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Measurements of X-rays produced when thick silicon targets are bombarded with 1.05 and 1.25 MeV electrons and comparison to Bethe-Heitler theory
Successful projects require an integrated approach to managing cost, schedule, and risk. This is especially true for complex, multi-year projects involving multiple organizations. To explore solutions and leverage valuable lessons learned, NASA's Virtual Project Management Challenge will kick off a three-part series examining some of the challenges faced by project and program managers when it comes to managing these important elements. In this first session of the series, we will look at cost management, with an emphasis on the critical roles of cost estimating and cost reporting. By taking a proactive approach to both of these activities, project managers can better control life cycle costs, maintain stakeholder confidence, and protect other current and future projects in the organization's portfolio. Speakers will be Doug Comstock, Director of NASA's Cost Analysis Division, Kristin Van Wychen, Senior Analyst in the GAO Acquisition and Sourcing Management Team, and Mary Beth Zimmerman, Branch Chief for NASA's Portfolio Analysis Branch, Strategic Investments Division. Moderator Ramien Pierre is from NASA's Academy for Program/Project and Engineering Leadership (APPEL).
Monte Carlo and Bethe methods for calculating neutron cross sections with effective scattering cross sections
Electron impact widths and shifts of isolated plasma ion lines, using Bethe-Born approximation for cross sections with semiempirical Gaunt factors
Bethe theory of low energy electron diffraction applied to computation of diffracted beam intensity as function of wavelength
In this article we have provided certain details of a nuclear-matter computation, based on the Brueckner-Bethe-Goldstone theory of nuclear reaction, which leads to an equation of state for matter in the density region of 10 to 500 trillion g/cu cm. We also explore the possibilities that at very high baryon densities or for very short baryon separations, the net baryon-baryon interaction may be negligible so that the results of dynamical models, like the statistical bootstrap model and the dual-resonance model, may be applicable to the study of dense baryon matter. Several plausible equations of state are constructed, and their effect on the limiting mass of the neutron star is examined.
A number of analytic forms are presented which have been used to represent electron impact excitation cross sections all the way from threshold to the high energy domain where they join approximately to the results of the Born-Bethe approximation. Techniques for estimating the parameters in these analytic forms are described in detail so that the reader can update his own parameter set when new experimental information becomes available. A short collection of parameters for excitations to key states of N2, O2 and O is given along with references to sources where more complete sets are available. The importance of analytic models as a means of communication to aeronomical users of cross sections is discussed.
Coincidence rates have been measured for inelastically scattered electrons and their associated bremsstrahlung for bombarding energies of 0.20 and 0.15 MeV. Measurements were made for an electron angle of 45 deg and a photon angle of 20 deg. Inelastic electron energies of 0.15 and 0.16 MeV were considered for an incident energy of 0.2 MeV and an inelastic electron energy of 0.12 MeV was considered for an incident energy of 0.15 MeV. To observe the trend with atomic number, Al and Au targets were used. The experimental cross section differentials in photon and electron angles and energy were found to be smaller than the predictions of the Bethe-Heitler theory.
The theory of dense hydrogenic plasmas beginning with the two component quantum grand partition function is reviewed. It is shown that ionization equilibrium and molecular dissociation equilibrium can be treated in the same manner with proper consideration of all two-body states. A quantum perturbation expansion is used to give an accurate calculation of the equation of state of the gas for any degree of dissociation and ionization. In this theory, the effective interaction between any two charges is the dynamic screened potential obtained from the plasma dielectric function. We make the static approximation; and we carry out detailed numerical calculations with the bound and scattering states of the Debye potential, using the Beth-Uhlenbeck form of the quantum second virial coefficient. We compare our results with calculations from the Saha equation.
A coincidence measurement was made of the absolute cross section for electron-atomic-field bremsstrahlung, differential in photon energy, photon-emission angle, and electron scattering angle. The incident electron energy was 140 keV and the scattering materials were thin films of aluminum and gold. The data are compared to the theoretical calculations of Elwert and Haug and of Bethe and Heitler. Both theories give generally satisfactory agreement for aluminum. The Elwert-Haug theory is somewhat more accurate for gold.
