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Articles 91 - 120 of 120
Full-Text Articles in Physics
Fabrication And Measurements Of 500 Mhz Superconducting Double Spoke Cavity, Hyekyoung Park, C. S. Hopper, J. R. Delayen
Fabrication And Measurements Of 500 Mhz Superconducting Double Spoke Cavity, Hyekyoung Park, C. S. Hopper, J. R. Delayen
Physics Faculty Publications
The 500 MHz double spoke cavity has been designed for a high velocity application such as a compact electron accelerator at Center for Accelerator Science at Old Dominion University and is being built at Jefferson Lab. The geometry specific to the double spoke cavity requires a variety of tooling and fixtures. Also a number of joints are expected to make it difficult to maintain the geometric deviation from the design minimal. This paper will report the fabrication technique, resulting tolerance from the design, and comparison between the measurements and simulations.
A Compact Beam Spreader Using Rf Deflecting Cavities For The Lcls-Ii, S.U. De Silva, J. R. Delayen, R. G. Olave, L. Doolittle, P. Emma
A Compact Beam Spreader Using Rf Deflecting Cavities For The Lcls-Ii, S.U. De Silva, J. R. Delayen, R. G. Olave, L. Doolittle, P. Emma
Physics Faculty Publications
The LCLS-II project currently under development is designed to accelerate electron bunches up to 4 GeV and transport them to one of two FEL undulators located more than 2 km downstream of the end of the LCLS-II linac. The upgrade requires a spreader system to separate the baseline electron bunches and transport them to two undulator lines or a local dump. Fast bipolar kickers (FK) or transverse electric rf deflectors (RFD) are considered as fast-switching devices (FSD). In the RFD approach described here three design options operating at 325 MHz are studied including a superconducting rf-dipole cavity, a normal conducting …
Compilation And Comparison Of Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist
Compilation And Comparison Of Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist
Senior Theses and Projects
The continuous-slow-down approximation (CSDA) is used to create a simple composite analytical formula to estimate the range or maximum penetration depth of bombarding electrons into traditional materials including conductors, semiconductors, and insulators. This formula generates an approximation to the range using a single fitting parameter, Nv, described as the effective number of valence electrons. This applicability of the formulation extends to electrons with energies from 10MeV. These calculations are of great value for studies of high electron bombardment, such as electron spectroscopy or the vacuum of space. A list comprised of 187 materials has been collected that greatly …
Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist, Blake Moore, Greg Wilson, Jr Dennison
Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist, Blake Moore, Greg Wilson, Jr Dennison
Posters
The Continuous-Slow-Down Approximation (CSDA) is used to create a simple composite analytical formula to estimate the range or maximum penetration depth of incident electrons into diverse materials including conductors, semiconductors, and insulators. This formula generates an approximation to the range using a single fitting parameter, Nv, described as the effective number of valence electrons. This range of the formulation extends to electrons with energies from <10 eV to >10MeV, with 20% accuracy. A list comprised of 222 materials has been collected that greatly extends the applicability of this model. Several key material constants were compiled for each material, including the atomic …10>
Electron Transport Models And Precision Measurements In A Constant Voltage Chamber, Justin Dekany, Alec Sim, Jerilyn Brunson, John R. Dennison
Electron Transport Models And Precision Measurements In A Constant Voltage Chamber, Justin Dekany, Alec Sim, Jerilyn Brunson, John R. Dennison
All Physics Faculty Publications
The conductivity of the material is a key transport parameter in spacecraft charging that determines how deposited charge will redistribute throughout the system, how rapidly charge imbalances will dissipate, and what equilibrium potential will be established under given environmental conditions. As the requirements for space missions extend to new regions of space and more stringent requirements are placed on spacecraft performance, it becomes necessary to better understand the underlying conduction mechanisms that determine the dynamic response of insulators to temperature, electric field dose rate, and sample conditioning and history. This study performed detailed measurements of the transient conductivity of representative …
Electron Induced Luminescence Of Insulating Polymeric Materials, Doug Ball
Electron Induced Luminescence Of Insulating Polymeric Materials, Doug Ball
Senior Theses and Projects
