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Long-range interatomic forces from thermal energy spectra, elastic scattering cross sections for atomic beams and limiting curve of dissociation
A fluid or fluid mixture, subjected to a vertical temperature and/or concentration gradient in a gravitational field, exhibits greatly enhanced light scattering at small angles. This effect is caused by coupling between the vertical velocity fluctuations due to thermal energy and the vertically varying refractive index. Physically, small upward or downward moving regions will be displaced into fluid having a refractive index different from that of the moving region, thus giving rise to the enhanced scattering. The scattered intensity is predicted to vary with scattering wave vector q, as q(sup -4), for sufficiently large q, but the divergence is quenched by gravity at small q. In the absence of gravity, the long wavelength fluctuations responsible for the enhanced scattering are predicted to grow until limited by the sample dimensions. It is thus of interest to measure the mean-squared amplitude of such fluctuations in the microgravity environment for comparison with existing theory and ground based measurements. The relevant wave vectors are extremely small, making traditional low-angle light scattering difficult or impossible because of stray elastically scattered light generated by optical surfaces. An alternative technique is offered by the shadowgraph method, which is normally used to visualize fluid flows, but which can also serve as a quantitative tool to measure fluctuations. A somewhat novel shadowgraph apparatus and the necessary data analysis methods will be described. The apparatus uses a spatially coherent, but temporally incoherent, light source consisting of a super-luminescent diode coupled to a single-mode optical fiber in order to achieve extremely high spatial resolution, while avoiding effects caused by interference of light reflected from the various optical surfaces that are present when using laser sources. Results obtained for a critical mixture of aniline and cyclohexane subjected to a vertical temperature gradient will be presented. The sample was confined between two horizontal parallel sapphire plates with a vertical spacing of 1 mm. The temperatures of the sapphire plates were controlled by independent circulating water loops that used Peltier devices to add or remove heat from the room air as required. For a mixture with a temperature gradient, two effects are involved in generating the vertical refractive index gradient, namely thermal expansion and the Soret effect, which generates a concentration gradient in response to the applied temperature gradient. For the aniline/cyclohexane system, the denser component (aniline) migrates toward the colder surface. Consequently, when heating from above, both effects result in the sample density decreasing with altitude and are stabilizing in the sense that no convective motion occurs regardless of the magnitude of the applied temperature gradient. The Soret effect is strong near a binary liquid critical point, and thus the dominant effect is due to the induced concentration gradient. The results clearly show the divergence at low q and the predicted gravitational quenching. Results obtained for different applied temperature gradients at varying temperature differences from the critical temperature, clearly demonstrate the predicted divergence of the thermal diffusion ratio. Thus, the more closely the critical point is approached, the smaller becomes the temperature gradient required to generate the same signal. Two different methods have been used to generate pure concentration gradients. In the first, a sample cell was filled with a single fluid, ethylene glycol, and a denser miscible fluid, water, was added from below thus establishing a sharp interface to begin the experiment. As time went on the two fluids diffused into each other, and large amplitude fluctuations were clearly observed at low q. The effects of gravitational quenching were also evident. In the second method, the aniline/cyclohexane sample was used, and after applying a vertical temperature gradient for several hours, the top and bottom temperatures were set equal and the thermal gradient died on a time scale of seconds, leaving the Soret induced concentration gradient in place. Again, large-scale fluctuations were observed and died away slowly in amplitude as diffusion destroyed the initial concentration gradient.
The asymptotic effective potential for electron- or positron-hydrogen elastic scattering is derived, correct to order x to the -7th, where x is the positron projectile coordinate, using the Feshbach optical potential as a starting point in the manner of Kleinman et al (1968). To order x to the -6th the potential agrees with the close-coupling results of Seaton and Steenman-Clark (1977) but not to order x to the -7th, where the present calculation gives the result + or - 213/2(x to the 7th) for electron and positron respectively. This coefficient differs considerably from the approximate value of Seaton and Steenman-Clark, and the discrepancy is traced to the omission of d states in their calculation.
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.
