Showing papers on "Radiative transfer published in 1969"

Radiative Corrections to Elastic and Inelastic ep and up Scattering

Abstract: We have investigated and improved the reliability of many formulas used in the radiative corrections to elastic and inelastic electron scatterings when only the scattered electrons are detected. The radiative corrections to muon scattering are also investigated. A practical and reliable recipe for unfolding the entire inelastic spectra, including effects due to virtual photons, internal and external bremsstrahlungs, is given. Examples of actually unfolding the inelastic electron spectra are given using the experimental data obtained by the electron-scattering group at the Stanford Linear Accelerator Center.

Infrared emissivities of silicates: Experimental results and a cloudy atmosphere model of Spectral emission from condensed particulate mediums

Abstract: Infrared emissivities of powered silicates are shown by experiment to contain new maximums and minimums that are representative of both composition and particle size. A cloudy atmosphere model for radiative transfer in a condensed powder is developed in which the scatter is considered to be both nonconservative and linearly anisotropic. The scattering parameters are computed as functions of frequency from the Mie diffraction theory. Detailed calculations of the spectral emissivity of quartz are presented. The model is shown to account for many features observed experimentally in the spectrums of quartz powders and sand. Changes in the spectrum with particle size can be understood in terms of changes in the albedo for single scattering and the degree of forward scatter with particle size. The principal Christiansen frequencies of silicate powder films obtained from transmission measurements are shown to be diagnostic of mineralogy and to be frequencies of maximum emissivity for powders. The relationship is discussed in detail for quartz.

Long Radiative Lifetimes of Small Molecules

Abstract: In this paper, we apply a theory of electronic relaxation in polyatomic molecules for the study of the anomalously long radiative lifetimes of NO2, CS2, and SO2. We have classified medium‐size molecules which exhibit intramolecular vibronic coupling into two intermediate cases, which we call the sparse intermediate case and the dense intermediate case, characterized by low and high spacing of the vibronic levels relative to the radiative width. The radiative decay in the sparse intermediate case was considered in detail, taking advantage of the coarse level spacing and the extremely short intramolecular recurrence time encountered in this case. From our model calculations, we conclude that:(a) in the sparse case, the radiative decay rate is characterized by a superposition of slowly varying exponentials;(b) the mean radiative lifetime is expressed as a radiative lifetime calculated from the integrated oscillator strength and “diluted” by the number of states within the half‐width of the manifold of couple...

Radiative transfer by doubling very thin layers

Abstract: Doubling principle providing rapid and accurate results for problem of diffuse reflection from plane parallel atmosphere

The collisional deactivation of metastable atoms and molecules in the upper atmosphere

Abstract: It is now possible to produce comparatively large concentrations of highly reactive metastable species in laboratory sources and to study metastable atoms and molecules with very long radiative lifetimes by photoionization mass spectroscopy, by vacuum ultraviolet absorption techniques, or by direct observation of the feeble radiation emitted by these excited species. These methods are being used widely to study the collisional deactivation of aeronomically important metastable species by quenching or by reaction. New information on radiative lifetimes, diffusion coefficients, and reaction rate coefficients is now available. These results are tabulated and reviewed in the light of atmospheric measurements and current theories of the terrestrial airglow and aurora.

Electronic Relaxation in Large Molecules

Abstract: In this paper we consider the problem of the radiative decay of electronically excited states of a large molecule. We have considered both intramolecular vibronic coupling and the interaction with the radiation field. Compound states for a system of decaying indistinguishable levels are constructed using the Fano method. General expressions for the radiative decay rate are derived and applied for the statistical limit of intramolecular vibronic coupling. On a time scale shorter than a typical intramolecular recurrence time the radiative decay is exponential, and the reciprocal lifetime consists of independent contributions of radiative and nonradiative components. The experimental implications of these results for large and medium‐size molecules are discussed.

