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The Calculation of Diffusion Properties for Open Shell Molecules

- Navier-Stokes requires as input various collision integrals for gases - Diffusion, - Viscosity - Thermal conductivity - Thermal diffusion ... - Levin, Stallcop and Partridge state-of-the-art - Non-Relativistic Born-Oppenheimer Approximation (freeze nuclei first, let them move second) - Solve electron problem: Compute realistic Potential Curves (PC) from first principles, - Solve nuclei problem: Compute scattering properties for each PC using sophisticated semi-classical method - Compute cross sections - Compute appropriate thermal collision integrals

STMD↗

Studies of electron-molecule collisions - Applications to e-H2O

Elastic differential and momentum transfer cross sections for the elastic scattering of electrons by H2O are reported for collision energies from 2 to 20 eV. These fixed-nuclei static-exchange cross sections were obtained using the Schwinger variational approach. In these studies the exchange potential is directly evaluated and not approximated by local models. The calculated differential cross sections, obtained with a basis set expansion of the scattering wave function, agree well with available experimental data at intermediate and larger angles. As used here, the results cannot adequately describe the divergent cross sections at small angles. An interesting feature of the calculated cross sections, particularly at 15 and 20 eV, is their significant backward peaking. This peaking occurs in the experimentally inaccessible region beyond a scattering angle of 120 deg. The implication of this feature for the determination of momentum transfer cross sections is described.

Brescansin, L. M.↗

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.

Chandra, N.↗

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.

Chandra, N.↗

Quantum mechanical study of elastic scattering and rotational excitation of CO by electrons

Coupling calculations of differential, integral, and momentum transfer cross sections for pure elastic scattering and rotational excitation of CO by electron impact are reported. The calculations are based on a static charge distribution that has correct dipole and quadrupole moments, has cusps at the nuclei, and is augmented by an SCF treatment of charge polarization and a local approximation for exchange. The rotationally summed cross sections, with no adjustable parameters in the scattering calculation, are in reasonably good agreement with the experimental cross sections but are somewhat larger at small scattering angles.

Onda, K.↗

Electron-CF4 elastic scattering in the static-exchange approximation

Differential, integral, and momentum-transfer cross sections for the elastic scattering of electrons by CF4 from 5 to 35 eV are reported. The calculations were carried out at the fixed-nuclei, static-exchange level usign the Schwinger variational principle. Analyses of the partial channel amplitudes show four broad shape resonances; two in T2, one in A1, and one in E symmetries. The positions of these resonances agree with experimental data from total-cross-section measurements, dissociative attachment studies, and low-energy electron excitation spectra, the only exception being the 8.9-eV structure in the total-cross-section data. No experimental measurements on differential cross sections are available, but comparing with the corresponding static-exchange calculations for the e-CH4 system, the e-CF4 cross sections generally are less backward peaked.

Huo, Winifred M.↗

Nonthermal electron-positron pair production and the 'universal' X-ray spectrum of active galactic nuclei

A nonthermal model for power-law X-ray and gamma-ray sources is considered. An initial, primary distribution of relativistic electrons is injected and cooled via Compton scattering of soft photons (produced either externally or by the synchrotron mechanism). The scattered photons, constituting a primary gamma-ray source, produce electron-positron pairs that act as a secondary electron injection, which in turn produce a secondary photon spectrum. Pairs formed by a part of the photon spectrum optically thin to pair production are taken into account. The distribution of particles and photons is obtained, and numerical results as well as analytical solutions to certain special cases are presented. For the case of a delta-function primary electron injection it is found that the photon spectrum in the X-ray region is well approximated by a power law, with the energy spectral index alpha(X) lying in the relatively narrow range 0.5-0.9 as the compactness parameter L(x)/R (where L(x) is the X-ray luminosity and R is the source radius) varies over many orders of magnitude. This is proposed as a possible mechanism to explain the universal X-ray spectra observed from active galactic nuclei.

