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Articles 34051 - 34080 of 36548

Full-Text Articles in Physical Sciences and Mathematics

Hydrodynamic Fluctuations In A Fluid Under Constant Shear, Alejandro Garcia, M. Malek Mansour, G. Lie, E. Clementi, M. Mareschal Jan 1987

Hydrodynamic Fluctuations In A Fluid Under Constant Shear, Alejandro Garcia, M. Malek Mansour, G. Lie, E. Clementi, M. Mareschal

Alejandro Garcia

No abstract provided.


Nonorthogonal Configuration-Interaction Calculations Of Molecular States: The Low-Lying Molecular States Of Arhsup+ And Two-Electron Charge Exchange In Ar-H+ Collisions, Gordon A. Gallup Jan 1987

Nonorthogonal Configuration-Interaction Calculations Of Molecular States: The Low-Lying Molecular States Of Arhsup+ And Two-Electron Charge Exchange In Ar-H+ Collisions, Gordon A. Gallup

Gordon Gallup Publications

A nonorthogonal configuration-interaction procedure has been used to calculate adiabatic energy curves of ArH+. The basis functions are a mixture of typical molecular-orbital configurations and typical valence-bond (Heitler-London) configurations. This gives an economical description of the wave functions, allowing an easy tracing of various diabatic states through the adiabatic states and a clear identification of the asymptotic states. The results are used to rationalize the unexpectedly large production of Ar2++H- from collisions of H+ with Ar.


Saddle-Point Electrons In Ionizing Ion-Atom Collisions, Ronald E. Olson, Timothy James Gay, H. G. Berry, Edward Boyd Hale, V. D. Irby Jan 1987

Saddle-Point Electrons In Ionizing Ion-Atom Collisions, Ronald E. Olson, Timothy James Gay, H. G. Berry, Edward Boyd Hale, V. D. Irby

Physics Faculty Research & Creative Works

We have studied H++He ionizing collisions, and find that electrons stranded between the two postcollision Coulomb centers dominate the ejected-electron spectra for intermediate (100 keV) projectile energies. The importance of these electrons is clearly established by our classical calculations which are in qualitative agreement, in both shape and magnitude, with experimental spectra taken by us, and with earlier measurements. These saddle-point electrons are produced by a classically understandable mechanism, and are unambiguously observed at nonzero scattering angles. © 1987 The American Physical Society.


Test Of Quasiclassical Theories Of Redistribution In Atomic Collisions, Ronald James Bieniek Jan 1987

Test Of Quasiclassical Theories Of Redistribution In Atomic Collisions, Ronald James Bieniek

Physics Faculty Research & Creative Works

The first numerical tests, for a real system, of the Quasi classical description of redistribution of polarized radiation through atomic collisions are presented. Polarization results are reported for red-wing redistribution of Sr (1S0 1P1) in the presence of Ar colliders. They compare favorably to recent quantal, nonadiabatic computations. It is shown that the effects of bent trajectories are important. Modified Quasi classical formulas to account for some of these are presented and tested. The results indicate that Quasi classical analysis can be used to probe the transformation from molecular to atomic states as atoms separate in a half-collision. © 1987 …


Contribution Of Transfer Ionization To Total Electron Capture From A Helium Target, J. A. Tanis, M. W. Clark, R. Price, Ronald E. Olson Jan 1987

Contribution Of Transfer Ionization To Total Electron Capture From A Helium Target, J. A. Tanis, M. W. Clark, R. Price, Ronald E. Olson

Physics Faculty Research & Creative Works

The contribution of transfer ionization (TI) to total electron capture has been measured for Oq+ ions (q=5, 6, 7, and 8) colliding with helium at energies from 0.5 to 1.5 MeV/u. These measurements, along with other published results, suggest a maximum TI contribution to total capture of 0.15q0.5 at E (in keV /u)q0.5100 The results demonstrate that the failure to account for transfer ionization in total single-charge-transfer cross sections may lead to large discrepancies between experiment and theory. © 1987 The American Physical Society.


