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At least 127 records · Page 7

Nuclear data for reactor production of 131 Ba and 133 Ba

The newest radioisotope for brachytherapy treatment of prostate cancer is 131 Cs (t 1/2 = 9.69 d, 100% EC). Generated via electron capture decay of 131 Ba (t 1/2 = 11.6 d, 100% EC), 131 Cs has been used in brachytherapy for prostate cancer since 2004. The 131 Ba parent is produced through neutron capture of enriched 130 Ba in a nuclear reactor. For large-scale production of 131 Ba, an accurate knowledge of production and burnup cross sections of 131 Ba are essential. Here, we report two group cross sections (thermal and resonance integrals) for 130 Ba and 131 Ba and a new measure of the half-life of 131 Ba. Targets consisting of milligram quantities of enriched 130Ba (~35%) were irradiated in Oak Ridge National Laboratory's High Flux Isotope Reactor at thermal and resonance neutron fluxes of (1.9–2.1) × 10 15 and (5.8–7.0) × 10 13 neutrons·cm -2 s -1 , respectively, for durations ranging from 3 to 26 days. In addition, cadmium covered samples of 130 Ba were irradiated for 1 hour at 12.6% full reactor power (10.7 MW). The yield of 131 Ba approaches a saturation value of ~60 GBq (~1.6 Ci) per mg of 130 Ba for 20 days irradiation at a thermal neutron flux of 1.8 × 10 15 n·s -1 ·cm -2 , with a thermal/epithermal ratio of ~30. Under the above experimental conditions, the two group cross sections of 130 Ba are 6.9 ± 0.5 b (thermal, σ 0 ) and 173 ± 7 b (resonance, I 0 ). These values represent the sum of cross sections to metastable and ground states of 131 Ba. For 131 Ba, the empirically measured thermal cross section is 200 ± 50 b assuming an I 0 /σ 0 of 10. This cross section is reported for the first time. Further, the half-life of 131 Ba was remeasured to be 11.657 ± 0.008 d. Lastly, this study also resulted in the co-production of 133 Ba (t 1/2 = 10.52 y, 100% EC). The experimental yield of 133 Ba is ~370 MBq (~10 mCi) per mg of 132 Ba (thin target) for one cycle irradiation in the High Flux Isotope Reactor, and measured two-group 132 Ba cross sections are 7.2 ± 0.2 b and 39.9 ± 1.3 b. These values also represent the sum of cross sections to metastable and ground states of 133 Ba.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Automation of Laser Plasma Focused Ion Beam Microscopy for Next-Gen Energy Materials

Automation can revolutionize the use of ultrafast laser ablation and plasma-focused ion beam (PFIB) techniques for high-throughput, reproducible cross-sectioning and various sample preparation in materials characterization. As these methods become essential for analyzing complex energy materials and next-generation devices, efficient, standardized workflows are needed to minimize variability and enhance precision. This work highlights our advancements in developing automated processes for sample preparation that integrates machine learning, workflow optimization, and large-scale data acquisition to improve efficiency and scalability in applications such as electrolyzers, photovoltaic cells, and microelectronics. To streamline cross-sectioning and lamella fabrication, we have implemented fully automated workflows that standardize laser ablation and PFIB milling sequences. These workflows incorporate pre-programmed protocols for material removal, alignment, and thinning, reducing user intervention and ensuring consistency across different sample types. Machine learning algorithms further enhance automation by predicting optimal milling strategies and adapting parameters based on material properties and sectioning requirements. This approach significantly improves throughput while maintaining the structural integrity of prepared samples for high-resolution imaging and analysis, including transmission electron microscopy. Beyond sample preparation, our automation platform enables the acquisition of large, high-resolution datasets through serial sectioning, image alignment, and 3D reconstruction. These automated routines facilitate multi-scale characterization, capturing structural and compositional details from the nanoscale to the device level. By reducing variability and increasing efficiency, our automated approach enhances defect analysis, failure diagnostics, and process optimization, accelerating advancements in materials research and device engineering.

