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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Photoluminescence line shapes of nanocrystals: Contributions from first- and second-order vibronic couplings

Here, we present a microscopic, parameter-free approach for computing the photoluminescence spectra of a single semiconductor nanocrystal. The method derives exciton–phonon coupling directly from the semi-empirical pseudopotential framework and systematically incorporates both diagonal and off-diagonal exciton-phonon interactions, expanded to second-order in the phonon coordinates. The dipole–dipole correlation function was calculated using a Dyson expansion within the Kubo–Toyozawa formalism, enabling a consistent description of the role of pure dephasing and population transfer on the photoluminescence spectral features. Applied to CdSe/CdS core–shell nanocrystals, the approach quantitatively reproduces experimental photoluminescence spectra over a wide temperature range, revealing that quadratic phonon couplings account for nearly half of the homogeneous linewidth above ≈ 100−150 K, while off-diagonal couplings leading to exciton thermalization play only a minor role and only as T → 300 K.

Dephasing Rate↗
DOE OSTI2025

A Parallel Alternative for Energy-Efficient Neural Network Training and Inferencing

Energy efficiency of training and inferencing with large neural network models is a critical challenge facing the future of sustainable large-scale machine learning workloads. This paper introduces an alternative strategy, called phantom parallelism, to minimize the net energy consumption of traditional tensor (model) parallelism, the most energy-inefficient component of large neural network training. The approach is presented in the context of feed-forward network architectures as a preliminary, but comprehensive, proof-of-principle study of the proposed methodology. We derive new forward and backward propagation operators for phantom parallelism, implement them as custom autograd operations within an end-to-end phantom parallel training pipeline and compare its parallel performance and energy-efficiency against those of conventional tensor parallel training pipelines. Formal analyses that predict lower bandwidth and FLOP counts are presented with supporting empirical results on up to 256 GPUs that corroborate these gains. Experiments are shown to deliver ∼50% reduction in the energy consumed to train FFNs using the proposed phantom parallel approach when compared with conventional tensor parallel methods. Additionally, the proposed approach is shown to train smaller phantom models to the same model loss on smaller GPU counts as larger tensor parallel models on larger GPU counts offering the possibility for even greater energy savings.

Seal, Sudip [ORNL] (ORCID:0000000332330656)↗
DOE OSTI2015

SU-E-T-364: Estimating the Minimum Number of Patients Required to Estimate the Required Planning Target Volume Margins for Prostate Glands

Purpose: To establish a minimum number of patients required to obtain statistically accurate Planning Target Volume (PTV) margins for prostate Intensity Modulated Radiation Therapy (IMRT). Methods: A total of 320 prostate patients, consisting of a total number of 9311 daily setups, were analyzed. These patients had gone under IMRT treatments. Daily localization was done using the skin marks and the proper shifts were determined by the CBCT to match the prostate gland. The Van Herk formalism is used to obtain the margins using the systematic and random setup variations. The total patient population was divided into different grouping sizes varying from 1 group of 320 patients to 64 groups of 5 patients. Each grouping was used to determine the average PTV margin and its associated standard deviation. Results: Analyzing all 320 patients lead to an average Superior-Inferior margin of 1.15 cm. The grouping with 10 patients per group (32 groups) resulted to an average PTV margin between 0.6–1.7 cm with the mean value of 1.09 cm and a standard deviation (STD) of 0.30 cm. As the number of patients in groups increases the mean value of average margin between groups tends to converge to the true average PTV of 1.15 cm and STD decreases. For groups of 20, 64, and 160 patients a Superior-Inferior margin of 1.12, 1.14, and 1.16 cm with STD of 0.22, 0.11, and 0.01 cm were found, respectively. Similar tendency was observed for Left-Right and Anterior-Posterior margins. Conclusion: The estimation of the required margin for PTV strongly depends on the number of patients studied. According to this study at least ∼60 patients are needed to calculate a statistically acceptable PTV margin for a criterion of STD < 0.1 cm. Numbers greater than ∼60 patients do little to increase the accuracy of the PTV margin estimation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Thermodynamics-informed latent space dynamics identification

This software showcases a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism. An abstract error estimate is established, which provides a new loss formulation involving the Jacobian computation of autoencoder. The autoencoder and the latent dynamics are simultaneously trained to minimize the new loss. Computational examples demonstrate the effectiveness of tLaSDI, which exhibits robust generalization ability, even in extrapolation. In addition, an intriguing correlation is empirically observed between a quantity from tLaSDI in the latent space and the behaviors of the full-state solution.

