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NASA NTRS1973

The scattering of low energy positrons by helium

Kohn's variational method is used to calculate the positron-helium scattering length and low energy S-wave phase shifts for a quite realistic Hylleraas type of helium function containing an electron-electron correlation term. The zero energy wavefunction is used to calculate the value of the annihilation rate parameter Z sub eff. All the results are significantly different from those for Drachman's helium model B, but are in better agreement with the available experimental data.

Humberston, J. W.↗

NASA NTRS1995

Exact, E = 0, classical and quantum solutions for general power-law oscillators

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

Nieto, Michael Martin↗

NASA NTRS1986

Measurements of electron attachment lineshapes and cross sections at ultralow electron energies for c-C6F10, c-C6F12, C8F16 and 1,1,2-C2Cl3F3

Electron attachment cross sections are reported in the electron energy range 0-160 meV and at energy resolutions of 4.5-7.5 meV (FWHM) for the molecules c-C6F10 (perfluorocyclohexene), c-C6F12 (perfluoro-1,2-dimethylcyclobutane), C8F16 (perfluoro-1,3-dimethylcyclohexane) and 1,1,2-C2Cl3F3 (1,1,2-trichlorotrifluoroethane). Use is made of the Kr photoionization technique, and measured attachment lineshapes are converted to cross sections by normalization through attachment rate constants. Comparisons are made with attachment cross sections derived from swarm-measured rate constants. Similar to previous results in eight other molecules, the present four molecules exhibit resolution-limited onsets at a threshold consistent with an s-wave attachment behavior and with a neutral-negative-ion curve crossing at zero energy.

Alajajian, S. H.↗

NASA NTRS1996

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Kaljevic, Igor↗

NASA NTRS1999

Ultralow Energy Electron Attachment at Sub-Millielectron Volt Resolution

The technique of rare-gas photoionization has been extended by use of direct laser ionization to electron energies epsilon in the range 0-100 meV, with a resolution Delta(epsilon) of 0.4-0.5 meV (FWHM). Tunable UV light at (Lambda)276 nm is produced using a pulsed Nd:YAG laser and nonlinear mixing techniques. The beam is frequency tripled in a pulsed jet of xenon. The VUV radiation, tunable at (Lambda)92 nm, is then used to photoionize Xe at its 2P(sub 1/2) threshold (single-photon ionization). The photoelectrons produced interact with admixed target gas to generate negative ions through the s-wave capture process. Recent results in electron attachment to SF(sub 6) will be reported which show resonance structure at the opening of the ground-state vibrational channels. This structure corresponds to the process of vibrational excitation + attachment, which is superimposed on the underlying s-wave (direct) capture process. It should be a general phenomenon, present in a wide variety of zero-energy electron attaching molecules.

Chutjian, A.↗

NASA NTRS1980

Semi-classical Reissner-Nordstrom model for the structure of charged leptons

The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.

Rosen, G.↗

NASA NTRS1989

Image wavelet decomposition and applications

The general problem of computer vision has been investigated for more that 20 years and is still one of the most challenging fields in artificial intelligence. Indeed, taking a look at the human visual system can give us an idea of the complexity of any solution to the problem of visual recognition. This general task can be decomposed into a whole hierarchy of problems ranging from pixel processing to high level segmentation and complex objects recognition. Contrasting an image at different representations provides useful information such as edges. An example of low level signal and image processing using the theory of wavelets is introduced which provides the basis for multiresolution representation. Like the human brain, we use a multiorientation process which detects features independently in different orientation sectors. So, images of the same orientation but of different resolutions are contrasted to gather information about an image. An interesting image representation using energy zero crossings is developed. This representation is shown to be experimentally complete and leads to some higher level applications such as edge and corner finding, which in turn provides two basic steps to image segmentation. The possibilities of feedback between different levels of processing are also discussed.