Adiabatic correlation function for variational lower bounds on positron-atom elastic scattering phase shifts for hydrogen and helium atoms
In situ measurements of fluctuation spectra and particle distribution functions have now been carried out throughout interplanetary space. The link between these observations is established by theories of wave particle interaction. Linear instability analysis for the actual nonMaxwellian particle distribution functions and an examination of the velocity dependence of microscopic diffusion coefficients form the basis of such an investigation. It is described in more detail for the short wavelength, ion acoustic like turbulence which is found by linear instability analysis to correspond to the observed electrostatic fluctuations. Of the transport processes associated with these fluctuations, electron heat conduction and electron ion energy transfer are of particular importance for macroscopic solar wind expansion. These effects are studied with the aid of an anomalous transport theory. This theory (Dum, 1978 a,b) is based on the dominance of elastic scattering of electrons by fluctuations, similar to (enhanced) electron ion collisions. It has a much wider range of applicability than classical transport theory, which assumes dominance of Coulomb collisions for elastic and inelastic scattering.
Calculations of inclusive inelastic scattering distributions for heavy ion collisions are considered within the high energy optical model. Using ground state sum rules, the inclusive projectile and complete projectile-target inelastic angular distributions are treated in both independent particle and correlated nuclear models. Comparisons between the models introduced are made for alpha particles colliding with He-4, C-12, and O-16 targets and protons colliding with O-16. Results indicate that correlations contribute significantly, at small momentum transfers, to the inelastic sum. Correlation effects are hidden, however, when total scattering distributions are considered because of the dominance of elastic scattering at small momentum transfers.
Ohio State University developed a new spectrally filtered light-scattering apparatus based on a diode laser injected-locked titanium: sapphire laser and rubidium vapor filter at 780.2 nm. When the device was combined with a stimulated Brillouin scattering phase conjugate mirror, the realizable peak attenuation of elastic scattering interferences exceeded 105. The potential of the system was demonstrated by performing Thomson scattering measurements. Under USAF-NASA funding, West Virginia University developed a Doppler global velocimetry system using inexpensive 8-bit charged coupled device cameras and digitizers and a CW argon ion laser. It has demonstrated a precision of +/- 2.5 m/sec in a swirling jet flow. Low-noise silicon-micromachined microphones developed and incorporated in a novel two-tier, hybrid packaging scheme at the University of Florida used printed circuit board technology to realize a MEMS-based directional acoustic array. The array demonstrated excellent performance relative to conventional sensor technologies and provides scaling technologies that can reduce cost and increase speed and mobility.
The collision terms in the Boltzmann equation associated with various processes are derived. For processes having a Fokker-Planck (F-P) limit, the associated F-P operator is derived by means of physical arguments to determine the form of the operator; its multiplying constant is fixed by calculating the total energy exchange rate and comparing with the rate computed by other means. In this manner, the F-P operator is derived for electron-ion scattering, electron-electron scattering in the high-velocity limit, electron-atom elastic scattering, Compton scattering, and the high-velocity limit for inelastic scattering. Other processes considered are bremsstrahlung, radiative-recombination, photoionization, collisional ionization of atoms, and suprathermal-particle ionization of atoms.
This paper examines the aerosol backscattering and extinction profiles measured at night by the NASA Goddard Space Flight Center Scanning Raman Lidar (SRL) during the remote cloud sensing (RCS) intensive operations period (IOP) at the Department of Energy Atmospheric Radiation Measurement (ARM) southern Great Plains (SGP) site in April 1994. These lidar data are used to derive aerosol profiles for altitudes between 0.0 1 5 and 5 km. Since this lidar detects Raman scattering from nitrogen and oxygen molecules as well as the elastic scattering from molecules and aerosols, it measures both aerosol backscattering and extinction simultaneously. The aerosol extinction/backscattering ratio varied between approximately 30 sr and 75 sr at 351 nm. Aerosol optical thicknesses derived by integrating the lidar profiles of aerosol extinction measured at night between 0. I and 5 km are found to be about 10-40% lower than those measured by a Sun photometer during the day. This difference is attributed to the contribution by stratospheric aerosols not included in the lidar estimates as well as to diurnal differences in aerosol properties and concentrations. Aerosol profiles close to the surface were acquired by pointing the lidar nearly horizontally. Measurements of aerosol scattering from a tower-mounted nephelometer are found to be 40% lower than lidar measurements of aerosol extinction over a wide range of relative humidities even after accounting for the difference in wavelengths. The reasons for this difference are not clear but may be due to the inability of the nephelometer to accurately measure scattering by large particles.
