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↗
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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.↗
Solid-liquid phase transition in argon
Starting from the Lennard-Jones interatomic potential, a modified cell theory has been used to describe the solid-liquid phase transition in argon. The cell-size variations may be evaluated by a self-consistent condition. With the inclusion of cell-size variations, the transition temperature, the solid and liquid densities, and the liquid-phase radial-distribution functions have been calculated. These ab initio results are in satisfactory agreement with molecular-dynamics calculations as well as experimental data on argon.
Tsang, T.↗
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.↗
Survey of some recent stellar-evolution calculations
The stellar-evolution program developed by Sweigart (1973) was used to compute main sequence turnoff, red giant sequences, and horizontal branch sequences for many values of helium abundance and heavy-element abundance. The immediate aim has been to produce a self-consistent set of evolutionary sequences for wide ranges in the composition and mass. The long-term aim involves application to cluster HR diagrams and the integrated properties of galaxies. Turnoff sequences, red giant sequences, and horizontal branch sequences are discussed.
Sweigart, A. V.↗
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.↗
Group-kinetic theory of turbulence
The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.
Tchen, C. M.↗
A reexamination of two-fluid solar wind models
The two-fluid solar-wind equations have been solved by a method which is approximately 50 times faster than any previously developed, through the use of asymptotic expansions which are self-consistently iterated upon to find a solution that passes through the critical point. The energy assumptions in two-fluid solar-wind models are reexamined, and the conclusions are as follows: (1) proton thermal conduction may not be neglected, (2) the Coulomb logarithm must be calculated as a function of radius, and (3) the electron and proton temperatures at the base need not be equal, even when the time scale for energy exchange between the species is an order of magnitude smaller than the expansion time at the base. It is possible to reproduce reasonable quiet-time solar-wind parameters at 1 AU, but only if the proton temperature is approximately twice the electron temperature at 1 solar radius. This may indicate that extended proton heating is important in the outer solar corona. Winds with velocities at 1 AU of 450 km/s are generated without nonthermal energy deposition but require high proton temperatures as well as very low densities at the base. Higher-velocity solutions are not possible in a spherically symmetric geometry for reasonable particle fluxes at 1 AU, and it is suggested that these higher-velocity states probably require additional heating, acceleration mechanisms, or nonradial flow.
Nerney, S.↗
Electrostatic protection of the Solar Power Satellite and rectenna
Several features of the interactions of the solar power satellite (SPS) with its space environment were examined theoretically. The voltages produced at various surfaces due to space plasmas and the plasma leakage currents through the kapton and sapphire solar cell blankets were calculated. At geosynchronous orbit, this parasitic power loss is only 0.7%, and is easily compensated by oversizing. At low-Earth orbit, the power loss is potentially much larger (3%), and anomalous arcing is expected for the EOTV high voltage negative surfaces. Preliminary results of a three dimensional self-consistent plasma and electric field computer program are presented, confirming the validity of the predictions made from the one dimensional models. Magnetic shielding of the satellite, to reduce the power drain and to protect the solar cells from energetic electron and plasma ion bombardment is considered. It is concluded that minor modifications can allow the SPS to operate safely and efficiently in its space environment. The SPS design employed in this study is the 1978 MSFC baseline design utilizing GaAs solar cells at CR-2 and an aluminum structure.
Freeman, J. W.↗
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↗
Theoretical investigation of protonated carbon dioxide
The equilibrium structure of CO2H(+) has been obtained from self-consistent field and configuration interaction wave functions. Only one stable form has been found, a linear O-C-O chain with the hydrogen bonded to oxygen and slightly off axis, in analogy with known isoelectronic species. A second structure protonated at carbon, which has been inferred from mass spectrometric studies, is found to be unstable with respect to spontaneous rearrangement. The proton affinity of CO2 is calculated to be 136 kcal/mole, in reasonable agreement with the most recent experimental value.
Green, S.↗
Accretion onto magnetized neutron stars - Structure and interchange instability of a model magnetosphere
A self-consistent model is analyzed for the spherical infall of weakly magnetized plasma into the magnetosphere of a slowly rotating, strongly magnetized neutron star. It is shown that spherical infall is probably a good approximation for X-ray sources which accrete from a stellar wind. The location of the standoff shock which halts the hypersonic infall is estimated along with the emission from the shocked layer. The location of the equilibrium magnetopause and the structure of the magnetic field within it are calculated; it is found that the magnetic poles are true cusps and that the entry of gas due to equilibrium flow across a cusp is almost certainly dominated by the interchange instability near the magnetic equator. The energy principle is applied to derive necessary conditions for the occurrence of this instability. The results indicate that the strong magnetic-pressure gradient stabilizes the gas unless moderately strong radiative cooling takes place and that the cooled plasma enters the magnetosphere as long filaments capable of moving between field lines. The rate at which the equilibrium magnetopause can 'absorb' mass and momentum is derived, the validity of the approximations employed is discussed, and the likely evolution of the sinking filaments is outlined to show that the spatial distribution of the plasma is determined mainly by the dynamics and thermodynamics of the filaments rather than the magnetic-field structure.