Treil, N.↗

NASA NTRS1991

Ground based preparation for microgravity growth of alloy semiconductors

Ground-based research conducted in order to prepare a microgravity space flight experiment is presented. The thermophysical properties of a PbSnTe alloy used for semiconductors are investigated, and furnace calibration and fluid-flow measurements are performed. The alloy has a zero energy crossing at approximately 40 percent SnTe in its band-gap vs composition diagram, which facilitates the design of long-wavelength IR detectors and lasers. The uniformity of devices made from this material depends on the ratio of PbTe and SnTe and requires the composition of the crystal growth to be closely controlled. The main obstacle to such control is the fact that liquid of this material is always solutally or thermally unstable, and, in a high-temperature gradient, the double convective instability cannot be made stable by balancing thermal and solutal expansion. In order to extend the science of crystal growth, the limits of suppression of convection have to be tested in low earth orbit.

Fripp, Archibald L.↗

NASA NTRS1992

An assessment of four-noded plate finite elements based on a generalized third-order theory

Plate finite elements based on the generalized third-order theory of Reddy and the first-order shear deformation theory are analyzed and compared on the basis of thick and thin plate modeling behavior, distortion sensitivity, overall accuracy, reliability, and efficiency. In particular, several four-noded Reddy-type elements and the nine-noded Lagrangian and heterosis (Mindlin-type) plate elements are analyzed to assess their behavior in bending, vibration, and stability of isotropic and laminated composite plates. A four-noded Reddy-type element is identified which is free of all spurious stiffness and zero energy modes, computationally efficient, and suitable for use in any general-purpose finite element program.

Averill, R. C.↗

NASA NTRS1992

Bulk parameters of water group ions at Comet Giacobini-Zinner

Measurements of water group ions at Comet Giacobini-Zinner are analyzed which have been obtained with the EPAS instrument on the ICE spacecraft, in order to determine the bulk parameters of these ions. The measured ion velocity distributions are extrapolated to zero energy and integrated to obtain estimates of both number and thermal energy density. The number density is compared to independent observational and theoretical estimates. Combining the EPAS results with magnetic field and plasma data, the beta and Mach numbers of the flow have been obtained in the region surrounding the comet.

Staines, K.↗

NASA NTRS1992

Increased response of the reversal electron attachment detector and modeling of ion space-charge effects

Design and sensitivity tests of a modified version of the so-called reversal electron attachment detector (READ) are presented. The new version uses a spherical cathode capable of emitting higher electron currents. As in the original READ (which used a planar emitter) electrons are focused into an electrostatic mirror which reverses their trajectories. In the reversal region electrons have essentially zero energy and attach to target molecules to form negative ions. The electron gun lens system has been modified using a field and trajectory code with space charge included. Electron trajectories have been calculated for 1-mA current focused into a reversal region of 3.5-mm diameter. The detection limit of the apparatus is approximately 25 times lower than for the original READ. Nonlinearity in the measured signal vs electron current is described by a model in which a spherical ball of ions expands outward with velocity determined by the space-charge force and the initial velocity of ion formation.

Boumsellek, S.↗

NASA NTRS1994

Thermodynamic models for bounding pressurant mass requirements of cryogenic tanks

Thermodynamic models have been formulated to predict lower and upper bounds for the mass of pressurant gas required to pressurize a cryogenic tank and then expel liquid from the tank. Limiting conditions are based on either thermal equilibrium or zero energy exchange between the pressurant gas and initial tank contents. The models are independent of gravity level and allow specification of autogenous or non-condensible pressurants. Partial liquid fill levels may be specified for initial and final conditions. Model predictions are shown to successfully bound results from limited normal-gravity tests with condensable and non-condensable pressurant gases. Representative maximum collapse factor maps are presented for liquid hydrogen to show the effects of initial and final fill level on the range of pressurant gas requirements. Maximum collapse factors occur for partial expulsions with large final liquid fill fractions.

Vandresar, Neil T.↗

NASA NTRS1996

Element Library for Three-Dimensional Stress Analysis by the Integrated Force Method

