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This paper extends recent work providing an elementary calculation of bremsstrahlung and opacity associated with the scattering of low-energy electrons by neutral atoms and molecules. The method applies when the scattering potential is 'hard' or when the collision time is short, applying the classical soft-photon emission probability formula for arbitrary bremsstrahlung photon energy. However, now, in addition to correcting the probability factor for finite bremsstrahlung photon energy, another factor corrects for the reduced phase space available to the outgoing electron. The bremsstrahlung cross section and opacity are then computed directly from the elastic scattering cross section, determined experimentally or calculated; a small (approximately 10 percent) correction is computed from the anisotropic term in the elastic scattering cross section. The opacity is evaluated for electron scattering by H, He, and H2 using experimentally determined values for the elastic scattering cross section, and is compared with more elaborate calculations. The agreement is good (within 10 percent), indicating an accuracy for the general method comparable to variations among the results of different elaborate theoretical computations. The agreement seems to validate the basic approximation of short collision time even at large bremsstrahlung photon energy for electron energies and temperatures up to a few eV.

General phase space theorems are discussed for the cases (A) with only energy conservation applied and (B) with energy and momentum conservation applied. It is shown that in the non-relativistic limit for N particles there is a very close relationship between the multiparticle phase space integral in case B and that for case A and N-1 particles.

The rate of breakup of helium nuclei by particle induced reactions is computed. It is shown that the rate is determined by the endothermic reaction p + 4He 3He + d, becoming effective at kT approx. few MeV. It is suggested that matter having been processed to these temperatures will be depleted in helium and in the elements C, N, O, and Ne.

By elementary methods, the cross section for electron-atom and electron-molecule bremsstrahlung is computed in the limit when the incident electron energy is much less than Ry. The procedure employs the classical soft-photon emission probability formula for general (h/2pi)(omega), yielding a simple expression for the bremsstrahlung cross section in terms of the total elastic scattering cross section. The validity of the method is discussed, and results are compared with more elaborate and accurate calculations. Comparison is made with ('free-free') opacity calculations for the associated process at the temperature (6300 K) of the solar atmosphere. For chi sub omega = (h/2pi)(omega)/kT = 1, the computed absorption coefficient is within 2, 7, and 12 percent of accurate calculations for scatterings by H, He, and H2, respectively. The general dependence of the opacity on chi sub omega is described well by the simple formula, although the error is larger for higher chi sub omega; it is suggested that the inaccuracy at high frequencies is due to the failure of the soft-photon approximation.

Graviton production in electron-electron (e-e) and electron-ion (e-z) scattering is evaluated in the Born approximation. The calculation is compared with that for photon production, that is, Coulomb quadrupole bremsstrahlung, and a number of results are taken over from that problem. Application is made to the sun, and it is found that for the solar plasma the main contribution to the graviton luminosity comes from the central core at r/R approximately 0.1. The total luminosity (Lg) in gravitons is about 7.9 x 10 to the 14th ergs/s, close to an earlier estimate by Weinberg (1965, 1972); about 33 percent of the total results from e-e collisions with the rest from e-z collisions (mainly e-p and e-alpha). Approximate corrections to Born formulas are evaluated, and this Lg includes the associated (approximately + or - 10 percent, respectively) modification. The quantum-mechanical aspects of the solar Lg problem are discussed, and it is shown why a previous classical calculation overestimated Lg by about an order of magnitude. Production of gravitons in binary collisions in other types of stars is discussed briefly. It is found that Lg varies very little along the main sequence. White dwarfs have a typical graviton luminosity LWD approximately 10 to the 19th ergs/s, while neutron stars have LNS approximately 10 to the 25th ergs/s; these estimates are very rough.

Employing elementary methods in nonrelativistic quantum electrodynamics, the cross section for gamma sub 0 + e yields e + gamma + gamma is computed for arbitrary energy in the spectrum of the outgoing photons. The final result is given, differential in the energy of one of these photons, for the case where the incident photon is unpolarized and has energy E sub 0 much less than mc-squared, a polarization sum and angular integration being performed for the final-state photons. The cross section has a simple algebraic form resulting from contributions from the sum of squared direct and exchange amplitudes; interference terms from these amplitudes do not contribute to the angular-integrated cross section.