Filtered Rayleigh scattering (FRS) is a laser diagnostic where the intensity of elastically scattered light is measured after it passes through a molecular absorption filter. The filter removes background interference that overwhelms the relatively weak scattering from the gas molecules. However, with a filter, the measured light intensity depends on many of the scattering gas properties, including pressure, density, temperature, and velocity. In this work, CFD simulations of an isolator shock train flow field are input into a physics-based model to predict the values of FRS intensity measurements in a proposed experiment. The goal is to evaluate if a simplistic FRS setup (that utilizes one camera, laser, and absorption filter) can be used to accurately quantify number density despite the fact that the scattered light intensity also depends on other gas properties. It is found that the experimental setup can be optimized such that a linear relationship describes the number density with an average prediction error of 2%. The vast majority of the flow exhibits prediction errors of less than 3%, but small regions of the flow reach up to 11% error. A sensitivity analysis shows that the prediction error increases with the central wavelength of the incident laser light and decreases with the angle between the camera and laser propagation directions. The optimal experimental parameters are chosen based on a compromise between the prediction error, spatial resolution, and the amount of unfiltered light. In the future, the proposed FRS setup will be implemented to acquire new and valuable information on an isolator shock train, a flow field that has been traditionally studied using wall static pressure measurements and path-integrated visualization techniques, such as schlieren and shadowgraphy.
A new forward-angle dispersion relation (DR) for electron-atom scattering is proposed. It is based on a subtraction of the static-exchange amplitude from the exact elastic scattering amplitude. Arguments are advanced to explain why this should obviate the difficulties associated with the Gerjuoy-Krall DR, specifically with the exchange Born amplitude. The new DR is tested in the elastic energy range for e-H scattering and compared with the GKDR.
Compound state resonance energies and widths in elastic scattering of diatomic molecule at energies below rotational excitation threshold
The ratio of the scattering intensity for the v double prime = 1 excitation to the elastic scattering intensity at 40- and 80-deg scattering angles has been determined for 10- to 90-eV impact energies for electron scattering by CO. These ratio curves exhibit broad peaks near 20-eV impact energy which cannot be accounted for by plane-wave calculations based on potential scattering models. The peaks are indicative of a resonant excitation process (or processes) in the v double prime = 1 channel in the range from 15 to 25 eV.
The crossed electron-beam - molecular-beam scattering technique has been used to measure relative values of differential 'elastic' scattering cross sections at electron impact energies of 5.4 and 20 eV for the angular range from 20 to 130 deg. The absolute values of these cross sections have been obtained by normalization to the classical perturbation theory of Dickinson (1977) at a scattering angle of 40 deg. These differential cross sections have then been used to calculate the integral and momentum-transfer cross sections. An energy-loss spectrum at 100 eV electron impact energy and 15 deg scattering angle has also been obtained. Two weak features at the energy losses of 6.74 and 8.82 eV appear. Their energy positions are compared with the recent calculations of Kahn et al. (1974).
Binary collision rates for arbitrary scattering cross sections are derived in the case of a beam of particles interacting with a Maxwell-Boltzmann (MB) plasma, or in the case of two MB plasmas interacting at generally different temperatures. The expressions are valid for all beam energies and plasma temperatures, from the nonrelativistic to the extreme relativistic limits. The calculated quantities include the reaction rate, the energy exchange rate, and the average rate of change of the squared transverse momentum component of a monoenergetic particle beam as a result of scatterings with particles of a MB plasma. Results are specialized to elastic scattering processes, two-temperature reaction rates, or the cold plasma limit, reproducing previous work.
A package of software computes the time-dependent propagation of a narrow laser beam in an arbitrary three- dimensional (3D) medium with absorption and scattering, using the transient-discrete-ordinates method and a direct integration method. Unlike prior software that utilizes a Monte Carlo method, this software enables simulation at very small signal-to-noise ratios. The ability to simulate propagation of a narrow laser beam in a 3D medium is an improvement over other discrete-ordinate software. Unlike other direct-integration software, this software is not limited to simulation of propagation of thermal radiation with broad angular spread in three dimensions or of a laser pulse with narrow angular spread in two dimensions. Uses for this software include (1) computing scattering of a pulsed laser beam on a material having given elastic scattering and absorption profiles, and (2) evaluating concepts for laser-based instruments for sensing oceanic turbulence and related measurements of oceanic mixed-layer depths. With suitable augmentation, this software could be used to compute radiative transfer in ultrasound imaging in biological tissues, radiative transfer in the upper Earth crust for oil exploration, and propagation of laser pulses in telecommunication applications.
Angular distributions of elastic and inelastic scattering of 42-MeV alpha particles measured for even tellurium isotopes