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Results for “Self-consistent calculations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Expansion of an ion cloud in the earth's magnetosphere.

The initial expansion of a barium ion cloud release in the distant earth's magnetosphere is numerically investigated by means of a computer model with self-consistent electric and magnetic interactions. Initial conditions for the calculations are an expanding neutral cloud that is photoionized with a time constant of 20 sec. The results show that after the first 30 sec, the large fluctuations in the magnetic field and in other parameters are damped out and the magnetic field in the central region of the cloud is reduced to near zero. Also, after only 10 sec, a relatively high central ion density has developed and remains for the duration of the calculations.

Hohl, F.↗
NASA NTRS1972

Deformed Brueckner-Hartree-Fock calculations

The renormalized Brueckner-Hartree-Fock (RBHF) theory for many-body nuclear systems is generalized to permit calculations for intrinsic states having permanent deformation. Both Hartree-Fock and Brueckner self-consistencies are satisfied, and details of the numerical techniques are discussed. The Hamada-Johnston interaction is used in a study of deformations, binding, size, and separation energies for several nuclei. Electromagnetic transition rates, moments, and electron scattering form factors are calculated using nuclear wave functions obtained by angular momentum projection. Comparison is made to experiment as well as to predictions of ordinary and density-dependent Hartree-Fock Theory.

Ford, W. F.↗
NASA NTRS1972

Deformed Brueckner-Hartree-Fock calculations.

The renormalized Brueckner-Hartree-Fock (RBHF) theory for many-body nuclear systems has been generalized to permit calculations for intrinsic states having permanent deformation. Both Hartree-Fock and Brueckner self-consistencies are satisfied, and details of the numerical techniques are discussed. The Hamada-Johnston interaction is used in a study of deformations, binding, size, and separation energies for several nuclei. Electromagnetic transition rates, moments, and electron scattering form factors are calculated using nuclear wave functions obtained by angular momentum projection. Comparison is made to experiment as well as to predictions of ordinary and density-dependent Hartree-Fock theory.

Ford, W. F.↗
NASA NTRS1973

Classical electromagnetic radiation of the Dirac electron

A wave-function-dependent four-vector potential is added to the Dirac equation in order to achieve conservation of energy and momentum for a Dirac electron and its emitted electromagnetic field. The resultant equation contains solutions which describe transitions between different energy states of the electron. As a consequence it is possible to follow the space-time evolution of such a process. This evolution is shown in the case of the spontaneous emission of an electromagnetic field by an electron bound in a hydrogen-like atom. The intensity of the radiation and the spectral distribution are calculated for transitions between two eigenstates. The theory gives a self-consistent deterministic description of some simple radiation processes without using quantum electrodynamics or the correspondence principle.

Lanyi, G.↗
NASA NTRS1972

Electric dipole moment of diatomic molecules by configuration interaction. IV.

The theory of basis set dependence in configuration interaction calculations is discussed, taking into account a perturbation model which is valid for small changes in the self-consistent field orbitals. It is found that basis set corrections are essentially additive through first order. It is shown that an error found in a previously published dipole moment calculation by Green (1972) for the metastable first excited state of CO was indeed due to an inadequate basis set as claimed.

Green, S.↗
NASA NTRS1967

Confirmation of the predicted Hartree-Fock limit in BeH sub 2.

We have recently estimated the total energy of the BeH 2 molecule as -15.918 ± 0.015 au. One of the steps in the analysis was to estimate the difference between the SCF energies computed with a minimal basis set of Slater orbits and with the best possible single-determinant wave function, the so-called Hartree-Fock limit and was predicted to be -15.773 ± 0.007 au for BeH 2 .

Molecular energy↗
NASA NTRS1969

Self-consistent many-electron theory of electron work functions and surface potential characteristics for selected metals

Electron work functions, surface potentials, and electron number density distributions and electric fields in the surface region of 26 metals were calculated from first principles within the free electron model. Calculation proceeded from an expression of the total energy as a functional of the electron number density, including exchange and correlation energies, as well as a first inhomogeneity term. The self-consistent solution was obtained via a variational procedure. Surface barriers were due principally to many-body effects; dipole barriers were small only for some alkali metals, becoming quite large for the transition metals. Surface energies were inadequately described by this model, which neglects atomistic effects. Reasonable results were obtained for electron work functions and surface potential characteristics, maximum electron densities varying by a factor of over 60.

Smith, J. R.↗
NASA NTRS1975

The calculation of theoretical chromospheric models and predicted OSO 1 spectra

Theoretical solar chromospheric and photospheric models are computed for use in analyzing OSO 8 spectra. The Vernazza, Avrett, and Loeser (1976) solar model is updated and self-consistent non-LTE number densities for H I, He I, He II, C I, Mg I, Al I, Si I, and H(-) are produced. These number densities are used in the calculation of a theoretical solar spectrum from 90 to 250 nm, including approximately 7000 lines in non-LTE. More than 60,000 lines of other elements are treated with approximate source functions.

Avrett, E. H.↗
NASA NTRS1973

A cylindrical shell model of the NASA-MPE barium ion cloud experiment.

A computer model is developed using infinitely long concentric cylindrical shells to represent the neutral atoms, ions and electrons in the barium cloud. The neutral shells are given a distribution of positions and velocities whose parameters are chosen to be consistent with the dynamics of the release. From this distribution, the ion and electron shells are generated at random using the observed time constant for photoionization. The ion and electron shells thus formed are followed using self-consistent equations of motion. Various averages which could be compared with observation of the actual cloud are calculated at regular time intervals. An unexpected result is the predicted very early return of the magnetic field within the cloud to its ambient value.

Grauer, A. D.↗
NASA NTRS1973

The wavelength dependence of the albedos of Uranus and Neptune from 0.3 to 1.1 micron.