The importance of cosmic blackbody photons as an absorbing gas for the attenuation of high-energy photons via pair production in photon-photon collision is examined for the specific case of gamma rays from Cyg X-3. Recent observational results on this photon flux in the range from 2 x 10 to the 15th to 2 x 10 to the 16th eV are corrected for this attenuation. The absorption optical depth to the source is about unity, and the corrected flux is about a factor of three higher; as a result, it does not extrapolate from the data at lower energies (10 to the 12th eV).

A number of investigations have been concerned with the kinetic theory and processes associated with a relativistic electron gas. Gould (1981) has considered a condition in which upon the ultimate thermalization the temperature can be such that the electron gas is highly relativistic while the gas of protons and other ions is nonrelativistic. With the nuclear component nonrelativistic but having energies in the MeV range and above, it is necessary to consider the effects of nuclear forces in the scattering of the ions in their thermalization. The effects of nuclear forces in the thermalization of ions in plasmas have been computed, principally in connection with problems of controlle; fusion. The present investigation is concerned with an attempt to express results in analytic form to as great a degree as possible. The p-p problem, which is the fundamental problem in astrophysical plasma, is studied. Attention is given to a low-energy formulation, the s-wave phase shift, the effective stopping number, Fokker-Planck operators, and the interaction with the electron gas.

The temperature of a source can be accurately measured, assuming that it is optically thin and exhibits a bremsstrahlung, on the basis of the shape of its spectral distribution. An explicit relation is derived for the temperature in terms of this slope, and as a sum of correction terms to the limiting form of the bremsstrahlung formula. The corrections can be evaluated easily in terms of simple, accurate asymptotic formulae. For the case where there is a distribution of temperatures in the plasma, an additional correction is derived in terms of the rms variation in the plasma temperature. Corrections due to a modified Bessel function, the Born approximation, plasma electron energy distribution and electron-electron bremsstrahlung are discussed

The establishment and maintenance of a Boltzmann distribution in particle kinetic energies is investigated for a plasma with theta = KTe/mc-squared much greater than unity, where m is the electron mass. It is shown that thermalization of the electron gas by binary collisions is not sufficiently effective to maintain the equilibrium distribution when other processes that perturb the equilibrium are taken into account. Electron-positron pair production in electron-electron and electron-ion collisions, and perturbations of a Boltzmann distribution by nonthermal processes are evaluated. Thermalization by means of other mechanisms, such as interaction with plasma waves is discussed, and the opacity of a relativistic plasma is computed for Compton scattering, pair production in the fields of electrons and ions, inverse bremsstrahlung, and synchrotron self-absorption.

Recent work on the kinetic theory of a highly relativistic electron gas and the associated photon opacity is discussed. The relaxation time for thermalization by Moller scattering is compared with the characteristic times associated with various loss processes acting to perturb the distribution away from equilibrium. For an optically thin plasma, bremsstrahlung is found to dominate Moller scattering when the dimensionless electron temperature is greater than about 3.5. Results are presented for the opacity from Compton scattering, pair production in the fields of electrons and ions, inverse bremsstrahlung, and synchrotron self-absorption.

The thermalization of particle kinetic motion by binary collisions is considered for a plasma with a Boltzmann constant-temperature product approximately equal to 10 to 100 times the product of the electron mass with the square of the speed of light. At this temperature, the principal mechanism for relaxation of electron motion is via radiationless electron-electron collisions (Moller scattering). Ions are nonrelativistic, but are energetic enough so that their Coulomb scattering can be treated in the Born approximation. Relaxation times are computed and Boltzmann-equation Fokker-Planck operators are derived for the various binary-collision processes. The expression for the rate of kinetic energy exchange between electron and ion gases is derived for the case where the gases are at different temperatures.