Cw Laser Oscillations And Tuning Characteristics Of Neodymium-Doped Lithium Niobate Crystals, Laird D. Schearer, Michèle Leduc, J. Zachorowski Jan 1987

Cw Laser Oscillations And Tuning Characteristics Of Neodymium-Doped Lithium Niobate Crystals, Laird D. Schearer, Michèle Leduc, J. Zachorowski

Physics Faculty Research & Creative Works

We have obtained over 250 mW of CW laser emission at 1084 nm from a neodymium-doped single crystal of lithium niobate when the rod was end pumped by 1 W from a Kr+ laser at 752 nm, Thresholds of less than 30 mW are obtained with a weak output coupler, rising to 220 mW with a 25 percent transmitting output mirror. The laser could be tuned over 3 nm around the peak at 1084.4 nm with a thirl, uncoated etalon in the cavity. Copyright © 1987 by The Institute of Electrical and Electronics Engineers, Inc.


Oxidation Kinetics Of Polycrystalline Lacro3, Chikung J. Yu, Don M. Sparlin, Harlan U. Anderson Jan 1987

Oxidation Kinetics Of Polycrystalline Lacro3, Chikung J. Yu, Don M. Sparlin, Harlan U. Anderson

Physics Faculty Research & Creative Works

The oxidation kinetics of polycrystalline LaCrO3 were determined by measuring the time and temperature dependence of the weight and conductivity change of reduced samples. A region of fast diffusion followed by a smaller, slower diffusion "tail" was observed in the thermogravimetric measurements. This observation can be interpreted as the rapid diffusion along the grain boundaries and subsequent diffusion into the body of the grain. The absence of the "tail" in the conductivity measurements is due to the high hole mobility along the boundaries. Copyright © 1987, Wiley Blackwell. All rights reserved.


Recoil-Ion Production From Zero-Impact-Parameter H+-Ar And H+-Kr Collisions At 20-70 Kev, Akio Itoh, M. Eugene Rudd Jan 1987

Recoil-Ion Production From Zero-Impact-Parameter H+-Ar And H+-Kr Collisions At 20-70 Kev, Akio Itoh, M. Eugene Rudd

M. Eugene Rudd Publications

Recoil ions emitted at 70° from H+-Ar and at 50° and 70° from H+-Kr collisions at 20-70 keV were analyzed by an electrostatic spectrometer. Ions selected in this way result from collisions at very small, essentially zero, impact parameters. Charge states up to 6 + were identified in the spectrum. The cross section for each charge state was measured. The data indicate that these close collisions produce a larger fraction of ions in high charge states than more distant collisions.


Temporary Anion States Of Polyatomic Hydrocarbons, Kenneth D. Jordan, Paul Burrow Jan 1987

Temporary Anion States Of Polyatomic Hydrocarbons, Kenneth D. Jordan, Paul Burrow

Paul Burrow Publications

Contents

I. Introduction

II. Electron Transmission Spectroscopy

A. Background

B. Interpretation of Transmission Data

III. Alkenes, Dienes, and Polyenes

A. Ethylene and Alkyl-Substituted Ethylenes

B. Butadiene, Hexatriene, and Octatetraene

C. Other Conjugated Dienes

D. Cyclooctatetraene

E. Nonconjugated Dienes

IV. Alkynes

A. Acetylene and Alkyl-Substituted Acetylenes

B. Cyclic Acetylenes

C. Butadiyne and 2,4-Hexadiyne

V. Aromatic Systems

A. Benzene and Alkyl-Substituted Benzenes

B. Naphthalene, Anthracene, and Tetracene

C. Styrene and cis- and trans-Stilbene

D. Biphenyls

E. Triptycene, Dibenzonorbornadiene, and Related Compounds

VI. Halogen-Containing Compounds

A. Saturated Compounds

B. Unsaturated Compounds

VII. Conclusions

VIII. Acknowledgment

IX. References

X. Bibliography of Studies …


Differential Cross Sections For Ionization Of Water Vapor By High-Velocity Bare Ions And Electrons, J. H. Miller, W. E. Wilson, S. T. Manson, M. Eugene Rudd Jan 1987

Differential Cross Sections For Ionization Of Water Vapor By High-Velocity Bare Ions And Electrons, J. H. Miller, W. E. Wilson, S. T. Manson, M. Eugene Rudd

M. Eugene Rudd Publications

A semiempirical model of single differential cross sections (SDCS) for ionization of water vapor by fast electrons and bare ions is presented. At low secondary-electron energy, the model is based on an asymptotic expansion of the first Born approximation with coefficients, that are independent of projectile properties, evaluated from experimental photoabsorption and protonimpact ionization data. As the secondary-electron energy increases, the model converges to a binary-encounter approximation. Comparisons with measured differential, total, and dissociative cross sections for ionization of water by fast electrons are used to test the model. For primary electrons with energy greater than about 500 eV, agreement …


