedure. Then, we additionally produce evaluations for 232 U, 237 U and 239 U $\overline{ν}$ as a byproduct. Elsewhere, we will report our efforts on a stand-alone 233 U $\overline{ν}$ evaluation. This report is organized in the following manner. In Sec. 2, we briefly outline the updates to CGMF that were needed to be able to calculate all of these minor U fission reactions. The experimental data overview is given in Sec. 3. The evaluation methodology and results are presented in Secs. 4 and 5, respectively. Finally, we conclude and outline work for FY26 in Sec. 6.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2021

r-process abundances in neutron-rich merger ejecta given different theoretical nuclear physics inputs

This data release contains nucleosynthesis predictions for the r-process abundances presented in Côté, Eichler, Yagüe, Vassh et al. (2021) for compact object merger ejecta based on the publicly available simulation trajectories of Rosswog et al. (2013). All ejecta for the merger scenarios considered here are very neutron-rich (Ye ~ 0.016-0.11). Calculations were performed with the PRISM code (Mumpower et al. 2018) which accounts for nuclear reheating (here with a reheating efficiency of 50%). Results are reported for several different theoretical nuclear physics inputs but all calculations make use of the GEF fission yield prescription (see Vassh et al. 2019). All abundances are given at 1 Myr (10^6 years) post-merger. Please see the README file for more details and references. When using these nucleosynthesis yields, please cite this Zenodo data release (Vassh et al. 2021), and refer to Vassh et al. (2019) and Côté, Eichler, Yagüe, Vassh et al. (2021) for further details on the nuclear data applied as well as Rosswog et al. (2013), Piran et al. (2013), and Korobkin et al. (2012) for further details on the merger ejecta trajectories.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Experimental Steps toward a Density Law for Chlorine-Crediting Criticality Models of Aqueous Plutonium solutions

Criticality accident prevention is an essential safety consideration for all operations involving fissionable and fissile materials. Predictive criticality calculations using advanced neutron transport codes, such as Monte Carlo N-Particle Transport (MCNP), are invaluable tools for designing and implementing operational limits. While indispensable, these tools are limited by the quality and accuracy of the inputs that the user provides to define the modeled system. Parameters such as atomic composition, shape, and material density must be accurately defined to obtain a meaningful result. In the case of material property details for a plutonium model, accurate material characterization data is sometimes sparse. Thus limitations in calculation accuracy can be reduced by improving our knowledge of material properties in the targeted fissile systems. One of the biggest remaining challenges to accurately defining fissile systems is the description of aqueous fissile solutions. Even simple properties, such as density, are not well-known for fissile solutions relevant to nuclear energy and security. Described here are initial efforts undertaken to improve criticality calculation inputs for fissile plutonium chloride solutions in water. This effort is focused on experimentally determining accurate solution characteristics for ternary plutonium chloride/hydrochloric acid/water systems, by measurement of water activity and solution density. The effect of inputting experimental densities for these solutions into MCNP criticality calculations is compared to the traditional approach of modeling an idealized (and fictitious) plutonium-water mixture. Expansion of these efforts to a working density law for aqueous plutonium chloride solutions is also discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