Cheung, Siu Wun↗
DOE OSTI2023

Measurements and computational analysis of the natural decay of 176 Lu

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176 Lu forbidden β decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments. Purpose: Perform the first precision measurements of 176 Lu β-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176 Lu β-decay Q value. Compare the shape of the precisely determined experimental β spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement. Method: Here, the 176 Lu β-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The β decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The β-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach. Results: Both β transitions of 176 Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of 6.3×10 –6 relative to its β decays. The 176 Lu β-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise β end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary β decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The β-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions. Conclusion: The implemented self-scintillation method has provided unmatched observations of 176 Lu, independently validated by the first direct measurements of its β-decay Q value by Penning trap mass spectrometry. Theoretical study of the main β transition led to the extraction of very different effective gA and log10f values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Investigating the Implications of a Variable RBE on Proton Dose Fractionation Across a Clinical Pencil Beam Scanned Spread-Out Bragg Peak

Purpose: To investigate the clinical implications of a variable relative biological effectiveness (RBE) on proton dose fractionation. Using acute exposures, the current clinical adoption of a generic, constant cell killing RBE has been shown to underestimate the effect of the sharp increase in linear energy transfer (LET) in the distal regions of the spread-out Bragg peak (SOBP). However, experimental data for the impact of dose fractionation in such scenarios are still limited. Methods and Materials: Human fibroblasts (AG01522) at 4 key depth positions on a clinical SOBP of maximum energy 219.65 MeV were subjected to various fractionation regimens with an interfraction period of 24 hours at Proton Therapy Center in Prague, Czech Republic. Cell killing RBE variations were measured using standard clonogenic assays and were further validated using Monte Carlo simulations and parameterized using a linear quadratic formalism. Results: Significant variations in the cell killing RBE for fractionated exposures along the proton dose profile were observed. RBE increased sharply toward the distal position, corresponding to a reduction in cell sparing effectiveness of fractionated proton exposures at higher LET. The effect was more pronounced at smaller doses per fraction. Experimental survival fractions were adequately predicted using a linear quadratic formalism assuming full repair between fractions. Data were also used to validate a parameterized variable RBE model based on linear α parameter response with LET that showed considerable deviations from clinically predicted isoeffective fractionation regimens. Conclusions: The RBE-weighted absorbed dose calculated using the clinically adopted generic RBE of 1.1 significantly underestimates the biological effective dose from variable RBE, particularly in fractionation regimens with low doses per fraction. Coupled with an increase in effective range in fractionated exposures, our study provides an RBE dataset that can be used by the modeling community for the optimization of fractionated proton therapy.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

Elastic Green’s Function in Anisotropic Bimaterials Considering Interfacial Elasticity

Here, the two-dimensional elastic Green’s function is calculated for a general anisotropic elastic bimaterial containing a line dislocation and a concentrated force while accounting for the interfacial structure by means of a generalized interfacial elasticity paradigm. The introduction of the interface elasticity model gives rise to boundary conditions that are effectively equivalent to those of a weakly bounded interface. The equations of elastic equilibrium are solved by complex variable techniques and the method of analytical continuation. The solution is decomposed into the sum of the Green’s function corresponding to the perfectly bonded interface and a perturbation term corresponding to the complex coupling nature between the interface structure and a line dislocation/concentrated force. Such construct can be implemented into the boundary integral equations and the boundary element method for analysis of nano-layered structures and epitaxial systems where the interface structure plays an important role.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Hydride and Seek: Comparing Crystallographic Hydride Placement Techniques with an Open-Shell Cobalt Complex

Locating hydrides is crucial in organometallic chemistry but difficult to do accurately using X-ray diffraction. Electron diffraction has been proposed as a way to overcome this problem but has not been systematically compared to neutron diffraction and to quantum crystallography (Hirshfeld atom refinement, HAR) to test this hypothesis. Here, we present a comparative analysis of methods for a terminal cobalt hydride complex by comparing a single-crystal neutron diffraction reference structure to results from single-crystal X-ray diffraction with and without Hirshfeld atom refinement (HAR, NoSpherA2), density functional theory (DFT), and electron diffraction (3D-ED/MicroED) refined under kinematical and dynamical formalisms. Conventional X-ray diffraction gives lower precision than neutron diffraction as expected. Despite expected improvements, HAR gives systematic deviation from the neutron benchmark. Interestingly, optimized DFT equilibrium geometries are closer to the neutron value than the value from HAR. On the other hand, electron diffraction with a high-quality data set coupled with dynamical refinement localizes the hydride in difference maps and gives excellent agreement with the neutron data. Dynamical refinement is crucial, as kinematical refinement does not allow assignment of a hydride peak. This cross-modal comparison defines the conditions under which 3D-ED/MicroED delivers high-precision metal–hydride distances for this open-shell cobalt hydride.