A two-variable expansion technique is used to solve for the mean Green's. function from the Dyson equation under the nonlinear approximation. The Bethe-Salpeter equation then gives rise to a set of modified radiative transfer (MRT) equations which accommodate coherent effects essential to bounded media. It is found that the nonlinear approximation, instead of the more popular bilocal approximation, should be used for the case of bounded media. The two approximations yield identical results for unbounded media. The MRT equations are then solved for a two-layer random medium. The MRT equations give rise to simple and useful solutions which are applicable to both active and passive microwave remote sensing.
Relativistic electron and proton impact cross sections are obtained and represented by analytic forms which span the energy range from threshold to 1 GeV. For ionization processes, the Massey-Mohr continuum generalized oscillator strength surface is parameterized. Parameters are determined by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization. Branching ratios for dissociation and predissociation from important states of N2 and O2 are determined. The efficiency for the production of atomic nitrogen and oxygen by protons with kinetic energy less than 1 GeV is determined using these branching ratio and cross section assignments.
Measured ranges of 600-MeV/amu Fe-56 ions in a variety of substances are shorter than predicted by the standard Bethe stopping-power theory. The ranges are consistent with values computed using high-order corrections to the Mott cross section.
Scaled electron-impact cross sections are calculated for ionization from the 3s sublevel of hydrogenic ions with Z equal infinity by use of the Born exchange or the Coulomb-Born Oppenheimer approximation (which is exact, apart from relativistic corrections, in this limit). The results are fitted to an analytic expression which goes into the correct Bethe approximation result at high energies and which can readily be integrated over a Maxwellian electron velocity distribution to obtain collision rates. These results permit calculation of the approximate cross section and collision rate for ionization from the 3s sublevel of any highly charged ion with Z/N larger than approximately 2. Results obtained by the described procedure for Fe-14(+) and Fe-15(+) are compared with results obtained by other procedures.
The two-variable expansion technique is used to solve for the mean Green's functions from the Dyson equation under the nonlinear approximation for a half-space random medium with three-dimensional correlation functions. The Bethe-Salpeter equations are then solved under the ladder approximation. The radiative transfer equations, which have been applied extensively in the study of microwave remote sensing problems, are derived under these approximations. The limiting cases of large and small horizontal correlation lengths are discussed. It is found that there is only one propagation constant except for the case of large horizontal correlation lengths, in which there are two propagation constants. It is shown that boundary layer appears in first-order solutions and does not appear in zeroth-order solutions.
The Bethe-Bloch stopping power relations for inelastic collisions were used to determine the absorption of electron and proton energy in cured neat epoxy resin and the absorption of electron energy in a graphite/epoxy composite. Absorption of electron energy due to bremsstrahlung was determined. Electron energies from 0.2 to 4.0 MeV and proton energies from 0.3 to 1.75 MeV were used. Monoenergetic electron energy absorption profiles for models of pure graphite, cured neat epoxy resin, and graphite/epoxy composites are reported. A relation is determined for depth of uniform energy absorption in a composite as a function of fiber volume fraction and initial electron energy. Monoenergetic proton energy absorption profiles are reported for the neat resin model. A relation for total proton penetration in the epoxy resin as a function of initial proton energy is determined. Electron energy absorption in the composite due to bremsstrahlung is reported. Electron and proton energy absorption profiles in cured neat epoxy resin are reported for environments approximating geosynchronous earth orbit.
The Z1(3) contribution of distant collisions to the average energy loss of heavy charged particles is obtained by extending Bethe's quantum-mechanical calculation to the next highest order in Z1. The second-order Born approximation for the inelastic-collision cross section is simplified by using two major approximations. The infinite summation over terms arising from the coupling to intermediate states of the target atom is approximated with the aid of a parameter and the closure relation. This parameter is proportional to the average excitation energy of the intermediate states as described in the literature. The atomic form factors are simplified through a dipole expansion. Results are obtained in terms of an average excitation energy of the medium. Exemplary results for stopping in Al are presented for estimated values of the average excitation energy of the intermediate states. These results approach the classical and experimental values as the velocity of the penetrating particle increases, agreeing within 20% at beta = 0.3.
Modified radiative transfer (MRT) equations appropriate for electromagnetic wave propagation in bounded random media are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The MRT equations are then solved with the first-order renormalization approximation to obtain analytical results for the backscattering cross sections of a two-layer random medium with arbitrary three-dimensional correlation functions. The coherent effects of the MRT theory are illustrated and comparisons are made with backscattering cross sections obtained with the first Born approximation to the wave equation.