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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.

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At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

12 C(e,e'pN) measurements of short range correlations in the tensor-to-scalar interaction transition region

High-momentum configurations of nucleon pairs at short-distance are probed using measurements of the $^{12}$C$(e,e'p)$ and $^{12}$C$(e,e'pN)$ reactions (where $N$ is either $n$ or $p$), at high-$Q^2$ and $x_B>1.1$. The data span a missing-momentum range of 300--1000 MeV/c and are predominantly sensitive to the transition region of the strong nuclear interaction from a Tensor to Scalar interaction. The data are well reproduced by theoretical calculations using the Generalized Contact Formalism with both chiral and phenomenological nucleon-nucleon ($NN$) interaction models. This agreement suggests that the measured high missing-momentum protons up to $1000$ MeV/c predominantly belong to short-ranged correlated (SRC) pairs. The measured $^{12}$C$(e,e'pN)$ / $^{12}$C$(e,e'p)$ and $^{12}$C$(e,e'pp)$ / $^{12}$C$(e,e'pn)$ cross-section ratios are consistent with a decrease in the fraction of proton-neutron SRC pairs and increase in the fraction of proton-proton SRC pairs with increasing missing momentum. This confirms the transition from an isospin-dependent tensor $NN$ interaction at $\sim 400$ MeV/c to an isospin-independent scalar interaction at high-momentum around $\sim 800$ MeV/c as predicted by theoretical calculation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Preliminary searches for spin-dependent interactions using sidebands of nuclear spin-precession signals

Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A new P-odd and T-odd interaction between polarized and unpolarized nucleons proportional to s⃗⋅r̂ is one such possibility, where r⃗=rr̂ is the spatial vector connecting the nucleons, and s⃗ is the spin of the polarized nucleon. Such an interaction involving a scalar coupling gsN at one vertex and a pseudoscalar coupling gpn at the polarized nucleon vertex can be induced by the exchange of spin-0 pseudoscalar bosons. We describe a new technique to search for interactions of this form and present the first measurements of this type. We show that future improvements to this technique can improve the laboratory upper bound on the product gsNgpn by two orders of magnitude for interaction ranges at the 100 micron scale.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Compact two-electron wave function for bond dissociation and Van der Waals interactions: A natural amplitude assessment

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r{sub 12}) depending on the interelectronic distance r{sub 12}. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r{sub 12}) needs to diverge for large r{sub 12} at large internuclear distances while for shorter bond distances it increases as a function of r{sub 12} to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2022

Ideas on the NASA Senior Review and Mission Extension Process

Extended mission budgets fund a significant part of our community, particularly young scientists who in a relatively short time are exposed to a broad range of experiences and opportunities available in space science and other STEM fields. In particular, mission-funded science offers a relatively stable funding stream that enables meaningful mentoring efforts and interactions, including apprenticeships ranging from project management, to mission operations, to data processing and analysis, to hardware and software development, to STEM-related education and outreach. It moreover provides professional contacts that fuel diversity in mission leadership and in the science and technical workforce at-large. Last but not least, it sustains the scientific productivity of NASA’s missions, which constitute major national investments meriting their full exploitation. Budgets cuts, however, are exercising pressure on the science and operations of the extended mission fleet despite being only a small portion of the overall Division budget. The history of Heliophysics has demonstrated that maintaining the operation of missions beyond their prime phase invariably leads to a much deeper knowledge of the original mission science goals, together with new applications often not foreseen during their original design. Their operation as part of the Heliophysics System Observatory (HSO)---a coordinated, 1eliophysics, multipoint observing system of the heliosphere, is a prime example. Some of the first activities undertaken by the Parker Solar Probe and Solar Orbiter missions required recreating the larger context of their new observations by using the diversity of HSO mission capabilities. The marginal cost of maintaining this valuable, working science resource, in the form of both continuing high quality data access and expertise, is small compared to the cost of the original missions or of new missions to achieve similar objectives, making the operation of extended missions, the best “science per dollar” investment in Heliophysics. We argue that reducing both extended mission operations and science budgets will have a ripple effect across the community, including reducing employment and training opportunities for young scientists, to lowering the quality/impact of the Heliophysics Systems Observatory. Instead, we suggest that the proposal process for mission extension should be re-examined. We offer several ideas for reducing costs of extended missions toward maintaining science output and streamlining the management process.