Discrete space theory of radiative transfer I. Fundamentals

Abstract: This paper sets out a formal theory of radiative transfer in one-dimensional scattering media of arbitrary physical constitution. The theory is based on an extension of the treatment of Redheffer, in which the response of a layer of arbitrary thickness to fluxes incident on its boundaries is described by a certain linear operator. Juxtaposition of two such layers gives a third layer, whose operator can be related to those of its constituents by an operation designated as the star product. It is shown that this set of operators constitutes a semigroup under the star product, and that the infinitesimal generators of the semigroup can be computed in term s of the physical properties of the medium , point by point. This makes it possible to write equivalent discrete and differential equations from both of which transmission and reflexion operators, the emission due to internal sources, and the internal fluxes at prescribed levels in the medium can be obtained.

Self-similar piston problems with radiative heat transfer

Abstract: A differential approximation for the equations of radiative transfer in a grey gas is applied in a study of the effects of thermal radiation upon the classical problem of the compressive action of a plane, cylindrical or spherical piston. The ambient gas ahead of the precursor shock wave is supposed cool and the shock wave transparent, whilst the piston is taken to be neither an emittor nor reflector of radiative energy. It is shown that self-similar flow patterns may arise if the ambient density and piston speed are both non-uniform with variations linked to the absorption coefficient which is assumed to be density and temperature dependent. Detailed flow patterns are obtained in the case of general opacity and also in the transparent limit from which it is deduced that under certain conditions the approximation provided by the latter may be rather dubious.

Radiative Decay of Polyatomic Molecules

Abstract: In this paper we present a quantum‐mechanical treatment of the radiative decay of polyatomic molecules. The decay of a manifold of closely spaced coupled levels is handled by applying the Green's function formalism for the transition probability, where the matrix elements are displayed in an energy representation which involves either the Born–Oppenheimer or the molecular eigenstate basis set. General criteria are obtained for the occurrence of an irreversible intramolecular electronic relaxation process. The features of radiationless transitions in large, medium‐sized, and small molecules are elucidated, deriving general expressions for the radiative decay times and for the fluorescence quantum yields. Some possibilities for studying radiative interference effects in intersystem crossing are explored. A general theoretical demonstration of the occurrence of long radiative lifetimes of small molecules is presented.

Radiative Transfer in an Atmosphere–Ocean System

Abstract: The radiation field for an atmosphere-ocean system is calculated by a Monte Carlo method. In the atmosphere, both Rayleigh scattering by the molecules and Mie scattering by the aerosols and water droplets, when present, as well as molecular and aerosol absorption are included in the model. Similarly, in the ocean, both Rayleigh scattering by the water molecules and Mie scattering by the hydrosols as well as absorption by the water molecules and hydrosols are considered. Separate scattering functions are calculated from the Mie theory for the water droplets in clouds, the aerosols, and the hydrosols with an appropriate and different size distribution in each case. The photon path is followed accurately in three dimensions with new scattering angles determined from the appropriate scattering function including the strong forward scattering peak. Both the reflected and refracted rays, as well as the rays that undergo total internal reflection, are followed at the ocean surface, which is assumed smooth. The ocean floor is represented by a Lambert surface. The radiance and flux are given for two wavelengths, three solar angles, shallow and deep oceans, various albedos of ocean floor, various depths in atmosphere and ocean, and with and without clouds in the atmosphere.

Temperature Distribution and Stresses in Circular Wafers in a Row During Radiative Cooling

Abstract: A model is proposed in which transient temperature profiles in circular wafers in a row during cooling are analyzed. Various effects such as the number of wafers in a row, the position of the wafer in a row, the ratio of the wafer radius to the wafer spacing, multiple reflections, and the contribution of conduction are considered. It is shown that drastic radial variations of temperature can occur because of the geometrical factor affecting the efficiency of radiative transfer in various parts of a wafer. Thermal stresses thus induced in the cooling wafer can often exceed the yield stress in silicon wafers, causing plastic deformation. The phenomenon of ``thermal warping'' is briefly discussed.