The study of luminescence and electron transport in disordered insulating materials provides detailed information about the material structure and interaction of incident electrons within a material. Electron induced luminescence of insulating polymeric materials has been observed in tests by the USU Materials Physics group. Conduction electrons can transition between extended states in the valence and conduction band and a distribution of localized trapped states within the band gap. Electron transport and luminescence is governed by the distribution of states and transition rates between them. This study investigates the exponentially decaying signatures of both luminescence and sample current of M55J under …
Electron-Induced Electron Yields Of Uncharged Insulating Materials, Ryan Carl Hoffmann
Electron-Induced Electron Yields Of Uncharged Insulating Materials, Ryan Carl Hoffmann
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Presented here are electron-induced electron yield measurements from high-resistivity, high-yield materials to support a model for the yield of uncharged insulators. These measurements are made using a low-fluence, pulsed electron beam and charge neutralization to minimize charge accumulation. They show charging induced changes in the total yield, as much as 75%, even for incident electron fluences of <3 fC/mm2, when compared to an uncharged yield. The evolution of the yield as charge accumulates in the material is described in terms of electron recapture, based on the extended Chung and Everhart model of the electron emission spectrum and the dual dynamic …3>
Measurement Methods Of Electron Emission Over A Full Range Of Sample Charging, R. Hoffman, John R. Dennison
Measurement Methods Of Electron Emission Over A Full Range Of Sample Charging, R. Hoffman, John R. Dennison
All Physics Faculty Publications
The electron emission properties of a material subject to incident radiation flux are key parameters in determining to what equilibrium charge a spacecraft will established under given environmental conditions. However, there is a complex relation between these emission properties and the charge built up in spacecraft insulators. Complex modeling codes have been developed to predict the potential a spacecraft will adopt as a consequence of its interaction with the space plasma. These require correct models of the electron yields as a function of charge to accurately predict the both the charge build up and the equilibrium potential of spacecraft components. …
Flight Experiments On The Effects Of Contamination On Electron Emission Of Materials, John R. Dennison, Joshua L. Hodges, Jeff Duce, Amberly Evans
Flight Experiments On The Effects Of Contamination On Electron Emission Of Materials, John R. Dennison, Joshua L. Hodges, Jeff Duce, Amberly Evans
All Physics Faculty Publications
We report on a study of the effects of prolonged exposure to the space environment and of chargeenhanced contamination on the electron emission and resistivity of spacecraft materials. The State of Utah Space Environment & Contamination Study (SUSpECS) was deployed on the International Space Station (ISS) in March 2008 onboard the MISSE-6 payload during STS-123. The Materials International Space Station Experiment (MISSE-6) program is designed to characterize the performance of candidate new space materials over the course of its ~17 month exposure to the LEO environment, with a target return date of August 2009 on STS-127. Approximately 165 samples are …
Low-Fluence Electron Yields Of Highly Insulating Materials, Ryan Hoffmann, Jr Dennison, Clint D. Thomson, Jennifer Albretson
Low-Fluence Electron Yields Of Highly Insulating Materials, Ryan Hoffmann, Jr Dennison, Clint D. Thomson, Jennifer Albretson
Journal Articles
Electron-induced electron yields of high-resistivity, high-yield materials - ceramic polycrystalline aluminum oxide and the polymer polyimide (Kapton HN), - were made by using a low-fluence, pulsed incident electron beam and charge neutralization electron source to minimize charge accumulation. Large changes in energy-dependent total yield curves and yield decay curves were observed, even for incident electron fluences of <3 fC/mm2. The evolution of the electron yield as charge accumulates in the material is modeled in terms of electron re-capture based on an extended Chung-Everhart model of the electron emission spectrum. This model is used to explain anomalies measured in highly insulating, …3>
Triggering Threshold Spacecraft Charging With Changes In Electron Emission From Materials, John R. Dennison, R. C. Hoffmann, J. Abbott
Triggering Threshold Spacecraft Charging With Changes In Electron Emission From Materials, John R. Dennison, R. C. Hoffmann, J. Abbott
All Physics Faculty Publications
Modest changes in spacecraft charging conditions can lead to abrupt changes in the spacecraft equilibrium, from small positive potentials to large negative potentials relative to the space plasma; this phenomenon is referred to as threshold charging. It is well known that temporal changes of the space plasma environment (electron plasma temperature or density) can cause threshold charging. Threshold charging can also result from by temporal changes in the juxtaposition of the spacecraft to the environment, including spacecraft orbit, orientation, and geometry. This study focuses on the effects of possible changes in electron emission properties of representative spacecraft materials. It is …