A. Vourlidas↗
DOE OSTI2016

Local chiral potentials with Δ -intermediate states and the structure of light nuclei

In this paper, we present fully local versions of the minimally nonlocal nucleon-nucleon potentials constructed in a previous paper [Piarulli et al., Phys. Rev. C 91, 024003 (2015)], and use them in hypersperical harmonics and quantum Monte Carlo calculations of ground and excited states of $^3$H, $^3$He, $^4$He, $^6$He, and $^6$Li nuclei. The long-range part of these local potentials includes one- and two-pion exchange contributions without and with $\Delta$-isobars in the intermediate states up to order $Q^3$ ($Q$ denotes generically the low momentum scale) in the chiral expansion, while the short-range part consists of contact interactions up to order $Q^4$. The low-energy constants multiplying these contact interactions are fitted to the 2013 Granada database in two different ranges of laboratory energies, either 0–125 MeV or 0–200 MeV, and to the deuteron binding energy and $nn$ singlet scattering length. Fits to these data are performed for three models characterized by long- and short-range cutoffs, $R_{\rm L}$ and $R_{\rm S}$, respectively, ranging from $(R_{\rm L},R_{\rm S})=(1.2,0.8)$ fm down to $(0.8,0.6)$ fm. Finally, the long-range (short-range) cutoff regularizes the one- and two-pion exchange (contact) part of the potential.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2014

Excitons in a quasi-one-dimensional quantum nanorod under a strong electric field

The response of an exciton in the ground and first excited states to a strong DC electric field is studied in a quasi-one-dimensional nano quantum well (i.e., nanorod) bounded by high symmetric barriers by studying the energy, the oscillator strength, the root-mean-square (RMS) average of the electron-hole (e-h) separation, and the average positions of the electron and the hole. The interplaying effect between the barrier confinement, e-h attraction, and the field-induced e-h separation for exciton binding is examined. We find that, for a long nanorod, the exciton energy, as well as, the oscillator strength drops abruptly as a function of the field near the exciton-dissociation field while the RMS average of the e-h separation rises rapidly. For shorter rods, the transition is more gradual due to the combined effect of the confinement and the long-range e-h interaction. A strong field is shown to transform the optically-inactive first excited state into an optically-active state in the field range between the dissociation field of the ground state and that of the first excited level. We also find that, in the ground state, the (lighter) electron is dragged by the (heavier) hole below the dissociation field. The dependence of the above mentioned properties on the rod length is also investigated for varying fields. The results are compared with those obtained for the rods with parabolic confinement.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Extending the Gutzwiller approximation to intersite interactions

In this work, we develop an extension of the Gutzwiller approximation (GA) formalism that includes the effects of Coulomb interactions of arbitrary range (including density density, exchange, pair hopping, and Coulomb-assisted hopping terms). This formalism reduces to the ordinary GA formalism for the multiband Hubbard models in the presence of only local interactions. This is accomplished by combining the 1 / z expansion—where z is the coordination number, and only the leading-order terms contribute in the limit of infinite dimensions—with a P R † P R - I expansion, where P R is the Gutzwiller projector on the site R . Furthermore, the method is conveniently formulated in terms of a Gutzwiller Lagrange function. We apply our theory to the extended single-band Hubbard model. Similarly to the usual Brinkman-Rice mechanism, we find a Mott transition. A valence skipping transition is observed, where the occupation of the empty and doubly occupied states for the Gutzwiller wave function is enhanced with respect to the uncorrelated Slater determinant wave function.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Residual mean field model of valence quarks in the nucleon

Abstract We develop a non-perturbative model for valence parton distribution functions (PDFs) based on the mean field interactions of valence quarks in the nucleonic interior. The main motivation for the model is to obtain a mean field description of the valence quarks as a baseline to study the short range quark–quark interactions that generate the high x tail of PDFs. The model is based on the separation of the valence three-quark cluster and residual system in the nucleon. Then the nucleon structure function is calculated within the effective light-front diagrammatic approach introducing nonperturbative light-front valence quark and residual wave functions. Within the model a new relation is obtained between the position, $$x_p$$ x p , of the peak of $$xq_V(x)$$ x q V ( x ) distribution of the valence quark and the effective mass of the residual system, $$m_R$$ m R , in the form: $$x_{p} \approx {1\over 4} (1-{m_R\over m_N})$$ x p ≈ 1 4 ( 1 - m R m N ) at starting $$Q^2$$ Q 2 . This relation explains the difference in the peak positions for d- and u-quarks through the expected difference of residual masses for valence d- and u-quark distributions. The parameters of the model are fixed by fitting the calculated valence quark distributions to the phenomenological PDFs. This allowed us to estimate the overall mean field contribution in baryonic and momentum sum rules for valence d- and u-quarks. Finally, the evaluated parameters of the non-perturbative wave functions of valence 3q-cluster and residual system can be used in calculation of other quantities such as nucleon form factors, generalized partonic and transverse momentum distributions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Extending accurate spectral induced polarization measurements into the kHz range: modelling and removal of errors from interactions between the parasitic capacitive coupling and the sample holder