Zdziarski, A. A.↗

X-ray heated winds in Seyfert galaxies

Recent observational work has shown that Type 2 Seyfert galaxies contain Type 1 nuclei. These are hidden from direct view by obscuring material of toroidal geometry, but are revealed by scattering off asymmetrically distributed warm electrons which gives the light net polarization. Warm, ionized gas of the right temperature and optical depth to match the observations is exactly what would be expected due to evaporation of material from the inner edge of the obscuring torus by the nuclear UV and X-ray continuum. In addition to revealing the nucleus by scattering, this warm gas also produces strong X-ray Fe K features.

Krolik, Julian H.↗

Electron scattering and the distances to cluster cooling flows

Cluster cooling flows have electron-scattering optical depths which are estimated to be about 0.01. Many of the cluster-dominant galaxies centered in cluster cooling flows have active nuclei, and about 1 percent of the luminosity from the active nuclei should appear as diffuse, scattered radiation. It is shown here that detection of this scattered radiation at radio wavelengths can provide a measure of the distance to the cluster that is independent of the Hubble constant. Observations of the scattered surface brightness profile can also be used to test for clumpiness in the gas, for variations in the central radio source on time scales less than 100,000 yr, and for the degree of beaming of radiation from the central source.

Wise, Michael W.↗

Particle Acceleration in Active Galactic Nuclei

The investigation of stochastic particle acceleration through resonant interactions with plasma waves that populate the magnetosphere surrounding an accreting black hole is presented. Stochastic acceleration has been successfully applied to the problem of ion and electron energization in solar flares, and is capable of accounting for a wide range of both neutral and charged particle emissions. It is also a component in diffusive shock acceleration, since pitch-angle scattering (which is necessary for multiple shock crossings) is accompanied by diffusion in momentum space, which in turn yields a net systematic energy gain; however, stochastic energization will dominate the first-order shock process only in certain parameter regimes. Although stochastic acceleration has been applied to particle energization in the lobes of radio galaxies, its application to the central regions of AGNs (active galactic nuclei) has only recently been considered, but not in detail. We proposed to systematically investigate the plasma processes responsible for stochastic particle acceleration in black hole magnetospheres along with the energy-loss processes which impede particle energization. To this end, we calculated acceleration rates and escape time scales for protons and electrons resonating with Alfven waves, and for electrons resonating with whistlers. We also considered the "hot" topic of gamma-ray line emission from the Orion complex. We proposed that the observed gamma-ray lines are produced by energetic ions that are stochastically accelerated by cascading Alfven waves in the accretion plasma near a black hole. Related research papers that were published in journals are listed.

Miller, James A.↗

An X-ray heated wind in NGC 1068

Recent work published by Antonucci and Miller in 1985 has demonstrated the existence of a type 1 Seyfert nucleus inside the archetypical type 2 Seyfert galaxy NGC 1068. This nucleus is surrounded by an obscuring torus and is visible only by reflection from a warm electron scattering region on the torus's axis. Here it is shown that the warm region must be in a dynamic state and out of radiative equilibrium with the nuclear continuum. It is suggested that the source of this moving gas is the cold obscuring torus itself, and that the warm region is part of a wind driven by heating due to the central continuum. The obscuring torus may be an inner extension of the starburst region already known in NGC 1068. This model gives estimates of the temperature and optical depth of the electron scattering region consistent with the observed values. Variations in viewing angle and optical thickness in the torus may account for the range of observed properties in active galactic nuclei.

Krolik, J. H.↗

Spectropolarimetric test of the relativistic disk model for the broad emission lines of active galactic nuclei

Previously, it was claimed that the broad emission lines of the radio galaxy Arp 102B can be fitted by the line profile from a simple relativistic Keplerian thin disk. It was argued that the lines originating from the relativistic accretion disk could be polarized due to electron scattering, which is likely to be the dominant opacity in the line-emitting region of Arp 102B. In the present work, the expected polarization properties of these broad emission lines are calculated. The percentage of polarization depends strongly on the inclination angle. For some angles, the red peak of the polarized, double-peaked line profile can be higher than the blue peak. This is in contrast to the total line profile, in which the blue peak is always higher than the red one. Spectropolarimetric observations could, therefore, provide an independent test of the relativistic disk model for the broad emission lines of Arp 102B and other active galactic nuclei.