Absorption and emission by carbon‐dioxide in the mesosphere

Abstract: Theoretical and experimental evidence is presented which leads to a vibrational relaxation time appropriate for the v2 vibration of CO2 at 15 μ under atmospheric conditions at 210°K and standard pressure of 6·0 × 10−6sec. The effect of this on the atmospheric cooling rate near 90 km due to emission by CO2 is discussed. It is shown that absorption of solar radiation by the v3 band (at 4·3 μ) and the combination bands of CO2 (at 2·7 μ) leads to a heating rate of about 2°C (12 hr)−1 near 80 km, this being one of the largest contributions to the radiative heating rate at this altitude. The processes by which relaxation from the v3 vibration of CO2 occurs involve vibrationally excited oxygen and the v2 vibration of H2O. The magnitude of heating-rate depends considerably, therefore, on the H2O concentration. For thermal radiative exchange by the v3 band, thermodynamic equilibrium begins to break down at 30 km; its contribution to the radiative budget of the mesosphere is consequently very small.

Radiative correction to the ground-state energy of an electron in an intense magnetic field

Abstract: ~OR astrophysical purposes, it has recently been investigated' ' how the ground-state energy Eo of an electron may be shifted from mc' in the presence of a very intense static uniform magnetic field H. Without radiative corrections, Eo does not depend on H. Assuming that the radiative corrections can be described by adding a term pe H to the Dirac Hamiltonian )where p = (n/2 )v(eh/2snc) is the Schwinger value for the anomalous magnetic moment, and where the components of e are the Pauli matricesf, one finds for the ground-state energy of an electron'4

Discrete space theory of radiative transfer II. Stability and non-negativity

Abstract: A number of algorithms for solving one-dimensional monochromatic radiative transfer problems were summarized in Grant & Hunt (1968 b ). This paper is concerned with the mathematical proofs of existence and non-negativity of the solutions, together with the stability of the algorithms. These results may be obtained with very general assumptions, and permit us to use the algorithms in practical problems with confidence. Numerical evi­dence is presented to support the main conclusions.

Discrete Space Theory of Radiative Transfer and its Application to Problems in Planetary Atmospheres

Abstract: The classical methods that have been devised to analyze theoretically the transfer of radiation in plane parallel atmospheres may produce an analytic solution provided that the medium is assumed to be homogeneous. Even then, when the results have been expressed in terms of tabulated functions, practical computations are difficult and tedious. It is therefore essential to employ numerical methods for solving realistic radiative transfer problems. We briefly describe a method of computation that uses discrete space techniques depending on concepts of invariance. The solution algorithms compute internal and external light fields for inhomogeneous plane parallel atmospheres with arbitrary internal, external source distributions and scattering diagrams. The stability and errors of our algorithms are susceptible to mathematical analysis and make it possible to identify the critical parameters in the calculation with precision. To illustrate our techniques, we briefly discuss the practical problem of ma...

Level‐Crossing Studies of Na2 Using Laser‐Induced Fluorescence

Abstract: The technique of using laser excitation to study level crossings in molecules has been developed and used to determine the radiative lifetime of an excited state of Na2. Optical detection of level crossing in the υ′ = 10, J′ = 12 level of the B 1Πu electronic state of Na2, excited by the 4765‐A argon‐ion laser line, has resulted in a precise measurement of the product gτ = 4.11 ± 0.12 × 10−11sec, corresponding to a magnetic field half‐width of 1385 ± 42 G. If the g value is calculated assuming Hund's coupling case (a), the radiative lifetime is determined to be τ = 6.41 ± 0.38 × 10−9sec. The influence of molecular hyperfine structure on this measurement is discussed and is found in general to contribute little uncertainty to the value of the radiative lifetime, provided the rotational angular momentum is much larger than the nuclear spin and/or provided the hyperfine interaction is much smaller than the natural width of the excited state.

Relations between the elements of the phase matrix for scattering

Abstract: The process of scattering of radiation is usually characterized by a 4 × 4 transformation matrix which relates the radiation field vector incident on the scatterer to the scattered field vector. The nine relations between the 16 elements of this phase matrix for scattering are derived explicitly for the three most commonly used representations of the intensity vector, viz., Wolf's coherency matrix formalism, Chandrasekhar's and Stokes's representations. The invariance of these relations under the action of any optical train containing one or more elements characterized by their Jones representation is demonstrated. These relations should be useful in the theory of polarization optics. The same relations are also shown to hold after rotation of the axes of reference for the electric vectors in the incident and scattered beams. Since such a transformation is required in the formulation of the theory of radiative transfer, the relations derived here may find use in multiple scattering problems as well.