SUMMARY Spectral induced polarization (SIP), describing the measurement of the frequency domain electrical impedance magnitude and phase of porous materials, has been widely used to characterize subsurface hydrological/biogeochemical properties and processes. SIP data collected at frequencies higher than 100 Hz are expected to describe the polarization of small particles providing insights into the physicochemical properties of clays, nanoparticles and microorganisms. However, the phase measurements at these high frequencies are often contaminated by errors due to the parasitic capacitive coupling of the SIP instrument, especially for lower conductivity samples. We developed a model showing the measured phase is the sum of the true sample phase and an error term ωCinZx, where ω is the angular frequency; Cin is the instrument input capacitance and Zx is a measurable impedance function related to the sample holder properties and the reference resistor. Based on this model, a new phase correction method is proposed that results in highly accurate SIP data up to 20 kHz as well as the determination of Cin. We tested the correction method using electric circuits, NaCl fluids and three unconsolidated samples (sand, sand-clay and sand-pyrite mixtures). The corrected phase for the circuit and NaCl fluid experiments showed excellent agreement with the theoretical phase response across the studied frequency range (errors <1 mrad). For unconsolidated samples, removal of errors results in phase spectra more consistent with expected polarization mechanisms, as based on phase peaks recorded for small pyrite and clay particles at high frequencies. These phase peaks could not be identified in the uncorrected data. Our approach can substantially enhance the value of the SIP method for the characterization of fine-grained sediments and rocks.

58 GEOSCIENCES↗
DOE OSTI2020

Nanoscale degeneracy lifting in a geometrically frustrated antiferromagnet

The local atomic and magnetic structures of the compounds A MnO 2 (A = Na, Cu), which realize a geometrically frustrated, spatially anisotropic triangular lattice of Mn spins, have been investigated by atomic and magnetic pair distribution function analysis of neutron total scattering data. Relief of frustration in CuMnO 2 is accompanied by a conventional cooperative symmetry-lowering lattice distortion driven by Néel order. In NaMnO 2 , however, the distortion has a short-range nature. A cooperative interaction between the locally broken symmetry and short-range magnetic correlations lifts the magnetic degeneracy on a nanometer length scale, enabling long-range magnetic order in the Na derivative. The degree of frustration, mediated by residual disorder, contributes to the rather differing pathways to a single, stable magnetic ground state in these two related compounds. This study demonstrates how nanoscale structural distortions that cause local-scale perturbations can lift the ground-state degeneracy and trigger macroscopic magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Partial muon capture rates in A = 3 and A = 6 nuclei with chiral effective field theory

Searches for neutrinoless-double beta decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless-double beta decays take place at momentum transfers on the order of 100 MeV/$c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this work, we present results of {\it ab initio} calculations of partial muon capture rates for $^3$He and $^6$Li nuclei using variational and Green's Function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon ($2N$) interactions, and the energy range of $2N$ scattering data used to fit these interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

Studies of aerothermal loads generated in regions of shock/shock interaction in hypersonic flow

Experimental studies were conducted to examine the aerothermal characteristics of shock/shock/boundary layer interaction regions generated by single and multiple incident shocks. The presented experimental studies were conducted over a Mach number range from 6 to 19 for a range of Reynolds numbers to obtain both laminar and turbulent interaction regions. Detailed heat transfer and pressure measurements were made for a range of interaction types and incident shock strengths over a transverse cylinder, with emphasis on the 3 and 4 type interaction regions. The measurements were compared with the simple Edney, Keyes, and Hains models for a range of interaction configurations and freestream conditions. The complex flowfields and aerothermal loads generated by multiple-shock impingement, while not generating as large peak loads, provide important test cases for code prediction. The detailed heat transfer and pressure measurements proved a good basis for evaluating the accuracy of simple prediction methods and detailed numerical solutions for laminar and transitional regions or shock/shock interactions.