The Integrated Force Method, a recently developed method for analyzing structures, is extended in this paper to three-dimensional structural analysis. First, a general formulation is developed to generate the stress interpolation matrix in terms of complete polynomials of the required order. The formulation is based on definitions of the stress tensor components in term of stress functions. The stress functions are written as complete polynomials and substituted into expressions for stress components. Then elimination of the dependent coefficients leaves the stress components expressed as complete polynomials whose coefficients are defined as generalized independent forces. Such derived components of the stress tensor identically satisfy homogenous Navier equations of equilibrium. The resulting element matrices are invariant with respect to coordinate transformation and are free of spurious zero-energy modes. The formulation provides a rational way to calculate the exact number of independent forces necessary to arrive at an approximation of the required order for complete polynomials. The influence of reducing the number of independent forces on the accuracy of the response is also analyzed. The stress fields derived are used to develop a comprehensive finite element library for three-dimensional structural analysis by the Integrated Force Method. Both tetrahedral- and hexahedral-shaped elements capable of modeling arbitrary geometric configurations are developed. A number of examples with known analytical solutions are solved by using the developments presented herein. The results are in good agreement with the analytical solutions. The responses obtained with the Integrated Force Method are also compared with those generated by the standard displacement method. In most cases, the performance of the Integrated Force Method is better overall.

Kaljevic, Igor↗

NASA NTRS1999

Growth of Compound Semiconductors in a Low Gravity Environment: Microgravity Growth of PbSnTe

Fripp, Archibald L.↗

NASA NTRS1999

Growth of Compound Semiconductors in a Low Gravity Environment: Microgravity Growth of PbSnTe

The growth of the alloy compound semiconductor lead tin telluride (PbSnTe) was chosen for a microgravity flight experiment in the Advanced Automated Directional Solidification Furnace (AADSF), on the United States Microgravity Payload-3 (USNP-3) in February, 1996 and on USNW- 4 in November, 1997. The objective of these experiments was to determine the effect of the reduction in convection, during the growth process, brought about by the microgravity environment. The properties of devices made from PbSnTe, an alloy of PbTe and SnTe, are dependent on the ratio of the elemental components in the starting crystal. Compositional uniformity in the crystal is only obtained if there is no significant mixing in the liquid during growth. The technological importance of PbSnTe lies in its band gap versus composition diagram which has a zero energy crossing at approximately 40% SnTe. This facilitates the construction of long wavelength (greater than 6 gm) infrared detectors and lasers. The properties and utilization of PbSnTe are the subject of other papers. 1,2 PbSnTe is also interesting from a purely scientific point of view. It is, potentially, both solutally and thermally unstable due to the temperature and density gradients present during growth. Density gradients, through thermal expansion, are imposed in directional solidification because temperature gradients are required to extract heat. Solutal gradients occur in directional solidification of alloys due to segregation at the interface. Usually the gradients vary with both experiment design and inherent materials properties. In a simplified one dimensional analysis with the growth axis parallel to the gravity vector, only one of the two instabilities work at a time. During growth, the temperature in the liquid increases ahead of the interface. Therefore the density, due to thermal expansion, is decreasing in that direction. However, the phase diagram shows that the lighter SnTe is preferentially rejected at the interface. This causes the liquid density to increase with distance away from the interface.

Fripp, A. L.↗

NASA NTRS2003

Re-examination of a Simplified Model for Positronium-Helium Scattering

Using a local effective potential to account for electron exchange, R J Drachman and S K Houston analyzed the zero-energy scattering of ortho-positronium by helium atoms in 1970. The idea was to use the existing static-exchange results to fit the parameters of the local potential and then to use the potential in a variational target-elastic calculation. The results were remarkably good, both for the scattering length and the annihilation parameter. Recently, however, a rigorous target-elastic calculation by Blackwood et al disagreed so strongly with these old results that we have undertaken a re-examination. We find that one of the apparently trivial assumptions of the local potential method is much more important than previously believed.

DiRienzi, Joseph↗

NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗

NASA NTRS2003

Re-Examination of a Simplified Model for Positronium-Helium Scattering

Using a local effective potential to account for electron exchange, R J Drachman and S K Houston analyzed the zero-energy scattering of ortho-positronium by helium atoms in 1970. The idea was to use the existing static-exchange results to fit the parameters of the local potential and then to use the potential in a variational target-elastic calculation. The results were remarkably good, both for the scattering length and the annihilation parameter. Recently, however, a rigorous target-elastic calculation by Blackwood et al disagreed so strongly with these old results that we have undertaken a re-examination. We find that the assumption made in the earlier work, that the direct potential is negligible compared with the exchange potential, is not quantitatively correct. But the original idea that omission of the direct potential might compensate approximately for the omission of the van der Waals potential still seems reasonable.

Drachman, Richard J.↗