36 MATERIALS SCIENCE↗

Dissipative dark matter on FIRE – I. Structural and kinematic properties of dwarf galaxies

We present the first set of cosmological baryonic zoom-in simulations of galaxies including dissipative self-interacting dark matter (dSIDM). These simulations utilize the Feedback In Realistic Environments galaxy formation physics, but allow the dark matter to have dissipative self-interactions analogous to standard model forces, parametrized by the self-interaction cross-section per unit mass, (σ/m), and the dimensionless degree of dissipation, 0 < f diss < 1. We survey this parameter space, including constant and velocity-dependent cross-sections, and focus on structural and kinematic properties of dwarf galaxies with $M_{\rm halo} \sim 10^{10-11}{\, \rm M_\odot }$ and $M_{\ast } \sim 10^{5-8}{\, \rm M_\odot }$. Central density profiles (parametrized as ρ ∝ rα) of simulated dwarfs become cuspy when $(\sigma /m)_{\rm eff} \gtrsim 0.1\, {\rm cm^{2}\, g^{-1}}$ (and f diss = 0.5 as fiducial). The power-law slopes asymptote to α ≈ -1.5 in low-mass dwarfs independent of cross-section, which arises from a dark matter ‘cooling flow’. Through comparisons with dark matter only simulations, we find the profile in this regime is insensitive to the inclusion of baryons. However, when $(\sigma /m)_{\rm eff} \ll 0.1\, {\rm cm^{2}\, g^{-1}}$, baryonic effects can produce cored density profiles comparable to non-dissipative cold dark matter (CDM) runs but at smaller radii. Simulated galaxies with $(\sigma /m) \gtrsim 10\, {\rm cm^{2}\, g^{-1}}$ and the fiducial fdiss develop significant coherent rotation of dark matter, accompanied by halo deformation, but this is unlike the well-defined thin ‘dark discs’ often attributed to baryon-like dSIDM. The density profiles in this high cross-section model exhibit lower normalizations given the onset of halo deformation. For our surveyed dSIDM parameters, halo masses and galaxy stellar masses do not show appreciable difference from CDM, but dark matter kinematics and halo concentrations/shapes can differ.

79 ASTRONOMY AND ASTROPHYSICS↗

Mapping Current Collection in Cross Section: The Case of Copper-Doped CdTe Solar Cells

For decades, copper has been used to improve the performance of cadmium telluride thin film solar cells. However, it has also been shown to be the main cause of metastability in CdTe. Recently a low activation energy has been reported for the thermal diffusion of Cu in CdTe explaining the ease of motion that it has under moderate temperatures. The community consensus is that copper segregates to the absorber grain boundaries, where it's either beneficial or detrimental to device performance depending on its concentration. Using nanoscale X-ray micrsocopy and a two-dimensional drift-diffusion model we present a preliminary correlation between local copper distribution and electrical performance of a single-junction CdTe/CdS solar cell.

CdTe↗

Accurate determination of production data of the non-standard positron emitter 86 Y via the 86 Sr(p,n)-reaction

In view of several significant discrepancies in the excitation function of the 86 Sr(p,n) 86g+xm Y reaction which is the method of choice for the production of the non-standard positron emitter 86 Y for theranostic application, we carried out a careful measurement of the cross sections of this reaction from its threshold up to 16.2 MeV at Forschungszentrum Jülich (FZJ) and from 14.3 to 24.5 MeV at LBNL. Thin samples of 96.4% enriched 86 SrCO 3 were prepared by sedimentation and, after irradiation with protons in a stacked-form, the induced radioactivity was measured by high-resolution γ -ray spectrometry. The projectile flux was determined by using the monitor reactions nat Cu(p,xn) 62,63,65 Zn and nat Ti(p,x) 48 V, and the calculated proton energy for each sample was verified by considering the ratios of two reaction products of different thresholds. Additionally, the experimental cross section data obtained agreed well with the results of a nuclear model calculation based on the code TALYS. From the cross section data, the integral yield of 86 Y was calculated. Over the optimum production energy range E p = 14 → 7 MeV the yield of 86 Y amounts to 291 MBq/μA for 1 h irradiation time. This value is appreciably lower than the previous literature values calculated from measured and evaluated excitation functions. It is, however, more compatible with the experimental yields of 86 Y obtained in clinical scale production runs. The levels of the isotopic impurities 87m Y, 87g Y, and 88 Y were also estimated and found to be <2% in sum.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Erratum: “History of atomic layer deposition and its relationship with the American Vacuum Society” [J. Vac. Sci. Technol. A 31, 050818 (2013)]

