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NASA NTRS1981

Evaluation and universal curves of the photon loss probability

In the transfer of radiation in a plasma, an important parameter (which measures the coupling between the radiation field and the electron gas) is the photon loss probability per scattering epsilon, defined as the ratio of collisional de-excitation to total de-excitation. The evaluation of epsilon requires normally knowledge of specific collisional excitation rates and radiative transition rate coefficients. In the considered investigation a general formula for epsilon is obtained which depends only on electron density, temperature, and line wavelength. Use is made of a simple Bethe-Coulomb expression recently derived by Kastner (1980) for the collisional excitation rate coefficient. Epsilon is obtained as a function of the three variables, and universal curves of it can be constructed with one of the variables as parameter. As an example of the application of the considered procedure, the variation of epsilon with height h in the solar atmosphere is shown in a graph for several solar lines.

Kastner, S. O.↗

NASA NTRS1982

Calculation of the relativistic Bloch correction to stopping power

Bloch's technique of joining the nonrelativistic Bethe and Bohr stopping-power expressions by taking into account wave-packet effects for close collisions is extended to the relativistic case. It is found that Bloch's nonrelativistic correction term must be modified and that charge asymmetric terms appear. Excellent agreement is observed by comparing the results of these calculations to recent data on the stopping power of relativistic heavy ions.

Ahlen, S. P.↗

NASA NTRS1984

Low-energy proton stopping power of N2, O2 and water vapor and deviations from Bragg's rule

A modified local plasma model, based on the works of Lindhard and Winther; and Bethe, Brown, and Walske, is established. The Gordon-Kim model for molecular electron density is used to calculate stopping power of N2, O2, and water vapor for protons of energy ranging from 40 keV to 2.5 MeV, resulting in good agreement with experimental data. Deviations from Bragg's rule are evaluated and are discussed under the present theoretical model.

Xu, Y. J.↗

NASA NTRS1984

Microscopic aspects of the effect of friction reducers at the lubrication limit

An attempt is made to analytically model the physicochemical properties of lubricants and their capacity to reduce friction. A technique of frozen fracturing of the lubricants was employed to study the dispersion of additives throughout a lubricant. Adsorption was observed at the liquid-solid interface, which was the region where the solid and lubricant met, and the molecular dispersion of the additive enhanced the effectiveness of the lubricant. The electrically conductive characteristics of the lubricant at the friction interface indicated the presence of tunneling effects. The Bethe model was used to examine the relationship between the coefficient of friction and the variation of interface thickness. The electron transport permitted an inelastic tunnel electron spectroscopic investigation of the molecular transformations undergone by the additive during friction episodes.

Mansot, J. L.↗

NASA NTRS1985

Missing energies at pair creation

Wilson cloud chamber measurements of the separated spectra of positrons and electrons produced by gamma quanta of 6.14 MeV differ considerably from the theoretically predicted spectra by BETHE and HEITLER, but are in good agreement with those of a modified theory of pair creation.

El-Ela, A. A.↗

NASA NTRS1983

Use of relativistic rise in ionization chambers for measurement of high energy heavy nuclei

A balloon-borne instrument has been constructed to measure the energy spectra of cosmic-ray heavy nuclei in the range of about 0.3 to about 100 GeV/amu. It makes use of the relativistic rise portion of the Bethe-Bloch curve in ionization chambers for energy determination in the 10- to 100-GeV/amu interval. The instrument consists of six layers of dual-gap ionization chambers for energy determination above 10 GeV/amu. Charge is determined with a NE114 scintillator and a Pilot 425 plastic Cerenkov counter. A CO2 gas Cerenkov detector (1 atm; threshold of 30 GeV/amu) calibrates the ion chambers in the relativistic rise region. The main emphasis of the instrument is the determination of the change of the ratio of Iron (26) to the Iron secondaries (21-25) in the energy range of 10 to 100 GeV/amu. Preliminary data from a balloon flight in the fall of 1982 from Palestine, TX is presented.

Barthelmy, S. D.↗

NASA NTRS1985

Theory of microwave remote sensing

Active and passive microwave remote sensing of earth terrains is studied. Electromagnetic wave scattering and emission from stratified media and rough surfaces are considered with particular application to the remote sensing of soil moisture. Radiative transfer theory for both the random and discrete scatterer models is examined. Vector radiative transfer equations for nonspherical particles are developed for both active and passive remote sensing. Single and multiple scattering solutions are illustrated with applications to remote sensing problems. Analytical wave theory using the Dyson and Bethe-Salpeter equations is employed to treat scattering by random media. The backscattering enhancement effects, strong permittivity fluctuation theory, and modified radiative transfer equations are addressed. The electromagnetic wave scattering from a dense distribution of discrete scatterers is studied. The effective propagation constants and backscattering coefficients are calculated and illustrated for dense media.