Electron-Induced Electron Yields Of Uncharged Insulating Materials, Ryan Carl Hoffmann, John R. Dennison, Jennifer Albretsen
Electron-Induced Electron Yields Of Uncharged Insulating Materials, Ryan Carl Hoffmann, John R. Dennison, Jennifer Albretsen
All Physics Faculty Publications
This study presents electron-induced electron yield measurements from high-resistivity, high-yield materials to validate a model for the yield of uncharged insulators. These measurements are accomplished by using a low-fluence, pulsed incident electron beam and charge neutralization to minimize charge accumulation. Our measurements show large changes in total yield curves and yield decay curves, even for incident electron fluences of/mm2. We model the evolution of the yield as charge accumulates in the material in terms of electron re-capture based on the extended Chung-Everhart model of the electron emission spectrum. This model is used to explain anomalies measured in high yield ceramics, …
Measurements Of The Secondary Electron Emission Properties Of Insulators, Clint D. Thomson
Measurements Of The Secondary Electron Emission Properties Of Insulators, Clint D. Thomson
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Measurements of the electron-induced electron emission properties of insulators are important to many applications including spacecraft charging, scanning electron microscopy, electron sources, and particle detection technology. However, these measurements are difficult to make since insulators can charge either negatively or positively under charge particle bombardment that in turn alters insulator emissions. In addition, incident electron bombardment can modify the conductivity, internal charge distribution, surface potential, and material structure in ways that are not well understood. A primary goal of this dissertation work has been to make consistent and accurate measurements of the uncharged electron yields for insulator materials using innovative …
State Of Utah Space Environment & Contamination Study (Suspecs) Misse-6 Payload To Investigate Their Effects On Electron Emission And Resistivity Of Spacecraft Materials, John R. Dennison, L. Pearson, L. Davis, J. W. Burns, R. S. Hyde, James S. Dyer, Tina Andrus, Andrew Jay Auman, Jeff Duce, Tim Neilsen, Rob Leishman
State Of Utah Space Environment & Contamination Study (Suspecs) Misse-6 Payload To Investigate Their Effects On Electron Emission And Resistivity Of Spacecraft Materials, John R. Dennison, L. Pearson, L. Davis, J. W. Burns, R. S. Hyde, James S. Dyer, Tina Andrus, Andrew Jay Auman, Jeff Duce, Tim Neilsen, Rob Leishman
All Physics Faculty Publications
A study of the effects of prolonged exposure to the space environment and of charge-enhanced contamination on the electron emission and resistivity of spacecraft materials, the State of Utah Space Environment & Contamination Study (SUSpECS), is planned for flight aboard the MISSE-6 payload. The Materials International Space Station Experiment (MISSE-6) program is designed to characterize the performance of candidate new space materials over the course of approximately four to eight month exposure periods on-orbit on the International Space Station, with a target flight date of mid-2006. The study is conducted by the Utah State University Materials Physics Group, in cooperation …
The Importance Of Accurate Computation Of Secondary Electron Emission For Modeling Spacecraft Charging, S. Clerc, John R. Dennison, C. D. Thomson
The Importance Of Accurate Computation Of Secondary Electron Emission For Modeling Spacecraft Charging, S. Clerc, John R. Dennison, C. D. Thomson
All Physics Faculty Publications
Secondary electron emission is a critical contributor to the current balance in spacecraft charging. Spacecraft charging codes use a parameterized expression for the secondary electron yield δ(Eo) as a function of incident electron energy Eo. Simple three-step physics models of the electron penetration, transport and emission from a solid are typically expressed in terms of the incident electron penetration depth at normal incidence or range R(Eo ), and the mean free path of the secondary electron, λ(E). We recall classical models for the range R(Eo): a power law expression of the form b1Eon1 …
Resonant Photoemission In F-Electron Systems: Pu And Gd, James G. Tobin, Brandon W. Chung, Roland K. Schulze, Jeff Russell Terry, John Douglas Farr, David K. Shuh, K. Heinzelman, Eli Rotenberg, George Daniel Waddill, Gerrit V. Van Der Laan
Resonant Photoemission In F-Electron Systems: Pu And Gd, James G. Tobin, Brandon W. Chung, Roland K. Schulze, Jeff Russell Terry, John Douglas Farr, David K. Shuh, K. Heinzelman, Eli Rotenberg, George Daniel Waddill, Gerrit V. Van Der Laan
Physics Faculty Research & Creative Works
Resonant photoemission in the Pu 5f and Pu 6p states is compared to that in the Gd 4f and Gd 5p states. Spectral simulations, based upon an atomic model with angular momentum coupling, are compared to the Gd and Pu results. Additional spectroscopic measurements of Pu, including core level photoemission and x-ray absorption, are also presented.