The authors of this review article published in 20131 would like to correct some text and references relating to the first observations and publications on molecular layering. In Sec. II, “Early Years of Atomic Layer Processes” in the original article,1 the first two sentences of the fourth paragraph should instead say “The ALD principle, where surface reactions follow a binary sequence of self-limiting half-reactions, was reported under the name ‘molecular layering’ in the 1960s by S. I. Kol’tsov from Leningrad Technological Institute.2–6 These experiments were conducted under the scientific supervision of V. B. Aleskovskii. The ‘framework hypothesis,’ an antecedent to molecular layering, was proposed by V. B. Aleskovskii in 1952.6” In addition, again in this same section and paragraph, the last two sentences should instead say “In the 1969 article,3 the authors report that the initial reaction between TiCl4 and Si–OH tends to involve 3 Si–OH, forming one Ti–Cl, whereas after the first water step, the second TiCl4 exposure reacts with 2 Ti–OH, forming Ti–Cl2 groups. In the 1969 paper,3 a planar thin film was not produced or evaluated, although nanolayers were prepared by molecular layering at that time.6” These corrections do not affect other sections or the conclusions drawn in the article.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance of the Pair Spectrometer in Hall D at Jefferson Lab

This article describes the performance of the pair spectrometer installed in experimental Hall D at Jefferson Lab and its successfully operation in multiple experiments with the GlueX detector. The primary purpose of the pair spectrometer is the precise determination of the flux of beam photons incident on the GlueX target, a critical input for physics analyses such as absolute cross-section measurements. The photon energy spectrum is determined by reconstructing electron–positron pairs produced in a thin converter inserted into the photon beam. The spectrometer is integrated into the GlueX trigger system, whose electronics enable continuous real-time monitoring of the photon flux and the recording of e+e- pair candidates for offline analysis. In addition, the pair spectrometer provides a versatile test facility for evaluating calorimeter prototypes using leptons with well-defined energies produced via electromagnetic pair production.

Somov, Alexander [Jefferson Lab]↗

Local Resistance Measurement for Degradation of c-Si Heterojunction with Intrinsic Thin Layer (HIT) Solar Modules

Silicon heterojunction with intrinsic thin layer (or HIT) modules typically degrade at a rate of less than 1% annually in solar fields with dominant degradation in open-circuit voltage and some degradation in series resistance. However, detailed mechanisms can differ from module to module. Here, we study increases in local series resistance that occur over long-term field deployment, indicated by cell areas where the photoluminescence intensity does not degrade but the electroluminescence degrades significantly. To directly measure the local series resistance, we have cored out the local electroluminescence-degraded area, and we measured the sheet resistance by 4-point-probe and local nm-scale resistance using scanning spreading resistance microscopy (SSRM). The results by 4-point-probe show scattered sheet resistance that can be caused, for example, by nonuniform current paths through the transparent conductive oxide layer, the a-Si:H emitter, or the near-junction c-Si inversion layer. In contrast, the SSRM results indicate a relatively uniform and non-degraded resistivity on smaller nanometer spatial scales. SSRM is an atomic force microscopy-based two-terminal resistance mapping technique that measures the local resistance in nm-volume beneath the probe. The consistent resistances measured on the control and degraded samples can exclude the degradation of transparent conductive oxide resistance.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Efficient calculation of self magnetic field, self-force, and self-inductance for electromagnetic coils with rectangular cross-section

