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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Two-electron bond-orbital model. I

The one-electron bond-orbital model of Harrison (1973) for tetrahedrally coordinated solids is modified to a two-electron model using a generalization of Falicov and Harris' (1969) method for treating the hydrogen molecule. Expressions for nuclear-exchange and pseudodipolar interactions are obtained in terms of bond-orbital model parameters. The eigenfunctions and eigenvalues of the Hamiltonian are employed along with standard perturbation theory to calculate the energy shifts resulting from the application of an external electric field and induced by the magnetic interaction between the nuclear spins and the bond-electron spins. The quantitative predictions of the derived formulas are examined for real semiconductors involving elements and compounds from periodic groups III, IV, and V. It is concluded that the present two-electron model makes it possible to assess the quantitative effects of electron correlation in the anion-cation bond for both nonmagnetic properties (electric susceptibility, dielectric constant) and magnetic properties (nuclear-exchange and pseudodipolar interactions) of various materials.

Huang, C.↗
NASA NTRS1975

Molecular spectroscopy and collisional excitation

The paper examines the basic principles underlying the molecular transitions responsible for interstellar molecular spectra. The energy levels of molecules are discussed in detail with special attention given to the Born-Oppenheimer approximation, the electronic Hamiltonian, and the parameters of vibrational and rotational energy. The probabilities for radiative and collisional transitions are calculated. A brief review of techniques for molecular spectroscopy is presented along with methods used to determine collision cross sections on both an experimental and a theoretical basis.

Green, S.↗
NASA NTRS1976

Two-photon coherent states of the radiation field

The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.

Yuen, H. P.↗
NASA NTRS1977

Atomic electron energies including relativistic effects and quantum electrodynamic corrections

Atomic electron energies have been calculated relativistically. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all orbitals in all atoms with 2 less than or equal to Z less than or equal to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. These results will serve for detailed comparison of calculations based on other approaches. The magnitude of quantum electrodynamic corrections is exhibited quantitatively for each state.

Aoyagi, M.↗
NASA NTRS1977

Adiabatic particle motion in a nearly drift-free magnetic field: Application to the geomagnetic tail

The guiding center motion of particles in a nearly drift free magnetic field is analyzed in order to investigate the dependence of mean drift velocity on equatorial pitch angle, the variation of local drift velocity along the trajectory, and other properties. The mean drift for adiabatic particles is expressed by means of elliptic integrals. Approximations to the twice-averaged Hamiltonian W near z = O are derived, permitting simple representation of drift paths if an electric potential also exists. In addition, the use of W or of expressions for the longitudinal invariant allows the derivation of the twice averaged Liouville equation and of the corresponding Vlasov equation. Bounce times are calculated (using the drift-free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for the mean drift.

Stern, D. P.↗
NASA NTRS1976

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations for Z between 2 and 106

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

Huang, K.-N.↗
NASA NTRS1977

Variational calculations of vibrational properties of ozone

A variational method is used to obtain vibrational-rotational properties for ozone from an experimental quartic force field. Band positions, average structures, matrix elements for calculating infrared intensities, and effective rotational constants are reported for (O-16)3 and its O-18 isotopic species. Also, the degree to which the vibrational energies and properties are converged is investigated as a function of the basis set parameters and basis set size, and of the method of obtaining the Hamiltonian matrix elements. A convenient procedure for assigning the vibrational states is developed for variational vibrational wavefunction expansions.

Carney, G. D.↗
NASA NTRS1977

Analysis of torsional spectra of molecules with two internal C3v rotors. II - Far infrared and low frequency Raman spectra of dimethylether isotopes

The torsional far infrared and Raman spectra of gaseous CH3OCH3, CD3OCH3, and CD3OCD3 are presented. They are analyzed using a computer program which is based on the results of an extensive investigation of the isometric groups and of the symmetry groups of the rotation-internal rotation Hamiltonians of a series of semirigid two-top models. Four or more Fourier coefficients of the potential functions in two variables could be determined for each isotope. Strong evidence was found for Fermi-resonance-type interactions with the COC bending mode.

Groner, P.↗
NASA NTRS1977

Theory of the rotation of the rigid earth

Equations of motion for a triaxial rigid earth are derived in Andoyer variables. The reference plane is the ecliptic of date which is moving as a result of planetary perturbations. By using this noninertial system, the development of the disturbing function for the sun and moon is simplified, with an additional term appearing in the Hamiltonian which, however, contributes only to precessional motion. The nutation terms derived are compared with those of Woolard.

Kinoshita, H.↗
NASA NTRS1978

Use of asymptotic methods in vibration analysis

The derivation of dynamic differential equations, suitable for studying the vibrations of rotating, curved, slender structures was examined, and the Hamiltonian procedure was advocated for this purpose. Various reductions of the full system are displayed, which govern the vibrating troposkien when various order of magnitude restrictions are placed on important parameters. Possible advantages of the WKB asymptotic method for solving these classes of problems are discussed. A special case of this method is used illustratively to calculate eigenvalues and eigenfunctions for a flat turbine blade with small flexural stiffness.