Secondary Electron Emission Study Of Annealed Graphitic Amorphous Carbon, Jodie Corbridge
Secondary Electron Emission Study Of Annealed Graphitic Amorphous Carbon, Jodie Corbridge
Senior Theses and Projects
In the 1880s a curious phenomena was observed: when a ray of light, no matter how weak, hit certain metals; electrons were emitted from the surface. Called the “photoelectric effect”, this puzzle was never explained until much later. In 1905, Albert Einstein put forth one possible explanation, which is currently accepted as correct. Einstein proposed that light propagated in discrete energy packets rather than as a continuous wave. While most scientists disbelieved Einstein theory, it was later proved in detail by Robert Milikan.1 Rays of light traveling in discrete packets hit metal surfaces, depositing energy. If the energy is high …
Electron Emission Properties Of Insulator Materials Pertinent To The International Space Station, C. D. Thomson, V. V. Zavyalov, John R. Dennison, Jodie Corbridge
Electron Emission Properties Of Insulator Materials Pertinent To The International Space Station, C. D. Thomson, V. V. Zavyalov, John R. Dennison, Jodie Corbridge
All Physics Faculty Publications
We present the results of our measurements of the electron emission properties of selected insulating and conducting materials used on the International Space Station (ISS). Utah State University (USU) has performed measurements of the electron-, ion-, and photon-induced electron emission properties of conductors for a few years, and has recently extended our capabilities to measure electron yields of insulators, allowing us to significantly expand current spacecraft material charging databases. These ISS materials data are used here to illustrate our various insulator measurement techniques that include: i) Studies of electron-induced secondary and backscattered electron yield curves using pulsed, low current electron …
Local Versus Nonlocal Order-Parameter Field Theories For Quantum Phase Transitions, Dietrich Belitz, Theodore R. Kirkpatrick, Thomas Vojta
Local Versus Nonlocal Order-Parameter Field Theories For Quantum Phase Transitions, Dietrich Belitz, Theodore R. Kirkpatrick, Thomas Vojta
Physics Faculty Research & Creative Works
General conditions are formulated that allow us to determine which quantum phase transitions in itinerant electron systems can be described by a local Landau-Ginzburg-Wilson (LGW) theory solely in terms of the order parameter. A crucial question is the degree to which the order parameter fluctuations couple to other soft modes. Three general classes of zero-wave-number order parameters, in the particle-hole spin-singlet and spin-triplet channels and in the particle-particle channel, respectively, are considered. It is shown that the particle-hole spin-singlet class does allow for a local LGW theory, while the other two classes do not. The implications of this result for …
Tunable Local Polariton Modes In Semiconductors, Michael G. Foygel, Alexey Yamilov, Lev I. Deych, Alexander A. Lisyansky
Tunable Local Polariton Modes In Semiconductors, Michael G. Foygel, Alexey Yamilov, Lev I. Deych, Alexander A. Lisyansky
Physics Faculty Research & Creative Works
We study the local states within the polariton band gap that arise due to deep defect centers with strong electron-phonon coupling. Electron transitions involving deep levels may result in alteration of local elastic constants. In this case, substantial reversible transformations of the impurity polariton density of states occur, which include the appearance/disappearance of the polariton impurity band, and its shift and/or the modification of its shape. These changes can be induced by thermo- and photoexcitation of the localized electron states or by trapping of injected charge carriers. We develop a simple model, which is applied to the Op center …