Questions of adiabatic expansion are considered along with aspects of Compton scattering, bremsstrahlung, electronic excitation, synchrotron radiation, and electron-positron pair production. It is found that, unless the intergalactic magnetic field is very small, synchrotron radiation will dominate all other energy loss processes at ultrahigh electron and positron energies. The dependence of the loss rates on the cosmic epoch is also discussed.

Recent Monte Carlo computations, based on a speculative extrapolation of the electron spectrum, suggested that repeated scatterings contribute most of the extragalactic X-ray background around 3 MeV in a Compton model. We have redone this calculation analytically with a similar electron spectrum, but with very different results. The double-scatter contribution near 3 MeV does not exceed 1 percent and cannot improve the fit to data. The effect is largest near 1 keV but will probably not be observable.

The collision terms in the Boltzmann equation associated with various processes are derived. For processes having a Fokker-Planck (F-P) limit, the associated F-P operator is derived by means of physical arguments to determine the form of the operator; its multiplying constant is fixed by calculating the total energy exchange rate and comparing with the rate computed by other means. In this manner, the F-P operator is derived for electron-ion scattering, electron-electron scattering in the high-velocity limit, electron-atom elastic scattering, Compton scattering, and the high-velocity limit for inelastic scattering. Other processes considered are bremsstrahlung, radiative-recombination, photoionization, collisional ionization of atoms, and suprathermal-particle ionization of atoms.

Analytic expressions are derived for the total bremsstrahlung energy-loss rate per unit volume and the spectral emission rate of a very hot (10 million K to 1 billion K) plasma. At these temperatures the principal contribution to emission can be computed from the nonrelativistic limit of electron-ion bremsstrahlung in the Born approximation. Modifications to this rate are evaluated from (1) relativistic corrections to the thermal-electron velocity distribution function, (2) relativistic and spin corrections to the nonrelativistic electron-ion bremsstrahlung cross section, (3) electron-electron bremsstrahlung, and (4) first-order Born approximation corrections to electron-ion bremsstrahlung.

A simplified procedure is proposed for calculating the cross section for photoionization from the K-shell for a general atomic system that contains an arbitrary number of outer-shell electrons. The procedure retains the formalism of the one-electron atom case (pure Coulomb-field problem) by determining the effective nuclear charge reduced from Z by 'screening parameters' associated with the other K-shell electron and the outer-bound electrons. The parameters are determined essentially by fitting the atom's radial electric field to Coulomb form at the distance from the nucleus where the integrand of the dipole radial integral is peaked.

A framework is developed for the accurate calculation of Compton and synchrotron processes in a special class of spherically-symmetric sources. The models considered take a distribution in magnetic field values and high-energy electron density that varies smoothly from central values to values at the outer boundary of the source. Further, the assumption is made that the magnetic field has local disorder (isotropy) and the high-energy electron distribution has local isotropy. Then, in terms of parameters of the source, the synchrotron brightness distribution, total synchrotron flux, Compton-synchrotron flux, and synchrotron self-absorption turnover are all computed accurately. Results are given with a view toward application to the analysis of compact non-thermal sources.

Higher-order electromagnetic processes involving particles at ultrahigh energies are discussed, with particular attention given to Compton scattering with the emission of an additional photon (double Compton scattering). Double Compton scattering may have significance in the interaction of a high-energy electron with the cosmic blackbody photon gas. At high energies the cross section for double Compton scattering is large, though this effect is largely canceled by the effects of radiative corrections to ordinary Compton scattering. A similar cancellation takes place for radiative pair production and the associated radiative corrections to the radiationless process. This cancellation is related to the well-known cancellation of the infrared divergence in electrodynamics.

The effective average energy loss for an energetic (at least about 10 to the 15th power eV) particle traversing the microwave background radiation is evaluated. Electron-photon transformations by Compton scattering and pair production (in photon-photon collisions) are computed, with the energy loss considered to be carried away by the least energetic of the outgoing particles. Considering the most energetic of the outgoing particles as the high-energy particle, the relative probability and mean time for the particle to be a photon or electron (or positron) is evaluated. The effects of synchrotron losses for electrons and positrons are emphasized and compared with Compton losses to determine a critical energy (for given magnetic field) above which synchrotron losses dominate. Magnetic deflections are also treated for the case where the magnetic field is disordered, having a characteristic 'cell' size.