Holden, Michael S.↗
DOE OSTI2024

Quantum simulation of an extended Dicke model with a magnetic solid

Abstract The Dicke model describes the cooperative interaction of an ensemble of two-level atoms with a single-mode photonic field and exhibits a quantum phase transition as a function of light–matter coupling strength. Extending this model by incorporating short-range atom–atom interactions makes the problem intractable but is expected to produce new physical phenomena and phases. Here, we simulate such an extended Dicke model using a crystal of ErFeO 3 , where the role of atoms (photons) is played by Er 3+ spins (Fe 3+ magnons). Through terahertz spectroscopy and magnetocaloric effect measurements as a function of temperature and magnetic field, we demonstrated the existence of a novel atomically ordered phase in addition to the superradiant and normal phases that are expected from the standard Dicke model. Further, we elucidated the nature of the phase boundaries in the temperature–magnetic-field phase diagram, identifying both first-order and second-order phase transitions. These results lay the foundation for studying multiatomic quantum optics models using well-characterized many-body solid-state systems.

Marquez Peraca, Nicolas↗
DOE OSTI2019

Tracking Aerosol Convective Interactions Experiment (TRACER) Science Plan

Convective clouds play an important role in the Earth’s climate system as a driver of large-scale circulations and a primary mechanism for the transport of heat, moisture, aerosols, and momentum throughout the troposphere. Despite their climatic importance, multi-scale models continue to have persistent biases produced by insufficient representation of convective clouds. This is the result of an incomplete understanding of key processes such as convective initiation, updraft and downdraft dynamics, cloud and precipitation microphysics, and aerosol-convection interactions. The Aerosol-Cloud-Precipitation-Climate Initiative, an international research group dedicated to advancing understanding of aerosol impacts on clouds relevant to climate, has identified the Houston, Texas region as an optimal location for targeted studies of aerosol-convection interactions within frequently developing isolated deep convection. Houston lies within a humid subtropical climate regime, where onshore flow and sea-breeze convection interact with a range of aerosol conditions associated with Houston’s urban and industrial emissions. Pilot studies have suggested that convective clouds in this region are potentially significantly impacted by the varying aerosol conditions. To increase our understanding of convective cloud life cycles and aerosol-convection interactions, the Tracking Aerosol Convection Interactions Experiment (TRACER) aims to collect a comprehensive data set focused on the evolution of convective clouds and the environment (including aerosol, cloud, thermodynamics, and lightning) in which the clouds initiate, grow, and decay. A unique component of TRACER is that a large number of individual, isolated convective cells will be tracked and measured in high spatial and temporal resolution for the purposes of: (i) Characterizing and linking convective cloud kinematic and microphysical life cycles, (ii) Quantifying environmental thermodynamic and kinematic controls on convective life cycle properties, (iii) Isolating and quantifying the impacts of aerosol properties on convective cloud kinematic and microphysical evolution. TRACER includes a one-year deployment of the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility’s first ARM Mobile Facility (AMF1) and second-generation C-Band Scanning ARM Precipitation Radar (CSAPR2) aimed at collecting statistical data sets of cloud, precipitation, atmospheric state, and aerosol under varying aerosol loading and local circulation (sea breeze and urban heat island) conditions. A four-month intensive operational period (IOP) from June through September will include deployment of an ancillary site with aerosol, atmospheric state, and precipitation measurements at a location rarely impacted by Houston’s anthropogenic emissions, which will be commonplace near the AMF1 site. Convective cell tracking by the CSAPR2 will provide high-resolution polarimetric and velocity observations under a range of environmental (including aerosol loading) conditions. High-frequency radiosonde launches will capture quickly evolving thermodynamic and kinematic conditions near convective cells, a requirement for isolating aerosol effects on clouds. TRACER will additionally leverage a lightning mapping array, surface meteorological networks, and air pollution networks, and proposals will be entered to deploy additional mobile radar and radiosonde assets during the IOP. This unique combination of cloud, precipitation, lightning, aerosol, and atmospheric state measurements associated with tracked convective cells will ultimately improve our understanding of the convective cloud life cycle and its interaction with individual environmental factors such that improved, next-generation cumulus, microphysics, turbulence, and aerosol parameterizations can be designed.