Compactification Of The Twisted Heterotic String, V. Parameswaran Nair, Alfred Shapere, Andrew Strominger, Frank Wilczek Jan 1987

Compactification Of The Twisted Heterotic String, V. Parameswaran Nair, Alfred Shapere, Andrew Strominger, Frank Wilczek

Publications and Research

We consider compactifications of the recently discovered tachyon free non-supersymmetric string on tori of Lorentzian self dual lattices. The one loop cosmological constant is computed as a function of the parameters characterizing the lattices. When the lattice parameters are treated as dynamical variables, their equations of motion require extremization of A. This extremization determines the allowed gauge groups and mass spectra. We explicitly find some extremes of A, valid to all orders in perturbation theory. A very general duality relation between compactifications is demonstrated, which leads to an equivalence of compactifications on tori of radii R aud 1/R.


Mössbauer Spectroscopy Of Reduced Ferritin, Richard B. Frankel, G. C. Papaefthymiou, G. D. Watt Jan 1987

Mössbauer Spectroscopy Of Reduced Ferritin, Richard B. Frankel, G. C. Papaefthymiou, G. D. Watt

Physics

No abstract provided.


Measurement Of The Condensation Coefficient Of Water In The Umr Simulation Chamber, Daniel R. White, James L. Kassner, John C. Carstens, Donald E. Hagen, John L. Schmitt, Darryl J. Alofs, Alfred R. Hopkins, Max B. Trueblood, Max W. Alcorn, William L. Walker Jan 1987

Measurement Of The Condensation Coefficient Of Water In The Umr Simulation Chamber, Daniel R. White, James L. Kassner, John C. Carstens, Donald E. Hagen, John L. Schmitt, Darryl J. Alofs, Alfred R. Hopkins, Max B. Trueblood, Max W. Alcorn, William L. Walker

Physics Faculty Research & Creative Works

The UMR Cloud Simulation Facility is described. The facility is designed to provide a controlled environment simulating the conditions of natural atmospheric processes. It consists of two cooled-wall expansion cloud chambers and peripheral instrumentation for generation and characterization of aerosols used for cloud formation studies. Results of initial studies of the growth of warm cloud droplets and inferred measurements of the condensation coefficient are described.


A Viable Form Of Weyl’S Theory, James Thomas Wheeler Jan 1987

A Viable Form Of Weyl’S Theory, James Thomas Wheeler

All Physics Faculty Publications

A reinterpretation of the Weyl vector in a Weyl geometry is shown to yield Dirac’s 1951 classical theory of the electron, thereby avoiding the most obvious problems of measurement inherent in Weyl’s original geometric formulation of electromagnetism. This paves the way for the consistency of recent metric-connection theories, for which similar questions of measurement can arise.


Theoretical Study Of The Effect Of Ionospheric Return Currents On The Electron Temperature, Robert W. Schunk, Jan Josef Sojka, M. D. Bowline Jan 1987

Theoretical Study Of The Effect Of Ionospheric Return Currents On The Electron Temperature, Robert W. Schunk, Jan Josef Sojka, M. D. Bowline

All Physics Faculty Publications

An electron heat flow can occur in a partially ionized plasma in response to either an electron temperature gradient (thermal conduction) or an electron current (thermoelectric heat flow). The former process has been extensively studied, while the latter process has received relatively little attention. Therefore a time-dependent three-dimensional model of the high-latitude ionosphere was used to study the effect of field-aligned ionospheric return currents on auroral electron temperatures for different seasonal and solar cycle conditions as well as for different upper boundary heat fluxes. The results of this study lead to the following conclusions: (1) The average, large-scale, return current …


Lower-Thermospheric Winds At High Latitude, R M. Johnson, Vincent B. Wickwar, R G. Roble, J G. Luhmann Jan 1987

Lower-Thermospheric Winds At High Latitude, R M. Johnson, Vincent B. Wickwar, R G. Roble, J G. Luhmann