Narrow-band photoelectric photometry was made of Uranus and Neptune over a wavelength interval from 0.3 to 1.1 micron. The wavelength dependence of the geometric albedo was determined for these planets. Evidence is given that the comparison star used resembles the sun very closely in its energy distribution. It is shown that, apart from methane, another opacity source seems to be necessary in the atmospheres of these planets to explain the observed wavelength dependence of the geometric albedo for the two planets simultaneously. Radiative transfer calculations were made to determine if the previously suggested pressure-induced dipole absorptions of H2 result in a self-consistent explanation. This seems to be the case. The H2 abundance in this case is limited for both planets between 350 km amagat less than or equal to N(H2) less than 800 km amagat. This agrees with a previous determination of the H2 abundance for Uranus.

Wamsteker, W.↗
NASA NTRS1975

N-body simulations of disks

The methods used in large-scale n-body simulations are discussed. However, the present review concentrates on results already obtained in n-body simulations using systems containing up to 200,000 simulation stars. Results are presented which show that the stability criterion developed for flattened systems applies only to truly axisymmetric instabilities. Purely stellar disks acquire rather large velocity dispersions, generally two or more times the velocity dispersion required by Toomre (1964) for axisymmetric stability. In computer simulations, the bar-forming instability can be prevented only by comparatively large velocity dispersions. However, simulations including the effects of the galactic halo and core as a fixed background field show that bar formation can be prevented for fixed halo components as large or larger than the self-consistent disk component. Experiments performed to determine the collisional relaxation time for large-scale gravitational n-body calculations show that these models are indeed 'collisionless'.

Hohl, F.↗
NASA NTRS1974

Numerical modelling of instantaneous plate tectonics

Assuming lithospheric plates to be rigid, 68 spreading rates, 62 fracture zones trends, and 106 earthquake slip vectors are systematically inverted to obtain a self-consistent model of instantaneous relative motions for eleven major plates. The inverse problem is linearized and solved iteratively by a maximum-likelihood procedure. Because the uncertainties in the data are small, Gaussian statistics are shown to be adequate. The use of a linear theory permits (1) the calculation of the uncertainties in the various angular velocity vectors caused by uncertainties in the data, and (2) quantitative examination of the distribution of information within the data set. The existence of a self-consistent model satisfying all the data is strong justification of the rigid plate assumption. Slow movement between North and South America is shown to be resolvable.

Minster, J. B.↗
NASA NTRS1967

Spin-projected and extended SCF calculations.

Spin restricted, unrestricted, projected unrestricted and extended SCF wave functions energies compared, discussing calculation method for spin extended SCF functions

WAVE FUNCTION↗
NASA NTRS1975

Measurement of the fluxes of galactic cosmic-ray H-2 and He-3 in 1972-1973

This paper reports measurements of the fluxes of cosmic-ray H-2 and He-3 during 1972-1973, carried out by instruments on board the IMP-7 and Pioneer 10 spacecraft. Energy spectra are generally consistent with a positive slope of unity, as would be expected for modulated secondary components. A self-consistent data set is proposed spanning the period from 1965 to 1973 wherein all spectra have the same kinematic behavior. The measured spectra for 1972-1973 are compared with calculated interstellar spectra, and it is concluded that only very broad limits can be placed on the amount of modulation. Ratios of the form H-2/He-4 and He-3/He-4 are examined and compared with calculated values based on an assumed exponential path-length distribution for galactic propagation. It is concluded that unless extreme assumptions are made about the modulation (e.g., no energy loss), it is impossible to reconcile the simple theory and observation. A nearby source is apparently required to supply enough low-energy He-4 to account for the low values of the H-2/He-4 and He-3/He-4 ratios. The possible relationship between this source and the recently discovered enhancements of cosmic-ray N and O is discussed.

Teegarden, B. J.↗
NASA NTRS1969

Numerical results in the statistical theory of thermal turbulence

Several statistical theories of turbulence are applied to thermal convection problem, and are compared in a series of numerical calculations. Results are presented for both the case of very large and very small Prandtl numbers, and for moderate Rayleigh numbers. The theories compared are the direct-interaction approximation, the self-consistent field approximation, the quasi-linear approximation, the quasi-normal approximation, and a 'Markovianized' quasi-normal approximation. Results for these theories are then compared with some simple exact solutions to the statistical problem. The results indicate that the direct-interaction and the self-consistent field method give satisfactory results at all Rayleigh numbers investigated, whereas the procedures based on the quasi-normal approximation give sensible results only at small Rayleigh numbers.

Herring, J. R.↗
NASA NTRS1974

Theoretical helium I emission-line intensities for quiescent prominences

Self-consistent solutions of the combined statistical equilibrium and transfer equations have been carried out for a rather complete multilevel, multi-ion model helium atom in model quiescent prominences. The excitation and ionization of both He I and He II were considered simultaneously, and detailed calculations of the radiative transfer in the resonance lines and ground-state continua of both these ions were made, allowing for the effects of overlapping hydrogen transitions. A large number of excited states have been included in the computation, so that a fairly comprehensive set of predicted subordinate line intensities are now available for comparison with observation. A preliminary comparison of the predicted values with published singlet/triplet ratio observations shows good agreement for all the pairs of lines considered.

Heasley, J. N.↗
NASA NTRS1967

Estimate of the Total Energy of the Beh(sub 2) Molecule

The existence of gaseous BeH 2 , predicted from simple valence theory, has still not been established experimentally. We have estimated the total energy of this molecule, assumed linear symmetric, as the sum of four negative terms; the calculated SCF energy, the SCF error to the Hartree-Fock limit, the correlation energy to the exact nonrelativistic energy, and the relativistic energy.

Molecular energy↗