Chen, Kaiyou↗

Extragalactic X-ray sources.

The extended X-ray sources associated with the Virgo, Perseus, and Coma clusters of galaxies can best be explained as a result of the Compton scattering of relativistic electrons (generated in the radio sources which are present in each of these clusters) on the microwave background radiation. The same physical process involving microwave infrared or optical photons generated in the nuclei of active galaxies may account for the more compact X-ray sources. Thermal bremsstrahlung of hot gas in clusters of galaxies is a less likely source of X-rays.

Brecher, K.↗

Power-law X-ray and gamma-ray emission from relativistic thermal plasmas

A common characteristic of cosmic sources is power-law X-ray emission. Extragalactic sources of this type include compact components of active galactic nuclei (AGN). The present study is concerned with a theoretical model of such sources, taking into account the assumption that the power-law spectra are produced by repeated Compton scatterings of soft photons by relativistic thermal electrons. This is one of several possible physical mechanisms leading to the formation of a power-law spectrum. Attention is given to the Comptonization of soft photon sources, the rates of pair processes, the solution of the pair equilibrium equation, and the constraints on a soft photon source and an energy source. It is concluded that the compactness parameters L/R of most of the cosmic sources observed to date lie below the maximum luminosity curves considered.

Zdziarski, A. A.↗

Evolution of photon and particle spectra in compact, luminous objects

The physics of high energy photons and particles (especially electrons and positrons) in the compact, high-energy-density of galactic nuclei and quasars was investigated. A numerical code was developed which follows the nonlinear spectral evolution of a pair/photon plasma, due to two-body scattering and interaction process, in an unmagnetized system. The code was applied both to static plasmas and to relativistic expanding winds.

Eilek, Jean A.↗

Hybrid theory calculation of electron-N2 scattering at 5 and 10 eV

Hybrid theory results pertaining to e-N2 scattering have been evaluated for differential elastic and first vibrational excitation cross sections at 5 and 10 eV. Comparison with the recent experiment of Chutjian, Srivastava, and Trajmar is good (1976), although there is an indication that the calculated nonresonant (adiabatic-nuclei) contribution is somewhat too small. A short discussion engendered by this point is given.

Chandra, N.↗

Radiation force on a relativistic plasma and the Eddington limit

Calculations of the radiation force due to Thomson scattering on a relativistic plasma are presented and discussed in relation to certain astronomical objects which operate within a few orders of magnitude of their Eddington luminosity. The radiation force on a hot isotropic plasma is shown to exceed that on a cold plasma by a factor depending on the electron Lorentz factor, which can be substantial in a relativistic plasma. In such a plasma, radiative bulk acceleration is found to occur through the anisotropic loss of internal energy during the Thomson scattering, resulting in an effect termed a Compton rocket. The Compton rocket is shown to be a relevant acceleration mechanism in situations where a relativistic electron plasma lies in the vicinity of a luminous source operating near the classical Eddington limit, including compact galactic X-ray sources and objects associated with active galactic nuclei (quasars, blazars, and Seyfert nuclei).

Odell, S. L.↗

Accretion-disk modeling of the UV spectrum of quasars

The thin accretion disk spectrum, including the effect of electron scattering, is calculated for a grid of the accretion parameters. It is shown that the luminosity and spectral slope in the UV and optical bands are uniquely determined by these parameters and depend only weakly on the viscosity parameter. When the model calculations are compared with observations of a sample of QSOs and Seyfert 1 nuclei, the black hole mass is in the range 10 to the 8th to 10 to the 9.5 solar for the QSOs and 10 to the 7.5 to 10 to the 8.5 solar for the Seyferts and for low-luminosity objects. The correlation between the spectral slope and luminosity of QSOs in the UV can be explained by evolution along curves of constant black hole mass and decreasing accretion rate. The relation between the spectrum and the accretion parameters can be used to constrain the cosmological evolution of the objects and imposes severe constraints on the pure luminosity evolution interpretation function for QSOs and Seyferts.

Wandel, Amri↗