anions↗
DOE OSTI2015

A new approach to the analysis of the phase space of f(R)-gravity

We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models which cannot be investigated using the standard technique. Differently form previously proposed similar techniques, the new method is constructed in such a way to associate to the fixed points scale factors, which contain four integration constants (i.e. solutions of fourth order differential equations). In this way a new light is shed on the physical meaning of the fixed points. We apply this technique to some f(R) Lagrangians relevant for inflationary and dark energy models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

From Optimization to Sampling Through Gradient Flows

Optimization and sampling algorithms play a central role in science and engineering as they enable finding optimal predictions, policies, and recommendations, as well as expected and equilibrium states of complex systems. The notion of “optimality” is formalized by the choice of an objective function, while the notion of an “expected” state is specified by a probabilistic model for the distribution of states. Optimizing rugged objective functions and sampling multimodal distributions is computationally challenging, especially in high-dimensional problems. Here, for this reason, many optimization and sampling methods have been developed by researchers working in disparate fields such as Bayesian statistics, molecular dynamics, genetics, quantum chemistry, machine learning, weather forecasting, econometrics, and medical imaging.

Trillos, N. García↗
DOE OSTI2014

Correlation matrix renormalization approximation for total-energy calculations of correlated electron systems

We generalized the commonly used Gutzwiller approximation for calculating the electronic structure and total energy of strongly correlated electron systems. In our method, the evaluation of one-body and two-body density matrix elements of the Hamiltonian is simplified using a renormalization approximation to achieve better scaling of the computational effort as a function of system size. To achieve a clear presentation of the concept and methodology, we describe the detailed formalism for a finite hydrogen system with minimal basis set. We applied the correlation matrix renormalization approximation approach to a H 2 dimer and H 8 cubic fragment with minimal basis sets, as well as a H 2 molecule with a large basis set. The results compare favorably with sophisticated quantum chemical calculations. We believe our approach can serve as an alternative way to build up the exchange-correlation energy functional for an improved density functional theory description of systems with strong electron correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Generalized multiband typical medium dynamical cluster approximation: Application to (Ga,Mn)N

We generalize the multiband typical medium dynamical cluster approximation and the formalism introduced by Blackman, Esterling, and Berk so that it can deal with localization in multiband disordered systems with both diagonal and off-diagonal disorder with complicated potentials. We also introduce an ansatz for the momentum-resolved typical density of states that greatly improves the numerical stability of the method while preserving the independence of scattering events at different frequencies. Starting from the first-principles effective Hamiltonian, we apply this method to the diluted magnetic semiconductor Ga 1 - x Mn x N , and find the impurity band is completely localized for Mn concentrations x < 0.03 , while for 0.03 < x < 0.10 the impurity band has delocalized states but the chemical potential resides at or above the mobility edge. So, the system is always insulating within the experimental compositional limit ( x ≈ 0.10 ) due to Anderson localization. But, for 0.03 < x < 0.10 hole doping could make the system metallic, allowing double-exchange mediated, or enhanced, ferromagnetism. Finally, this developed method is expected to have a large impact on first-principles studies of Anderson localization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2013

Global Identification of Previously Undetected Pre-Satellite-Era Tropical Cyclone Candidates in NOAA/CIRES Twentieth-Century Reanalysis Data

Prior to the satellite era, limited synoptic observation networks led to an indefinite number of tropical cyclones (TCs) remaining undetected. This period of decreased confidence in the TC climatological record includes the first two-thirds of the twentieth century. While prior studies found that this undersampling exists, disagreement regarding its magnitude has caused difficulties in interpreting multidecadal changes in TC activity. Previous research also demonstrated that reanalyses can be used to extend TC climatology, utilizing the NOAA/Cooperative Institute for Research in Environmental Sciences (CIRES) Twentieth-Century Reanalysis to manually identify previously unknown Atlantic Ocean basin potential TCs. This study expands the spatiotemporal scope of the earlier work by presenting a filtering algorithm that dramatically improves the efficiency with which candidate events are identified in the reanalysis. This algorithm was applied to all tropical basins for the years 1871–1979, resulting in the first quantitative and objective global TC candidate event counts for the decades prior to formal recordkeeping. Observational verification performed on a subset of these events indicates that the algorithm identifies potential missing TCs at a success rate approximating that of earlier work with a significant decrease in the amount of time required. Extrapolating these proportions to all of the candidate events identified suggests that this method may help to locate hundreds of previously unknown TCs worldwide for future study and cataloging. As such, the dataset produced by this research is a source of independent guidance for use in ongoing and future TC climatology revision efforts to produce a more complete historical record more quickly than with current methods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Scaling Turbulent Combustion Fields in Explosions