All Physics Faculty Publications

Observations made of the high-latitude E-region with the Chatanika, Alaska (65° N), incoherent scatter radar facility during the summer months of 1976 to 1982 are presented. Fourteen 24-h experiments were performed with altitude resolution between 9 and 24 km. Ion drifts measured during these experiments have been analysed to obtain neutral winds at lower-thermospheric heights. Tidal oscillations are the predominant feature of the neutral winds from 90 to 125 km. The semidiurnal oscillation is particularly strong, attaining peak amplitudes of ≈50 m/s at 110 km. Average semidiurnal tidal phases are in good agreement with previous mid- to hight-latitude observations. …


Heterotic String From Four-Dimensional Geometry, James Thomas Wheeler Jan 1987

Heterotic String From Four-Dimensional Geometry, James Thomas Wheeler

All Physics Faculty Publications

In any conformally invariant metric-connection theory of 4-dimensional spacetime, there are 26 ways that a body can distort. This follows from the absence of any preferred metric, and is equivalent to the ability of an observer to consider objects on any given world line to be distortion free. Within the simplest conformally invariant theory of distortions that allow metric compatible spaces as trivial solutions, we find the maximal classical solution. This solution corresponds to the bosonic sector of the heterotic string: 26 left-moving fields plus 10 right-moving fields.


Hemispherical Emissivity Of V, Nb, Ta, Mo, And W From 300 To 1000 K, S. X. Cheng, P. Cebe, L. M. Hanssen, D. Mark Riffe, A. J. Sievers Jan 1987

Hemispherical Emissivity Of V, Nb, Ta, Mo, And W From 300 To 1000 K, S. X. Cheng, P. Cebe, L. M. Hanssen, D. Mark Riffe, A. J. Sievers

All Physics Faculty Publications

The hemispherical emissivities of five transition elements, V, Nb, Ta, Mo, and W, have been measured from 300 to 1000 K, complementing earlier higher-temperature results. These low-temperature data, which are similar, are fitted to a Drude model in which the room-temperature parameters have been obtained from optical measurements and the temperature dependence of the dc resistivity is used as input to calculate the temperature dependence of the emissivity. A frequency-dependent free-carrier relaxation rate is found to have a similar magnitude for all these elements. For temperatures larger than 1200 K the calculated emissivity is always greater than the measured value, …


A Substorm Resulting From Energy Storage In The Magnetosphere, T S. Jorgensen, K Larsen, W J. Heikkila, Vincent B. Wickwar, G Haerendel Jan 1987

A Substorm Resulting From Energy Storage In The Magnetosphere, T S. Jorgensen, K Larsen, W J. Heikkila, Vincent B. Wickwar, G Haerendel

All Physics Faculty Publications

In order to study the problem whether magnetospheric substorms are directly driven by solar wind energy or result from unloading of such energy temporarily stored in the magnetosphere, it is necessary to investigate substorms following long quiescent periods and to observe solar wind parameters in proximity of the magnetsosphere as well as many high-latitude ionosphere parameters with good temporal resolution.

In this study we present such observations obtained on November 29, 1984 by the AMPTE-IRM spacecraft just outside the bow shock and by the Sondrestrom incoherent scatter radar plus several other instruments in the earth's polar region.

We infer from …


Brst Structure Of General Relativity In Terms Of New Variables, Charles G. Torre Jan 1987

Brst Structure Of General Relativity In Terms Of New Variables, Charles G. Torre

All Physics Faculty Publications

The structure of the Poisson-brackets algebra of constraints of general relativity is reexamined using the recently introduced spinorial variables. Three different combinations of constraints are analyzed and their relative merits are discussed. In each case we construct the corresponding expression of the Becchi-Rouet-Stora-Tyutin charge. These expressions provide a point of departure for a nonperturbative quantization scheme for general relativity.


Optical And Radar Characterization Of A Short-Lived Auroral Event At High Latitude, A Vallance-Jones, R L. Gattinger, P Shih, J W. Meriwether, Vincent B. Wickwar, J D. Kelly Jan 1987

Optical And Radar Characterization Of A Short-Lived Auroral Event At High Latitude, A Vallance-Jones, R L. Gattinger, P Shih, J W. Meriwether, Vincent B. Wickwar, J D. Kelly

All Physics Faculty Publications

Observations of optical emission intensities and incoherent scatter radar returns in the magnetic zenith were compared in a study carried out at Sondre Stromfjord (Λ = 76.1°) in Greenland. The results were used to test the consistency of a theoretical model of ion chemistry and optical emissions in aurora and to explore the accuracy of relations between optical measurements and the average energy of the incident electrons. The incident primary electron spectrum and its temporal variation were inferred from zenith electron density profiles from the radar. The inferred primary energy spectrum at the peak intensity of the event approximated a …