Arons, J.↗
The continuous UV flux of Alpha Lyrae - Non-LTE results
Non-LTE calculations for the ultraviolet C I and Si I continuous opacity show that LTE results overestimate the importance of these sources of opacity and underestimate the emergent flux in Alpha Lyr. The largest errors occur between 1100 and 1160 A, where the predicted flux in non-LTE is as much as 50 times larger than in LTE, in reasonable accord with Copernicus observations. The discrepancy between LTE models and observations has been interpreted to result from the existence of a chromosphere. Until a self-consistent non-LTE model atmosphere becomes available, such an interpretation is premature.
Snijders, M. A. J.↗
Boundary-value problem of configurations with compressible free vortex flow
A self-consistent version of the compressible boundary-value problem for configurations with leading-edge vortex separation is formulated, based on the assumption that the compressible flow field is controlled by the linearized potential equation. The stream surface boundary condition and the zero pressure jump condition of the compressible free vortex flows are analyzed; application of the Goethert rule permits the compressible nonlinear boundary-value problem for the subsonic flow domain to be transformed into an equivalent nonlinear incompressible problem. The compressibility corrections developed are used in numerical calculations of subsonic leading-edge vortex flows about planar wing geometries. The sample calculations, employing an inviscid flow model in which the wing and vortex sheets are represented by piecewise continuous quadratic doublet sheet distributions, are applicable to high subsonic Mach numbers.
Brune, G. W.↗
Effect of temperature coupling on ozone depletion prediction
The effects of chlorine perturbations on both the temperature and the ozone distribution in the stratosphere have been studied using a simplified radiative-photochemical model. The model solves the hydrostatic equation for total density in a self-consistent manner as the temperature is changed. Radiative coupling is found to have a significant effect on both the thermal structure and the ozone distribution, particularly in the 35-50-km region. By increasing the ClX mixing ratio by 5.0 ppbv, the temperature in this region is decreased by 5 to 10 K with a slight increase below 30 km. The local ozone depletion around 40 km due to added ClX is smaller compared with the estimate made by keeping the temperature fixed to the ambient condition. However, the integrated effect of radiative coupling is to increase the calculated column ozone depletion by 15% to 25% in this model.
Chandra, S.↗
Temperature and density structure of thermal proton flows
Thermal proton flows along magnetic field lines are an important feature of magnetosphere-ionosphere coupling. In this paper we report the results of a theoretical study of the thermal structure of such flows. The adopted steady state model is based upon O+, H+, and electrons with self-consistent solutions for the separate O+, H+, and electron temperatures, the O+ and H+ densities and the H+ drift velocity. Through investigation of a number of parameters affecting the model, it is shown that Joule heating arising from the flow of H+ through O+ preferentially heats H+, so that the H+ temperature is substantially greater than the O+ temperature. Low O+ densities characteristic of the trough region appear to give high H+/O+ temperature ratios. Typical O+ densities characteristic of polar wind flow regions give moderate H+/O3 temperature ratios. The Mach number of H+ outflow is substantially reduced in the present models in comparison with the older fixed temperature calculations.
Banks, P. M.↗
On the stability of self-consistent large amplitude waves in a cold plasma. I - Transverse circularly polarized waves in the absence of a large scale magnetic field
It is demonstrated that a self-consistent circularly polarized wave in an otherwise field-free homogeneous cold plasma is unstable to small amplitude perturbations. For either an electron-positron plasma or an electron-proton plasma the instability rate is at least about the order of the effective plasma frequency when the bulk flow speed is zero. For finite bulk flow speeds of the plasma, it is shown that the electron-positron plasma is unstable, again with a growth rate of the order of the effective plasma frequency; it is also shown that the electron-proton plasma is unstable (at least at small wave numbers, k) with a growth rate proportional to k. The calculated instability rates are conservative, for other modes not investigated here may be more unstable. The results of these calculations bear directly on the understanding of plasma systems thought to be driven by large amplitude waves.
Lee, M. A.↗
Departures of the electron energy distribution from a Maxwellian in hydrogen. I - Formulation and solution of the electron kinetic equation. II - Consequences
The problem of calculating the steady-state free-electron energy distribution in a hydrogen gas is considered in order to study departures of that distribution from a Maxwellian at sufficiently low degrees of ionization. A model kinetic equation is formulated and solved analytically for the one-particle electron distribution function in a steady-state partially ionized hydrogen gas, and it is shown that the formal solution can be accurately approximated by using the WKB method. The solutions obtained indicate that the high-energy tail of the distribution is susceptible to distortion by imbalanced inelastic collisions for ionization fractions not exceeding about 0.1 and that such departures from a Maxwellian can lead to significant changes in the collisional excitation and ionization rates of ground-state hydrogen atoms. Expressions for the electron-hydrogen collision rates are derived which explicitly display their dependence on the hydrogen departure coefficients. The results are applied in order to compare self-consistent predictions with those based on the a priori assumption of a Maxwellian distribution for models of the thermal ionization equilibrium of hydrogen in the optically thin limit, spectral-line formation by a gas consisting of two-level atoms, and radiative transfer in finite slabs by a gas of four-level hydrogen atoms.
Shoub, E. C.↗