Abstract For designing high-field electromagnets, the Lorentz force on coils needs to be computed in order to design suitable support structures, and the inductance should be computed to evaluate the stored energy and dynamics. Also, the magnetic field and its variation inside the conductor is of interest for computing stress and strain, and due to superconducting quench limits. For these force, inductance, energy, and internal field calculations, the coils cannot be naively approximated as infinitesimally thin filaments due to divergences when the source and evaluation points coincide, so more computationally demanding calculations are usually required, resolving the finite cross-section of the conductors. Here, we present a new alternative method that enables the internal magnetic field vector, self-force, and self-inductance to be computed rapidly and accurately within a 1D filament model. The method is applicable to coils for which the curve center-line can have general noncircular shape, as long as the conductor width is small compared to the radius of curvature. This paper extends a previous calculation for circular-cross-section conductors (Hurwitz et al 2024 IEEE Trans. Magn. ) to consider the case of rectangular cross-section. The reduced model is derived by rigorous analysis of the singularity, regularizing the filament integrals such that they match the true high-dimensional integrals at high coil aspect ratio. The new filament model exactly recovers analytic results for a circular coil, and is shown to accurately reproduce full finite-cross-section calculations for a non-planar coil of a stellarator magnetic fusion device. Due to the efficiency of the model here, it is well suited for use inside design optimization.

Landreman, Matt (ORCID:000000027233577X)↗

Crystallographic registry in epitaxial V3O5 thin films

Crystallographic orientation plays a central role in determining transport properties in correlated oxides with low-hysteresis metal–insulator transitions. Here, V3O5 thin films were grown on Al2O3 (0001) and their crystallographic registry was evaluated using x-ray diffraction and cross-sectional transmission electron microscopy. θ–2θ measurements show a single out-of-plane orientation defined by the (202) reflection. Azimuthal φ-scans of the V3O5 (310) reflection exhibit twelve discrete maxima over 360°, indicating a finite set of in-plane orientations imposed by the substrate symmetry. High-resolution TEM and fast Fourier transform analysis confirm crystallographic coherence at the film–substrate interface. The electrical conductivity exhibits a metal–insulator transition at TMIT ≈ 423 K with no measurable thermal hysteresis and a total change of ~1.6 orders of magnitude between 300 and 480 K. These results establish crystallographic registry in epitaxial V3O5 thin films and provide a structurally well-defined system for future studies of orientation-dependent transport.\r\nT

36 MATERIALS SCIENCE↗

Chemical and elemental mapping of spent nuclear fuel sections by soft X-ray spectromicroscopy

Soft X-ray spectromicroscopy at the O K -edge, U N 4,5 -edges and Ce M 4,5 -edges has been performed on focused ion beam sections of spent nuclear fuel for the first time, yielding chemical information on the sub-micrometer scale. To analyze these data, a modification to non-negative matrix factorization (NMF) was developed, in which the data are no longer required to be non-negative, but the non-negativity of the spectral components and fit coefficients is largely preserved. The modified NMF method was utilized at the O K -edge to distinguish between two components, one present in the bulk of the sample similar to UO 2 and one present at the interface of the sample which is a hyperstoichiometric UO 2+ x species. The species maps are consistent with a model of a thin layer of UO 2+ x over the entire sample, which is likely explained by oxidation after focused ion beam (FIB) sectioning. In addition to the uranium oxide bulk of the sample, Ce measurements were also performed to investigate the oxidation state of that fission product, which is the subject of considerable interest. Analysis of the Ce spectra shows that Ce is in a predominantly trivalent state, with a possible contribution from tetravalent Ce. Atom probe analysis was performed to provide confirmation of the presence and localization of Ce in the spent fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hadron Production Measurements at NA61/SHINE

In current day measurements of neutrino oscillation parameters with accelerator-based neutrino experiments, neutrino flux uncertainties are frequently a leading systematic uncertainty. Precise measurements of primary and secondary hadron production processes for neutrino beams, performed by the NA61/SHINE experiment at CERN's Super Proton Synchrotron, can significantly constrain these uncertainties; the T2K experiment has incorporated previous NA61/SHINE measurements for a substantial flux uncertainty reduction. For these measurements, NA61/SHINE analyzes the interactions of charged hadrons with materials relevant to long-baseline experiments, measuring the differential cross sections of produced particles. This poster will review the NA61/SHINE experiment, including recent, ongoing, and future measurements with thin and replica targets, such as proton-carbon interactions at 31 GeV/c and 120 GeV/c for the T2K and DUNE experiments, respectively.