Tsang, L.↗

NASA NTRS1988

Modified radiative transfer theory for a two-layer anisotropic random medium

The modified radiative transfer (MRT) equations which describe propagation and scattering of the electromagnetic field intensity in a layered anisotropic random medium are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The extinction matrices and scattering phase matrices for both mean and incoherent field intensities are obtained. Backscattering enhancement is observed due to the spatial coherent effect between upward and downward propagating waves. It also occurs for the half-space case, because of coupling between ordinary and extraordinary waves. The depolarization effect is predicted in the first-order renormalization approximation to the MRT equation.

Lee, J. K.↗

NASA NTRS1988

Transport of low- and medium-energy electron and ion beams in seawater and its vapors

A general theory of stopping power for electrons and ions in a target medium (gas, liquid, or thin solid foil) containing neutral as well as positive and negative ions is developed. The approach is quite accurate in the low- and medium-energy range (less than 1 MeV), where the Bethe stopping-power cross section is inaccurate. The energy transfer during individual collisions is treated by the binary-encounter approximation. The theory is applied to determine the stopping power of seawater, whose major components are H2O molecules and Na(+) and Cl(-) ions. The stopping-power cross sections for low- and medium-energy protons in water show excellent agreement with existing measurements.

Erwin, Daniel A.↗

NASA NTRS1989

Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

Zhang, Shoucheng↗

NASA NTRS1991

Energy degradation of fast electrons in hydrogen gas

An equation is derived for calculating the energy distribution of fast electrons in a partially ionized gas and a method is provided to solve for the electron degradation spectrum and the energy deposition in different forms (ionization, excitation, or heating). As an example, the energy degradation of fast electrons in a gas of pure hydrogen is calculated, considering excitations to the lowest 10 atomic levels. The Bethe approximation and the continuous slowing-down approximation are discussed and it is concluded that these approximations are accurate to the order of 20 percent for electrons with initial energy of greater than about keV. The method and results can be used to determine heating, excitations, and ionizations by high-energy photoelectrons or cosmic-ray particles in various astrophysical circumstances, such as the interstellar medium, supernova envelopes, and QSO emission-line clouds.

Xu, Yueming↗

NASA NTRS1992

Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

Maung, Khin Maung↗

NASA NTRS1992

Effects of retardation in relativistic equations with confining interaction

A method has been developed for solving two body relativistic bound state equations in momentum space with a confining interaction. A total of six different three dimensional reductions of the Bethe-Salpeter equations are studied with particular emphasis placed on the competing roles of relativistic kinematics and retardation. The results indicate that these two effects counteract each other and this sheds some light on why nonrelativistic models of meson spectroscopy have been quite successful.

Maung, Khin Maung↗

NASA NTRS1993

Hard apex transition in quasi-periodic oscillators - Closing of the accretion gap

We propose that the 'hard apex' transition in the X-ray two-color diagrams for low-mass X-ray binaries exhibiting quasi-periodic oscillation is associated with closure of a gap between the accretion disk and the star. At low accretion rates, gas crosses this gap intermittently. However, when the mass accretion rate increases, the disk thickens and its inner edge touches the star, thus forming a boundary layer through which the gas flows steadily. This explanation is viable provided that the equation of state of nuclear matter is not significantly harder than the Bethe-Johnson I prescription. Accretion gap scenarios are possibly distinguishable from models which invoke a small magnetosphere around the neutron star, in that they preclude large stellar magnetic fields and associate the high-frequency (horizontal-branch) oscillations with different sites.

Biehle, Garrett T.↗

NASA NTRS1993

Relativistic proton-nucleus scattering and one-boson-exchange models

Relativistic p-(Ca-40) elastic scattering observables are calculated using four sets of relativistic NN amplitudes obtained from different one-boson-exchange (OBE) models. The first two sets are based upon a relativistic equation in which one particle is on mass shell and the other two sets are obtained from a quasipotential reduction of the Bethe-Salpeter equation. Results at 200, 300, and 500 MeV are presented for these amplitudes. Differences between the predictions of these models provide a study of the uncertainty in constructing Dirac optical potentials from OBE-based NN amplitudes.