Ashley, H.↗
NASA NTRS1978

Study of diatomic molecules. 2: Intensities

The theory of perturbations, giving the diatomic effective Hamiltonian, is used for calculating actual molecular wave functions and intensity factors involved in transitions between states arising from Hund's coupling cases a,b, intermediate a-b, and c tendency. The Herman and Wallis corrections are derived, without any knowledge of the analytical expressions of the wave functions, and generalized to transitions between electronic states with whatever symmetry and multiplicity. A general method for studying perturbed intensities is presented using primarily modern spectroscopic numerical approaches. The method is used in the study of the ScO optical emission spectrum.

Femenias, J. L.↗
NASA NTRS1976

The development of the Poincare-similar elements with true anomaly as the independent variable

In reference 1, the Hamiltonian of the unperturbed two-body problem in extended phase space is established. Depending on the type of time transformation, eight canonical elements were developed with the true anomaly or the eccentric anomaly as the independent variable. These two new sets, DS(phi) and DS(u), however contain singularities for small eccentricities and inclinations. In reference 2, these singularities are removed by a transformation from DS(u) to eight canonical PS(u) elements. In reference 3, the DS(phi) variables are transformed to the PS(phi) elements to remove the singularities. However, no direct relation was established between the eight canonical PS(phi) elements and the Cartesian coordinates. It is the purpose of this report to establish those relations and to develop the perturbed equations of motion in the PS(phi) space. This report also demonstrates the accuracy of this new set when it is applied to numerical orbit prediction problems.

Mueller, A.↗
NASA NTRS1977

Diagrammatic perturbation theory - The ground state of the carbon monosulfide molecule

Diagrammatic many-body perturbation theory is employed in a study of the ground state of the carbon monosulfide molecule for bond lengths close to the equilibrium value. The calculations are complete through third order in the energy within the algebraic approximation. Two different zero-order Hamiltonians are considered, and all two-, three-, and four-body terms are determined for the corresponding perturbation expansions. Many-body effects are found to be very important. Pade approximants to the energy expansion are constructed, and upper bounds evaluated. Almost 53 percent of the estimated correlation energy is recovered. The variation of components of the correlation energy with nuclear separation is investigated. Spectroscopic constants are also calculated.

Wilson, S.↗
NASA NTRS1977

Comparison of some optimal control methods for the design of turbine blades

This paper attempts a comparative study of some numerical methods for the optimal control design of turbine blades whose vibration characteristics are approximated by Timoshenko beam idealizations with shear and incorporating simple boundary conditions. The blade was synthesized using the following methods: (1) conjugate gradient minimization of the system Hamiltonian in function space incorporating penalty function transformations, (2) projection operator methods in a function space which includes the frequencies of vibration and the control function, (3) epsilon-technique penalty function transformation resulting in a highly nonlinear programming problem, (4) finite difference discretization of the state equations again resulting in a nonlinear program, (5) second variation methods with complex state differential equations to include damping effects resulting in systems of inhomogeneous matrix Riccatti equations some of which are stiff, (6) quasi-linear methods based on iterative linearization of the state and adjoint equation. The paper includes a discussion of some substantial computational difficulties encountered in the implementation of these techniques together with a resume of work presently in progress using a differential dynamic programming approach.

Desilva, B. M. E.↗
NASA NTRS1977

ADRF experiments using near n.pi pulse strings

Adiabatic demagnetization (ADRF) can be achieved in a dipolar coupled nuclear spin system in solids by applying a string of short RF pulses and gradually modulating the pulse amplitudes or pulse angles. This letter reports an adiabatic inverse polarization effect in solids and a rotary spin echo phenomenon observed in liquids when the pulse angle is gradually changed across integral multiples of pi during a string of RF pulses. The RF pulse sequence used is illustrated along with the NMR signal from a CaF2 single crystal as observed between the RF pulses and the rotary spin echo signal observed in liquid C6F6 for n = 2. The observed effects are explained qualitatively on the basis of average Hamiltonian theory.

Rhim, W. K.↗
NASA NTRS1978

Adiabatic particle motion in a nearly drift-free magnetic field - Application to the geomagnetic tail

An investigation is made of the adiabatic particle motion occurring in an almost drift-free magnetic field. The dependence of the mean drift velocity on the equatorial pitch angle and the variation of the local drift velocity along the trajectories is studied. The fields considered are two-dimensional and resemble the geomagnetic tail. Derivations are presented for instantaneous and average drift velocities, bounce times, longitudinal invariants, and approximations to the adiabatic Hamiltonian. As expected, the mean drift velocity is significantly smaller than the instantaneous drift velocities found at typical points on the trajectory. The slow drift indicates that particles advance in the dawn-dusk direction rather slowly in the plasma sheet of the magnetospheric tail.

Stern, D. P.↗
NASA NTRS1978

A note on the averaging method

A simple problem of a two-body system perturbed by the disturbing function epsilon/r-squared is considered to show that the time-averaged equations of the true and mean anomaly are not necessarily equal. Secular effects due to perturbations in the mean and true anomalies are different not only in value but also in sign. A more general case where the disturbing function is periodic with respect to the mean anomaly is also considered. Here a discrepancy in the time-averaged solutions is due to the fact that the mean anomaly is an action-angle variable conjugate to the action variable L, while the true anomaly is not. When the action-angle variables are chosen as dependent variables, the Hamiltonian is a function only of action variables. One must first derive first-order solutions, substitute them into the right-hand side of the equations of motion, and then take time averages.

Kinoshita, H.↗
NASA NTRS1978

A strictly Markovian expansion for plasma turbulence theory

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest non-trivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.

Jones, F. C.↗