Allison, Kyle↗

Quantifying resonance behavior in the fusion of O 17 with C 12 at above-barrier energies

Recent measurement of the fusion excitation function for 17 O + 12 C reported the significant suppression of the fusion cross section at E c.m. ≈ 14 MeV. This suppression was hypothesized to signal the existence of a 16 O + n + 12 C molecular configuration. Using the active-target detector MuSIC@Indiana provided an effective means of reexamining the fusion excitation function for 17 O + 12 C.The accuracy of this thick-target measurement is strengthened through comparison with the thin-target measurement of the excitation function for 17 F + 12 C. Furthermore, the result provides important information about the dependence of the average fusion cross section for the oxygen isotopic chain on neutron excess.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Extracting single fiber transverse and shear moduli from off-axis misalignment fiber tensile testing

Small diameter (<100 μm) fibers (e.g. carbon fibers, Kevlar, and fiberglass) and wires (e.g. ultrafine copper and aluminum wires) are frequently used in many different engineering applications, such as for light weighting structures, electromagnetic shielding for aircraft/infrastructure/EVs, vibration damping, biological sensors, aerospace electrical devices, and electric windings just to name a few. Due to the manufacturing process, the fibers and wires are pulled and stretched to produce a preferential alignment. Therefore, thin fibers and wires typically display different properties along the length of the fiber as opposed to their cross section and many fibers/wires are considered transversely isotropic. The axial properties of fibers/wires can be ascertained via tensile testing of single-filaments or fiber tows, but the radial properties require much more effort to measure. Knowing these properties is important for the accurate prediction of micromechanical models and manipulation of fibers during micromanufacturing. In this paper, a new technique was developed to determine the transverse/shear moduli and strength of a material by conducting tensile tests of the material at increasing misalignment angles from the tensile axis. Due to the transversely isotropic nature of the material, the transverse/shear moduli and strength influence the experimental results recorded by the test machine to different degrees based on the amount of misalignment in the test setup. An equation was derived to determine the influence of each of the material properties based on the misalignment angle by manipulating the stiffness matrix for transversely isotropic materials using the transformation matrices. Then, curve fitted coefficients were used to identify the material properties. Here, the strengths were similarly determined by curve fitting an off-axis Tsai-Hill failure criteria to determine the influence of transverse, shear, and tensile strengths based on the complex loading condition provided by the off-axis tensile test. Zoltek Panex 35 carbon fibers were used to demonstrate this new technique and the determined properties were then compared to those obtained from nanoindentation and from literature. Fracture surfaces provide insight into the different failure mechanisms at various misalignment angles.

36 MATERIALS SCIENCE↗

Tensile and compressive plastic deformation behavior of medium-entropy Cr-Co-Ni single crystals from cryogenic to elevated temperatures

The equiatomic Cr-Co-Ni medium-entropy alloy has the face-centered cubic (FCC) structure. Bulk single crystals of this alloy were grown and tested in tension and compression between 14 K and 1373 K with the loading axis parallel to [23]. At room temperature, the critical resolved shear stress (CRSS) for {111}<10> slip is 65 ± 5 MPa and does not exhibit a tension-compression asymmetry. It does, however, increase significantly as the test temperature decreases. A dulling of this temperature dependence occurs below 50 K, which may be due to the inertia effect. When the measured values above 50 K are extrapolated to lower temperatures, a value of 225 MPa is estimated for the CRSS at 0 K. This is larger than that (168 MPa) previously determined for the equiatomic Cr-Mn-Fe-Co-Ni high-entropy alloy using a similar procedure. The stacking fault energy of the present Cr-Co-Ni is estimated to be about 14 mJm-2, which is sufficiently low to account for deformation twinning both at 77 K and room temperature. Twinning at 77 K occurs on conjugate (1) planes at an onset shear stress of 482 MPa after primary slip and propagates in the form of Lüders deformation. At room temperature, twinning occurs uniformly throughout the gauge section on primary (111) planes at an onset shear stress of 381 MPa after primary and subsequent conjugate slip. Thin layers with the hexagonal close-packed stacking are observed in association with twinning both at 77 K and room temperature.