A Theoretical Study Of The Lifetime And Transport Of Large Ionospheric Density Structures, Robert W. Schunk, Jan Josef Sojka Jan 1987

A Theoretical Study Of The Lifetime And Transport Of Large Ionospheric Density Structures, Robert W. Schunk, Jan Josef Sojka

All Physics Faculty Publications

Large-scale density structures are a common feature in the high-latitude ionosphere. They have been observed in the dayside cusp, polar cap, and nocturnal auroral region. Relative to background densities, the perturbations associated with large-scale structures vary from about 10% to a factor of 100. The lifetime and transport characteristics of “large” ionospheric structures (factor of 10 to 100) were studied with the aid of a three-dimensional time-dependent ionospheric model. Both density depletions and enhancements were considered. A density structure was created at a specific location in the high latitude F region and the subsequent evolution was followed for different seasonal …


Theoretical Study Of The High-Latitude Ionosphere’S Response To Multicell Convection Patterns, Jan Josef Sojka, Robert W. Schunk Jan 1987

Theoretical Study Of The High-Latitude Ionosphere’S Response To Multicell Convection Patterns, Jan Josef Sojka, Robert W. Schunk

All Physics Faculty Publications

It is well known that convection electric fields have an important effect on the ionosphere at high latitudes and that a quantitative understanding of their effect requires a knowledge of the plasma convection pattern. When the interplanetary magnetic field (IMF) is southward, plasma convection at F region altitudes displays a two-cell pattern with antisunward flow over the polar cap and return flow at lower latitudes. However, when the IMF is northward, multiple convection cells can exist, with both sunward flow and auroral precipitation (theta aurora) in the polar cap. The characteristic ionospheric signatures associated with multicell convection patterns were studied …


Higher-Dimensional Self-Consistent Solution With Deformed Internal Spaces, T. -C. Shen, J. Sobczyk Jan 1987

Higher-Dimensional Self-Consistent Solution With Deformed Internal Spaces, T. -C. Shen, J. Sobczyk

T. -C. Shen

We study a system of gravity and free massless scalar fields minimally coupled to gravity in a 7- dimensional background which is a direct product of a 4-dimensional Minkowski space and a 3- dimensional homogeneously deformed three-sphere. Compactification is caused by the vacuum energy of scalar fields. The effective potential as a function of two parameters (scale and deformation) is calculated numerically after dimensional regularization. We find the effective potential decreases rapidly toward negative infinity in both prolate and oblate directions. The classical curvature, however, can balance the quantum effect and yields three extrema. In addition to the round S …


Slow Collisions Of Hydride Ion And Deuteride Ion With Sodium, Potassium And Cesium, Yicheng Wang Jan 1987

Slow Collisions Of Hydride Ion And Deuteride Ion With Sodium, Potassium And Cesium, Yicheng Wang

Dissertations, Theses, and Masters Projects

The cross sections of charge transfer and electron detachment in collisions of H$\sp{-}$ and D$\sp{-}$ with Na, K and Cs have been measured for collision energies ranging from 3 to 300 eV. Both charge transfer and electron detachment are significant electron-loss mechanisms for H$\sp{-}$(D$\sp{-}$); both processes exhibit velocity-dependent isotope effects for H$\sp{-}$ and D$\sp{-}$. $\sigma\sb{\rm cg}$(E) displays high energetic thresholds for Na and K (about 20 eV for H$\sp{-}$ + Na and 40 eV for H$\sp{-}$ + K) yet no obvious one for Cs. $\sigma\sb{\rm e}$(E) does not depend on the target as much as $\sigma\sb{\rm ct}$(E) and displays near …


Molecular Dynamics In Hydrogen‐Bonded Interactions: A Preliminary Experimentally Determined Harmonic Stretching Force Field For Hcn‐‐‐Hf, B. A. Wofford, Shannon Lieb, J. W. Bevan Jan 1987

Molecular Dynamics In Hydrogen‐Bonded Interactions: A Preliminary Experimentally Determined Harmonic Stretching Force Field For Hcn‐‐‐Hf, B. A. Wofford, Shannon Lieb, J. W. Bevan