We considered the topic of explosions from spherical high-explosive (HE) charges. We studied how the turbulent combustion fields scale. On the basis of theories of dimensional analysis by Bridgman and similarity theories of Sedov and Barenblatt, we found that all fields scaled with the explosion length scale r0. This included the blast wave, the mean and root mean squared (RMS) profiles of thermodynamic variables, combustion variables, velocities, vorticity, and turbulent Reynolds stresses. This was a consequence of the formulation of the problem and our numerical method, which both satisfied the similarity conditions of Sedov. We performed numerical simulations of 1 g charges and 1 kg charges; the solutions were identical (within roundoff error) when plotted in scaled variables. We also explored scaling laws related to three-phase pyrotechnic explosions. We show that although the scaling formally broke down, the fireball still essentially scaled with the explosion length scale r0. However, the discrete Lagrange particles (DLP) (phase 2) and the heterogeneous continuum model (HCM) of the DLP wakes (phase 3) did not scale with r0, and mean and RMS profiles could differ by a factor of 10 in some regions. This was because the DLP particles and wakes introduced an additional scale that broke the similarity conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Semi-local Density Functional Approximations for Bulk, Surface, and Confinement Physics

Due to its balance of accuracy and computational cost, density functional theory has become the method of choice for computing the electronic structure and related properties of materials. However, present-day semi-local approximations to the exchange-correlation energy of density functional theory break down for materials containing d and f electrons. In this report we summarize the results of our research efforts within the LDRD 200202 titled "Making density functional theory work for all materials" in addressing this issue. Our efforts are grouped into two research thrusts. In the first thrust, we develop an exchange-correlation functional (BSC functional) within the subsystem functional formalism. It enables us to capture bulk, surface, and confinement physics with a single, semi-local exchange-correlation functional in density functional theory calculations. We present the analytical properties of the BSC functional and demonstrate that the BSC functional is able to capture confinement physics more accurately than standard semi-local exchange-correlation functionals. The second research thrust focusses on developing a database for transition metal binary compounds. The database consists of materials properties (formation energies, ground-state energies, lattice constants, and elastic constants) of 26 transition metal elements and 89 transition metal alloys. It serves as a reference for benchmarking computational models (such as lower-level modeling methods and exchange-correlation functionals). We expect that our database will significantly impact the materials science community. We conclude with a brief discussion on the future research directions and impact of our results.

36 MATERIALS SCIENCE↗
DOE OSTI2014

ITAR: A modified TAR method to determine depth dose distribution for an ophthalmic device that performs kilovoltage x-ray pencil-beam stereotaxy

Purpose: New technology has been developed to treat age-related macular degeneration (AMD) using 100 kVp pencil-beams that enter the patient through the radio-resistant sclera with a depth of interest between 1.6 and 2.6 cm. Measurement of reference and relative dose in a kilovoltage x-ray beam with a 0.42 cm diameter field size and a 15 cm source to axis distance (SAD) is a challenge that is not fully addressed in current guidelines to medical physicists. AAPM's TG-61 gives dosimetry recommendations for low and medium energy x-rays, but not all of them are feasible to follow for this modality. Methods: An investigation was conducted to select appropriate equipment for the application. PTW's Type 34013 Soft X-Ray Chamber (Freiburg, Germany) and CIRS's Plastic Water LR (Norfolk, VA) were found to be the best available options. Attenuation curves were measured with minimal scatter contribution and thus called Low Scatter Tissue Air Ratio (LSTAR). A scatter conversion coefficient (C{sub scat}) was derived through Monte Carlo radiation transport simulation using MCNPX (LANL, Los Alamos, NM) to quantify the difference between a traditional TAR curve and the LSTAR curve. A material conversion coefficient (C{sub mat}) was determined through experimentation to evaluate the difference in attenuation properties between water and Plastic Water LR. Validity of performing direct dosimetry measurements with a source to detector distance other than the treatment distance, and therefore a different field size due to a fixed collimator, was explored. A method—Integrated Tissue Air Ratio (ITAR)—has been developed that isolates each of the three main radiological effects (distance from source, attenuation, and scatter) during measurement, and integrates them to determine the dose rate to the macula during treatment. Results: LSTAR curves were determined to be field size independent within the range explored, indicating that direct dosimetry measurements may be performed with a source to detector distance of 20 cm even though the SAD is 15 cm during treatment. C{sub scat} varied from 1.102 to 1.106 within the range of depths of interest. The experimental variance among repeated measurements of C{sub mat} was larger than depth dependence, so C{sub mat} was estimated as1.019 for all depths of interest. Conclusions: Equipment selection, measurement techniques, and formalism for the determination of dose rate to the macula during stereotaxy for AMD have been determined and are strongly recommended by the authors of this paper to be used by clinical medical physicists.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2015