Convective clouds, aerosols, cloud life cycle, atm↗
DOE OSTI2024

Role of Dynamic Polarization Interactions in the Electrical Double Layer at Calcite (104) Interfaces with Aqueous Solutions

Reactions at mineral interfaces with aqueous solutions control many geochemical and biogeochemical processes in the Earth’s critical zone. At the molecular level, insights into important properties such as the structure of the electrical double layer (EDL) at specific mineral interfaces continue to improve due to the increasing fidelity of laboratory instrumentation and computational approaches. However, molecular simulation approaches suffer from limited reach into relevant scales of time, length, and system complexity. To span this gap, a novel hybrid approach that couples first principle plane-wave density functional theory (DFT) with classical DFT (cDFT) is demonstrated and applied to calcite (104) interfaces with various electrolytes. In this approach, a region of interest described using DFT interacts with the surrounding medium described using cDFT to arrive at a self-consistent ground state. Benchmarking against experimental observations and entirely first principle DFT simulations demonstrates that this hybrid model efficiently encompasses the key short-range and collective interactions in the EDL. Simulations of calcite (104)/solution interfaces reveal the key static and dynamic polarization interactions that give rise to structuring of ions and water. Ion hydration interactions have the strongest effect on the depth of the first minimum in the density distribution of counterions at the surface, and the position and width of the first density peak is largely determined by the strength of ion-correlation forces. Finer details of ion distributions are controlled by mutual polarization of the calcite surface and interfacial electrolyte. Finally, this new ability to efficiently and rigorously predict EDL structure at mineral surfaces in contact with complex solutions paves the way to accurately modeling sorption, nucleation, dissolution, and growth in realistic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Solute atmospheres at dislocations

In this study, a two-dimensional plane strain elastic solution is determined for the Cottrell solute atmosphere around an edge dislocation in an infinitely long cylinder of finite radius (the matrix), in which rows of solutes are represented by cylindrical rods with in-plane hydrostatic misfit (axial misfit is also considered). The periphery of the matrix is traction-free, thus introducing an image solute field which generates a solute-solute interaction energy that has not been considered previously. The relevant energy for the field of any distribution of solutes coexistent with a single edge dislocation along the (matrix) cylinder axis is determined, and coherency effects are discussed and studied. Monte Carlo simulations accounting for all pertinent interactions over a range of temperatures are found to yield solute distributions different from classical results, namely, (1) Fermi-Dirac condensations at low temperatures at the free surface, (2) the majority of the atmosphere lying within an unexpectedly large non-linear interaction region near the dislocation core, and (3) temperature-dependent asymmetrical solute arrangements that promote bending. The solute distributions at intermediate temperatures show a 1/r dependence in agreement with previous linearized approximations. With a standard state of solute corresponding to a mean concentration, c 0 , the relevant interaction energy expression presented in this work is valid when extended to large concentrations for which Henry's Law and Vegard's Law do not apply.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Solid Oganesson via a Many-Body Interaction Expansion Based on Relativistic Coupled-Cluster Theory and from Plane-Wave Relativistic Density Functional Theory

In this work, many-body potentials up to fourth order in the expansion are constructed using non-relativistic, scalar-relativistic and relativistic coupled-cluster theory to accurately describe the interaction between superheavy oganesson atoms. The obtained distance dependent energy values were fitted to extended two-body Lennard-Jones and three-body Axilrod-Teller-Muto potentials, with the fourth-order term treated through a classical long-range Drude dipole interaction model. From these interac tion potentials, spectroscopic constants for the oganesson dimer and solid state properties were obtained. Furthermore, these high-level results are compared to scalar relativistic and two-component plane-wave DFT calculations based on a tailor-made projector augmented-wave pseudopotential (PAW-PP) and newly derived parameters for Grimme’s dispersion correction. It is shown that the functionals PBE-D3(BJ), PBEsol and in particular SCAN provide excellent agreement with the many-body ref erence for solid Og. Finally, the results for Og are compared and related to the lighter rare gas elements and periodic trends are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2005

Measurement of Recoil Losses and Ranges for Spallation Products Produced in Proton Interactions with Al, Si, Mg at 200 and 500 MeV

Cosmic rays interact with extraterrestrial materials to produce a variety of spallation products. If these cosmogenic nuclides are produced within an inclusion in such material, then an important consideration is the loss of the product nuclei, which recoil out of the inclusion. Of course, at the same time, some atoms of the product nuclei under study may be knocked into the inclusion from the surrounding material, which is likely to have a different composition to that of the inclusion [1]. For example, Ne-21 would be produced in presolar grains, such as SiC, when irradiated in interstellar space. However, to calculate a presolar age, one needs to know how much 21Ne is retained in the grain. For small grains, the recoil losses might be large [2, 3] To study this effect under laboratory conditions, recoil measurements were made using protons with energies from 66 - 1600 MeV on Si, Al and Ba targets [3, 4, 5].

Sisterson, J. M.↗