Scholarship and Professional Work - LAS

Observation of the 2ν1 overtone band in the hydrogen‐bonded complex HCN‐‐‐HF permits evaluation of the anharmonicity constant X 1 1=−116.9(1) cm 1 and determination of the anharmonicity corrected fundamental frequency ω1. This information, and available data from previous rovibrational analyses in the common and perdeuterated isotopic species of HCN‐‐‐HF, offer an opportunity for calculation of an approximate stretching harmonic force field. With the assumptions f 1 2=f 2 4=0.0, the remaining force constants (in mdyn/Å) are evaluated as: f 1 1=8.600(20), f 2 2=6.228(9), f 3 3=19.115(40), f 4 …


A Mössbauer Effect Study Of The Structural And Magnetic Properties Of Y₂(Fe₁₋ₓalₓ)₁₄B, Ying-Chang Yang, Dwayne E. Tharp, Gary J. Long, Oran Allan Pringle, William Joseph James Jan 1987

A Mössbauer Effect Study Of The Structural And Magnetic Properties Of Y₂(Fe₁₋ₓalₓ)₁₄B, Ying-Chang Yang, Dwayne E. Tharp, Gary J. Long, Oran Allan Pringle, William Joseph James

Chemistry Faculty Research & Creative Works

The crystallographic and magnetic properties of Y₂(Fe₁₋ₓAlₓ)₁₄B, where x equals 0.00, 0.02, 0.04, 0.06, and 0.08, have been investigated by Mössbauer spectroscopy and magnetic measurements at room temperature and 85 K. Magnetic anisotropy and magnetization changes with aluminum substitution indicate that, because of size, the aluminum preferentially occupies the j₂ site over the remaining five crystallographically nonequivalent iron sites. This preferential occupation has been confirmed by Mössbauer spectral studies, which indicate that the compositional variation of the hyperfine field for each site is related to the number of near-neighbor aluminum atoms for the site. This compositional variation is helpful in …


Comment On "Orientation, Alignment, And Hyperfine Effects On Dissociation Of Diatomic Molecules To Open Shell Atoms", Mark D. Havey, Linda L. Vahala Jan 1987

Comment On "Orientation, Alignment, And Hyperfine Effects On Dissociation Of Diatomic Molecules To Open Shell Atoms", Mark D. Havey, Linda L. Vahala

Electrical & Computer Engineering Faculty Publications

A recent paper in this journal [Y. B. Band e t a l., J. Chem. Phys. 8 4, 3762 (1986)] reported parameters describing orientation and alignment produced, in an axial recoil limit, by one photondissociation of diatomic molecules. Reported also were values, applicable to the resonance transitions of the alkali atoms, for orientation and alignment depolarization coefficients. Most of the numerical values reported for the coefficients were incorrect, in some cases by as much as a factor of 2. We report a tabulation of correct depolarization coefficients applicable to the resonance transitions of common alkali isotopes. Further, the coefficients …


Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman Jan 1987

Limit Theorems In The Area Of Large Deviations For Some Dependent Random Variables, Narasinga Rao Chaganty, Jayaram Sethuraman

Mathematics & Statistics Faculty Publications

A magnetic body can be considered to consist of n sites, where n is large. The magnetic spins at these n sites, whose sum is the total magnetization present in the body, can be modelled by a triangular array of random variables (X(n) 1,..., X(n) n). Standard theory of physics would dictate that the joint distribution of the spins can be modelled by dQn(x) = zn-1 exp[ -Hn(x)]Π dP(xj), where x = (x1,..., xn) ∈ Rn, where Hn is the Hamiltonian, zn is …


Evaluation Of The Reduction Of The Nonadiabatic Hyperspherical Radial Equation To The First Order, Steven L. Carbon Jan 1987

Evaluation Of The Reduction Of The Nonadiabatic Hyperspherical Radial Equation To The First Order, Steven L. Carbon

Retrospective Theses and Dissertations

In this paper we examine the effectiveness of reducing the second order radial equation, of the hyperspherical coordinate solution to the two-electron Schrodinger equation, into a set of coupled first order linear equations as suggested by Klar. All results have been obtained in a completely nonadiabatic formalism thereby ensuring accuracy. We arrive at the conclusion that our application of the reduction process is in some way inconsistent and suggest a possible resolution to this anomaly.