36 MATERIALS SCIENCE↗

Topological magnetic hysteresis in single crystals of CeAgSb 2 ferromagnet

Closed-topology magnetic domains are usually observed in thin films and in an applied magnetic field. In this work, we report the observation of rectangular cross-section tubular ferromagnetic domains in thick single crystals of CeAgSb 2 in zero applied field. Relatively low exchange energy, small net magnetic moment, and anisotropic in-plane crystal electric fields lower the domain wall energy and allow for the formation of the closed-topology patterns. The tubular domain structure irreversibly transforms into a dendritic pattern upon cycling the magnetic field. This transition between closed and open topologies results in a ‘topological magnetic hysteresis’— the actual hysteresis in magnetization, not due to the imperfections and pinning, but due to the difference in the pattern morphology. Similar physics was suggested before in pure type-I superconductors and is believed to be a generic feature of other nonlinear single (present case), or two-phase (type-I superconductor) systems where the effects similar to demagnetization (shape-dependent macroscopic variation of properties) lead to pattern formation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

One-step sputtering of MoSSe metastable phase as thin film and predicted thermodynamic stability by computational methods

Abstract We present the fabrication of a MoS 2−x Se x thin film from a co-sputtering process using MoS 2 and MoSe 2 commercial targets with 99.9% purity. The sputtering of the MoS 2 and MoSe 2 was carried out using a straight and low-cost magnetron radio frequency sputtering recipe to achieve a MoS 2−x Se x phase with x = 1 and sharp interface formation as confirmed by Raman spectroscopy, time-of-flight secondary ion mass spectroscopy, and cross-sectional scanning electron microscopy. The sulfur and selenium atoms prefer to distribute randomly at the octahedral geometry of molybdenum inside the MoS 2−x Se x thin film, indicated by a blue shift in the A 1g and E 1 g vibrational modes at 355 cm −1 and 255 cm −1 , respectively. This work is complemented by computing the thermodynamic stability of a MoS 2−x Se x phase whereby density functional theory up to a maximum selenium concentration of 33.33 at.% in both a Janus-like and random distribution. Although the Janus-like and the random structures are in the same metastable state, the Janus-like structure is hindered by an energy barrier below selenium concentrations of 8 at.%. This research highlights the potential of transition metal dichalcogenides in mixed phases and the need for further exploration employing low-energy, large-scale methods to improve the materials’ fabrication and target latent applications of such structures.

36 MATERIALS SCIENCE↗

Which nuclear data can be validated with LLNL pulsed-sphere experiments?

It is shown here that 14-MeV D+T LLNL pulsed-sphere experiments bring complementary information into the process of validating nuclear data compared to experiments that are traditionally used for this purpose—such as critical assemblies. To be more specific, the 14-MeV D+T LLNL pulsed-sphere neutron-leakage spectra enable to validate scattering and fission nuclear data up to 15 MeV (compared to approximately up to 5 MeV when using criticality experiments) and employ to this end simple compound targets containing only few isotopes. In this work, sensitivity profiles of the spectra to nuclear data are calculated in order to understand in detail which isotopes, observables, and energy ranges of nuclear data contribute significantly to their simulation. These profiles are presented for a few selected spheres containing 16 O, 12 C, 56 Fe, and 239 Pu. It is shown that the neutron-leakage spectra of spheres containing light elements are mostly sensitive to elastic- and inelastic-scattering cross sections on discrete levels and corresponding angular distributions. Spheres of structural materials are sensitive to elastic- and inelastic-scattering cross sections, including scattering on discrete levels and the continuum, and double-differential cross sections. Actinide spheres are also strongly sensitive to the fission observables, in particular to the total-fission neutron spectrum. Thin spheres (in which neutrons experience on average less than one scatter) are mostly sensitive to data near the elastic peak, in the energy range from 12–15 MeV, while thicker ones can be sensitive to data at lower incident-neutron energies due to multiple-scattering effects. This information is brought together with simulations of 71 pulsed-sphere neutron-leakage spectra using the ENDF/B-VII.1 and ENDF/B-VIII.0 nuclear-data libraries. This analysis highlights ENDF/B-VIII.0 data that could be further investigated for potential shortcomings ( 6 Li, 12 C, 16 O, 24-26 Mg, 27 Al, 48 Ti, 56 Fe, and 208 Pb) or are likely reliable ( 1,2 H, 7 Li, 9 Be, 14 N, 235,238 U, and 239 Pu) as indicated by validating with LLNL pulsed-sphere experiments.

14-MeV D+T LLNL pulsed-sphere neutron-leakage spec↗