Development of a phantom to validate high-dose-rate brachytherapy treatment planning systems with heterogeneous algorithms

Purpose: This work presents the development of a phantom to verify the treatment planning system (TPS) algorithms used for high-dose-rate (HDR) brachytherapy. It is designed to measure the relative dose in a heterogeneous media. The experimental details used, simulation methods, and comparisons with a commercial TPS are also provided. Methods: To simulate heterogeneous conditions, four materials were used: Virtual Water™ (VM), BR50/50™, cork, and aluminum. The materials were arranged in 11 heterogeneity configurations. Three dosimeters were used to measure the relative response from a HDR {sup 192}Ir source: TLD-100™, Gafchromic{sup ®} EBT3 film, and an Exradin™ A1SL ionization chamber. To compare the results from the experimental measurements, the various configurations were modeled in the PENELOPE/penEasy Monte Carlo code. Images of each setup geometry were acquired from a CT scanner and imported into BrachyVision™ TPS software, which includes a grid-based Boltzmann solver Acuros™. The results of the measurements performed in the heterogeneous setups were normalized to the dose values measured in the homogeneous Virtual Water™ setup and the respective differences due to the heterogeneities were considered. Additionally, dose values calculated based on the American Association of Physicists in Medicine-Task Group 43 formalism were compared to dose values calculated with the Acuros™ algorithm in the phantom. Calculated doses were compared at the same points, where measurements have been performed. Results: Differences in the relative response as high as 11.5% were found from the homogeneous setup when the heterogeneous materials were inserted into the experimental phantom. The aluminum and cork materials produced larger differences than the plastic materials, with the BR50/50™ material producing results similar to the Virtual Water™ results. Our experimental methods agree with the PENELOPE/penEasy simulations for most setups and dosimeters. The TPS relative differences with the Acuros™ algorithm were similar in both experimental and simulated setups. The discrepancy between the BrachyVision™, Acuros™, and TG-43 dose responses in the phantom described by this work exceeded 12% for certain setups. Conclusions: The results derived from the phantom measurements show good agreement with the simulations and TPS calculations, using Acuros™ algorithm. Differences in the dose responses were evident in the experimental results when heterogeneous materials were introduced. These measurements prove the usefulness of the heterogeneous phantom for verification of HDR treatment planning systems based on model-based dose calculation algorithms.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2014

TH-C-19A-01: Analytic Design Method to Make a 2D Planar, Segmented Ion Chamber Water-Equivalent for Proton Dose Measurements

Purpose: Quality Assurance (QA) measurements of proton therapy fields must accurately measure steep longitudinal dose gradients as well as characterize the dose distribution laterally. Currently, available devices for two-dimensional field measurements perturb the dose distribution such that routine QA measurements performed at multiple depths require multiple field deliveries and are time consuming. Methods: A design procedure for a two-dimensional detector array is introduced whereby the proton energy loss and scatter are adjusted so that the downstream dose distribution is maintained to be equivalent to that which would occur in uniform water. Starting with the design for an existing, functional two-dimensional segmented ion chamber prototype, a compensating material is introduced downstream of the detector to simultaneously equate the energy loss and lateral scatter in the detector assembly to the values in water. An analytic formalism and procedure is demonstrated to calculate the properties of the compensating material in the general case of multiple layers of arbitrary material. The resulting design is validated with Monte Carlo simulations. Results: With respect to the specific prototype design considered, the results indicate that a graphite compensating layer of the proper dimensions can yield proton beam range perturbation less than 0.1mm and beam sigma perturbation less than 2% across the energy range of therapeutic proton beams. Conclusion: We have shown that, for a 2D gas-filled detector array, a graphite-compensating layer can balance the energy loss and multiple Coulomb scattering relative to uniform water. We have demonstrated an analytic formalism and procedure to determine a compensating material in the general case of multiple layers of arbitrary material. This work was supported by the US Army Medical Research and Materiel Command under Contract Agreement No. DAMD17-W81XWH-04-2-0022. Opinions, interpretations, conclusions and recommendations are those of the author and are not necessarily endorsed by the US Army.

07 ISOTOPE AND RADIATION SOURCES↗