Quantum Phase Transition Of Itinerant Helimagnets, Thomas Vojta, Rastko Sknepnek
Quantum Phase Transition Of Itinerant Helimagnets, Thomas Vojta, Rastko Sknepnek
Physics Faculty Research & Creative Works
We investigate the quantum phase transition of itinerant electrons from a paramagnet to a state which displays long-period helical structures due to a Dzyaloshinskii instability of the ferromagnetic state. In particular, we study how the self-generated effective long-range interaction recently identified in itinerant quantum ferromagnets is cut off by the helical ordering. We find that for a sufficiently strong Dzyaloshinskii instability the helimagnetic quantum phase transition is of second order with mean-field exponents. In contrast, for a weak Dzyaloshinskii instability the transition is analogous to that in itinerant quantum ferromagnets, i.e., it is of first order, as has been observed …
Electronic Structure Of Superconducting Mgb₂ And Related Binary And Ternary Borides, Nadezhda I. Medvedeva, Alexander L. Ivanovskii, Julia E. Medvedeva, Arthur J. Freeman
Electronic Structure Of Superconducting Mgb₂ And Related Binary And Ternary Borides, Nadezhda I. Medvedeva, Alexander L. Ivanovskii, Julia E. Medvedeva, Arthur J. Freeman
Physics Faculty Research & Creative Works
First-principles full potential linear muffin-tin orbital-generalized gradient approximation electronic structure calculations of the new medium-Tc superconductor (MTSC) MgB2 and related diborides indicate that superconductivity in these compounds is related to the existence of Px,y-band holes at the γ point. Based on these calculations, we explain the absence of medium-Tc superconductivity for BeB2, AlB2, ScB2, and YB2. The simulation of a number of MgB2-based ternary systems using a supercell approach demonstrates that (i) the electron doping of MgB2 (i.e., MgB2-yXy with X=Be, …
Excitation Plus Ionization In Electron-Atom Collisions To He^{+} (N=2): (E,2e), (E, E\Gamma ) And (E, 2e\Gamma ) Studies, Mevlut Dogan, Albert Crowe
Excitation Plus Ionization In Electron-Atom Collisions To He^{+} (N=2): (E,2e), (E, E\Gamma ) And (E, 2e\Gamma ) Studies, Mevlut Dogan, Albert Crowe
Turkish Journal of Physics
Simultaneous excitation-ionization of helium atoms by electron impact is observed by the coincidence detection of the outgoing particles. The relationship between (e,2e), (e,e\gamma ) and (e,2e\gamma ) experiments is discussed.
Instrumentation And Measurement Of Secondary Electron Emission For Spacecraft Charging, Neal Nickles, John R. Dennison
Instrumentation And Measurement Of Secondary Electron Emission For Spacecraft Charging, Neal Nickles, John R. Dennison
All Physics Faculty Publications
Secondary electron emission is an important physical mechanism in the problem of spacecraft charging. The NASA Space Environments and Effects branch is currently revising NASA’s strategy for mitigating damage due to spacecraft charging. In an effort to substantially improve the modeling of spacecraft charging, measurements of secondary electron emission parameters are being made. The design of the apparatus needed to measure these parameters is discussed in detail. Various measurement techniques are explained and conclusions are drawn about the suitability of the final design.