The rates of radiative capture by atomic systems is computed for the first four ionization stages of the abundant elements C, N, O, Ne, Mg, Si, S, and Ar. A simple prescription is given for calculating the rates for systems in higher ionization stages. Results for capture to atomic helium are also given. In the general case, recent calculations of photoionization cross sections have been used to compute capture rates to levels of the ground-state configuration of the recombined species. Captures to other levels of the valence shell and to the higher shells are evaluated using hydrogenic formulae but with a correction factor which takes into account the nonhydrogenic nature of these states. This correction factor is due to the incomplete shielding by the inner electrons and represents essentially an effective charge for the recombining ion; it is determined semiempirically from an appropriate weighting of values derived from the observed level structure for each species. In some cases, for the capture to neutral atomic systems, its application increases the resulting computed recombination rate by a significant amount (about 50%). Computed recombination rates are tabulated for the four ionization stages at an electron temperature of 10,000 K and for the first stage at 100 K. A convenient procedure is outlined for evaluating the rates at other temperatures in the general neighborhood of these values.

Based on data on the X-ray spectrum of the Coma cluster, interpreted as thermal bremsstrahlung, the expected brightness depletion from Compton scattering of the microwave background in the direction of the cluster is computed. The calculated depletion is about one-third that recently observed by Gull and Northover, and the discrepancy is discussed. In comparing the observed microwave depletion in the direction of other clusters which are X-ray sources it is found that there is no correlation with the cluster X-ray luminosity. Consequently, the microwave depletion observations cannot yet be taken as good evidence for a thermal bremsstrahlung origin for the X-ray emission. The perturbation from Compton scattering of photons on the high-frequency (Wien) tail of the blackbody distribution is computed and found to be much larger than predicted in previous calculations. In the Wien tail the effect is a relative increase in the blackbody intensity that is appreciably greater in magnitude than the depletion in the Rayleigh-Jeans domain.

The continuum spectral flux distribution of the Seyfert galaxy NGC 1068 is analyzed by detailed models of radiative transfer in an optically thick cloud of dust grains. For wavelengths short of 30 microns, models invoking a spherical dust cloud with visual optical depth near 10 in the nucleus of the galaxy can reproduce the observed spectrum in a way consistent with information derived from spectral lines. The far-infrared emission cannot be explained easily by dust in the nucleus, but it is hypothesized that this radiation is emitted by dust associated with the observed molecular clouds, and that these clouds lie outside the nucleus. This far-infrared emission, therefore, should be extended to the same degree as the molecular-cloud distribution. High angular resolution mapping will be necessary to confirm this hypothesis.

The deviation from a Maxwellian velocity distribution caused by excitation of the J = 2 rotational level of parahydrogen (followed by radiative decay) in a molecular hydrogen gas is investigated. It is noted that inelastic collisions deplete the high-velocity tail of the distribution, while elastic collisions tend to refill it; the resulting steady-state distribution has a small depletion in the tail which slightly reduces the cooling rate of the gas. The elastic-collision transport is approximated by a continuous process, a simplified expression is obtained for the inelastic-collision operator, and the Boltzmann equation is then solved analytically. A correction to the inelastic-collision rate is evaluated, and it is found that the relative magnitude of the effect of tail depletion on the inelastic-collision rate is strongly temperature-dependent. The critical molecular density above which the J = 2 level deexcites by superelastic collisions is shown to be a weak function of temperature.

Low density plasma electron velocity distribution deviation due to Maxwellian photon radiation resulting from inelastic collisions with atoms

Collision rates in photon and relativistic particle gases, noting importance for cosmic radio and X ray sources processes calculations

Temperature dependence of H-beta emission from hot hydrogen-helium plasmas, calculating production rate at 10,000-100,000,000 K