Maung, Khin Maung↗

NASA NTRS1993

Second order distorted born approximation for backscattering from a layer of discrete random medium

In recent years there has been increasing interest in scattering and depolarization characteristics of the vegetation canopies. Scattering models applied to the microwave remote sensing of vegetation canopies showed that multiple scattering effects can be important in simulating the backscattering coefficients correctly. In particular, in most applications, the cross-polarized backscattering coefficients are often underestimated by single scattering models. Recently, there have been concerted efforts to include the second order terms in the radiative transfer models of vegetation canopies in order to account for multiple scattering within the canopy. The coherent wave theory approach is extended to include multiple scattering effects to predict the coherent and incoherent backscattering contributions from a layer of vegetation canopy. The problem is initially formulated in terms of the exact equation for the correlation function of the field, i.e., the Bethe-Salpeter equation. Using fractional volume as a small parameter, a Foldy type approximation is made to obtain a more manageable correlation equation. This equation is iterated to obtain first and second order solutions. The iteration procedure assumes the variance of the field fluctuations are small compared to the coherent intensity. This assumption proved to be particularly successful in computing backscattering coefficients. First and second order backscattering coefficients are calculated from the iterants of the correlation equation. It is shown that the first order coefficients are the same as the distorted Born results used previously by the authors. These results contained enhancement terms in the direct-reflected contributions. The important contributions to second order backscattering are examined and interpreted in terms of scattering diagrams. Examples of situations in which second order backscattering coefficients are important are given.

Lang, Roger H.↗

NASA NTRS1995

HZETRN: Description of a free-space ion and nucleon transport and shielding computer program

The high-charge-and energy (HZE) transport computer program HZETRN is developed to address the problems of free-space radiation transport and shielding. The HZETRN program is intended specifically for the design engineer who is interested in obtaining fast and accurate dosimetric information for the design and construction of space modules and devices. The program is based on a one-dimensional space-marching formulation of the Boltzmann transport equation with a straight-ahead approximation. The effect of the long-range Coulomb force and electron interaction is treated as a continuous slowing-down process. Atomic (electronic) stopping power coefficients with energies above a few A MeV are calculated by using Bethe's theory including Bragg's rule, Ziegler's shell corrections, and effective charge. Nuclear absorption cross sections are obtained from fits to quantum calculations and total cross sections are obtained with a Ramsauer formalism. Nuclear fragmentation cross sections are calculated with a semiempirical abrasion-ablation fragmentation model. The relation of the final computer code to the Boltzmann equation is discussed in the context of simplifying assumptions. A detailed description of the flow of the computer code, input requirements, sample output, and compatibility requirements for non-VAX platforms are provided.

Wilson, John W.↗

NASA NTRS1995

Bicycle ergometer instrumentation to determine muscle and bone forces during exercise

It is hypothesized that bone loss experienced by astronauts in zero gravity conditions may be curtailed by appropriate exercise. According to Wolf's law, bone regenerates when muscles produce stresses by pulling on the bone during daily activity and/or exercise on Earth. to use this theory to prevent or decrease bone loss, one needs to quantify musculoskeletal loads and relate them to bone density changes. In the context of the space program, it is desirable to determine musculoskeletal loads during exercise (using the bicycle ergometer in this case) so that one may make similar measurements on Earth and in space. In this manner, load measurements on Earth may be used as reference to generate similar loads during exercise in space. The work reported in this document entails a musculoskeletal load measurement system that, when complete, will provide forces at muscle insertion points and other contact points, on bone. This data will be used by Dr. Beth A. Todd, who is also a SSF working with Dr. Shackelford, as input to a finite element model of bone sections to determine stress distributions. A bicycle ergometer has been instrumented to measure parameters needed to determine musculoskeletal forces during exercise. A primary feature of the system is its compactness. It uses small/light sensors without line-of-sight requirements. The system developed includes sensors, signal processing, a data acquisition system, and software to collect the data. The sensors used include optical encoders to measure position and orientation of the pedal (foot), accelerometers to determine kinematic parameters of the shank and thigh, load cells to measure pedal forces on the sagittal plane, and EMG probes to measure muscle activity. The signals are processed using anti-aliasing filters and amplifiers. The sensors' output is digitized using 30 channels of a board mounted inside a 486 class PC. A program sets the data acquisition parameters and collects data during a time period specified by the user. The data is put directly into a file on the hard disk in binary form. The 30 channels are sampled at 200 KHz, and each 30 channel scan is done at a rate of 1000 Hz. The instrumented ergometer has been flown in the KC-135 zero-gravity (zero-g) flight to collect information needed to determine musculoskeletal forces under these conditions. Similar information has been collected in 1-g conditions for comparision with the results from the zero-g case. At this time, the sets of data from both experiments are being processed. An existing methodology will be used to determine the kinematic parameters of the shank and thigh using accelerometer and encoder data. This methodology was developed during the fellow's previous NASA/ASEE fellowship and thanks to a Director's Grant. In the future, a methodology to determine the musculoskeletal forces using Newton's Law of Motion and optimization techniques will be developed to determine forces exerted by particular muscles.

Figueroa, Fernando↗