Effects Of Spacecraft Potential On Secondary Electron Yields In Geosynchronous Orbit, Neal E. Nickles
Effects Of Spacecraft Potential On Secondary Electron Yields In Geosynchronous Orbit, Neal E. Nickles
All Physics Faculty Publications
Surface charging due to interactions with the earth=s plasma is a hazard for orbiting spacecraft. Secondary electron (SE) emission is an important physical process in spacecraft charging. Current spacecraft charging models do not consider the SE energy or angular distributions and their implications for estimating the return of SE to the spacecraft. Comprehensive work on the application of SE energy and angular distributions to spacecraft charging has been published [Nickles et al., 1999] and part of that work is summarized here. The application of SE energy distributions to the case of positive charging in geosynchronous orbit is discussed and shown …
Evolution Of Secondary Electron Emission Characteristics Of Spacecraft Surfaces: Importance To Spacecraft Charging, R. E. Davies, John R. Dennison
Evolution Of Secondary Electron Emission Characteristics Of Spacecraft Surfaces: Importance To Spacecraft Charging, R. E. Davies, John R. Dennison
All Physics Faculty Publications
Secondary electron emission (SEE) plays a key role in spacecraft charging [Garrett, 1981; Frooninckx and Sojka, 1992] . As a result, spacecraft charging codes require knowledge of the SEE characteristics of various materials in order to predict vehicle potentials in various orbital environments [Katz, et. al., 1986]. Because SEE is a surface phenomenon, occurring in the first few atomic layers of a material, the SEE characteristics of a given surface are extremely sensitive to changes in surface condition—e.g., the addition or removal of surface contaminants, or changes in surface morphology. That spacecraft surfaces can and generally do undergo significant evolution …
The Effects Of Electron Radiation On The Glass Transition Temperature Of A Polyetherimide, Kristen Tulloch Kern
The Effects Of Electron Radiation On The Glass Transition Temperature Of A Polyetherimide, Kristen Tulloch Kern
Physics Theses & Dissertations
The effects of electron radiation on a polyetherimide (PEI), Ultem*, were investigated. In particular, the changes in the glass transition temperature (Tg) with absorbed radiation dose were studied. The polymer was exposed to mono-energetic beams of 100-keV electrons and 1.0-MeV electrons for doses up to 100 megagray (MGy). Dosimetry for the exposures was based on Monte-Carlo simulations of the transfer of energy from an energetic electron to the polymer and on comparison to Nylon standards. Dynamic mechanical analysis was used to determine the (Tg) for non-exposed PEI and the changes in (Tg) resulting from …
Electron Mean-Free Paths In The Alkali Metals, G. K. Wertheim, D. Mark Riffe, N. V. Smith, P. H. Citrin
Electron Mean-Free Paths In The Alkali Metals, G. K. Wertheim, D. Mark Riffe, N. V. Smith, P. H. Citrin
All Physics Faculty Publications
Photoemission data in which the signal from the first atomic layer is well resolved from that of the bulk are used to determine accurately the kinetic-energy dependence of the inelastic-electron mean free path in the alkali metals. At the higher kinetic energies, the data are in very good agreement with the theory of Penn. Below about 10 eV, the mean free path in the heavier alkali metals drops markedly below the theoretical values. This is attributed to electron decay processes involving the unoccupied d bands.
Structure And Optical Characterization Of Znxcd1-Xte Thin Films Prepared By The Close Spaced Vapor Transport Method, David D. Allred, Jesus González-Hernández, O. Zelaya, J. G. Mendoza-Alverez, E. López-Cruz, D. A. Pawlik
Structure And Optical Characterization Of Znxcd1-Xte Thin Films Prepared By The Close Spaced Vapor Transport Method, David D. Allred, Jesus González-Hernández, O. Zelaya, J. G. Mendoza-Alverez, E. López-Cruz, D. A. Pawlik
Faculty Publications
Zinc cadmium telluride (ZnxCd1-xTe) solid solution films with 0≤x≤0.12 were deposited by the close spaced vapor transport method and characterized using photoluminescence, x-ray diffraction, and scanning electron microscopy. The two former techniques indicate that films with high crystalline quality can be prepared with moderate substrate temperatures and low argon pressures. Under these conditions deposition rates of up to 1000 Å/s are achieved and Zn concentration in the film is the same as that of the source. The electron micrographs show grain sizes comparable to the film thickness.
A Relativistic One Pion Exchange Model Of Proton-Neutron Electron-Positron Pair Production, William A. Peterson
A Relativistic One Pion Exchange Model Of Proton-Neutron Electron-Positron Pair Production, William A. Peterson
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Proton-neutron electron-positron pair production cross sections are calculated in the framework of the pseudoscalar one-pion exchange model in a fully relativistic manner.
A computer program has been developed to evaluate invariants and Dirac traces for a given data point.
The sections for symmetric coplanar events for laboratory kinetic energies of 10 to 250 MeV were calculated for pair angles of 20° to 120°.
Frequency distributions were also calculated, at a laboratory energy of 200 MeV, using a random number generator to select data points. The frequency distributions are illustrated by curves.
It was noted that the inclusion of heavier bosons …