Relations of radiation fluxes over natural surfaces

Abstract: Radiation fluxes over surfaces of bare soil and short grass sod were measured on clear days at St. Paul, Minnesota. Widely diverse types of daily cycles describing the hourly dependence of net upon net solar radiation were found. Heating coefficients depended as much upon atmospheric radiative properties as upon surface properties. Causes for these relations are proposed and tentatively verified experimentally. The accuracy of regressions of solar on net radiation is shown to depend upon the uniform distribution of data points extending to the region of the origin. Controversies in the literature are illuminated by this analysis, both theoretically and experimentally. Two equations relating the slope of the regression of solar on net radiation to albedo are also considered. Finally, a relation between the long-wave radiation balance and the heating coefficient proposed by Ekern (1965) is qualitatively substantiated.

Experimental determination of the cross-sections for neutral Bremsstrahlung: I. Ne, Ar and Xe

Abstract: : Experimental measurements of the cross sections for radiative scattering of electrons from the neutral species Ne, Ar and Xe have been obtained. The experiments were performed in shock-heated gases from 8000-15,000 degrees K using a rapid scanning spectrometer to measure the absolute intensity of the neutral Bremsstrahlung continuum over the wavelength interval of 2.0 - 5.4 microns in the infrared. The data have been analyzed to obtain the effective nuclear charge squared (Z sub i) squared, of the species i, doing the scattering using a modified form of the Kramers-Unsold equation, and to obtain the radiative absorption cross section Qa sub i. Experimental information on the temperature and wavelength dependence of the neutral Bremsstrahlung has been determined. The experimental Qa's have been compared with calculations based on a simple theory of radiative scattering of electrons from neutral species. (Author)

Radiative effects in semiclassical theory.

Abstract: Unquantized field calculations extended to include atomic field effect on atom, predicting spontaneous decay rate from excited state and light frequency time dependence

Molecular‐Beam Measurements of the Emission Spectrum and Radiative Lifetime of N2 in the Metastable E 3Σg+ State

Abstract: Electron‐impact excitation of a molecular beam of nitrogen was used to produce the metastable E 3Σg+ state. This state, which lies 11.87 eV above the ground state, has recently been observed in a number of electron‐impact experiments. This paper reports the emission spectrum from the molecular beam, and identifies three forbidden electronic transitions, E 3Σg+ → A 3Σu+, E 3Σg+ → B 3Πg, and E 3Σg+ → C 3Πu. Approximate absolute transition probabilities are determined. The radiative lifetime of the E state is 270 ± 100 μsec, and the equilibrium internuclear distance is 1.16 ± 0.02 A.

Radiative Lifetimes and Total Transition Probabilities for Some Polyatomic Species

Abstract: Radiative lifetimes have been measured in CS2+, SO2, C2N2, and N2O+ systems using the phase‐shift technique and electron‐beam excitation. The measured lifetimes ranged from 12.2 ± 2.5 nsec for the SO2 emission in the 2300–2700‐A range to 294 ± 30 nsec for the CS2+ B 2Σu+−X 2Πg−(i) transition. The transitions ascribed to SO2 and C2N2 show complications due to radiative cascading, while the CS2+ and N2O+ transitions observed were cascade free. These new data are discussed in light of prior spectroscopic results.

Radiative Time Constants in the Atmosphere of Jupiter

Abstract: We have computed radiative decay times for thermal disturbances near the cloud tops of Jupiter and conclude that they are much larger than probable dynamical time constants. Under these circumstances radiative equilibrium calculations are of little significance.

Analysis of the Lyman‐alpha observations of Venus made from Mariner 5

Abstract: A detailed analysis is presented of the Lyman-α observations of Venus made from Mariner 5. In the analysis, we assume that the observed emission is the result of resonance scattering of the solar Lyman-α flux by hydrogen or hydrogen and deuterium atoms in the atmosphere. The variation of the atomic densities with altitude is taken from the exospheric models of Chamberlain and McAfee. Radiative transfer effects are included but are not of crucial importance to the analysis. We find that an exospheric model consisting only of atomic hydrogen fails to give an adequate representation of the data. Instead, two constituents with mass ratios in the range 2 to 3 are required. A reasonable fit to the data is made with the hydrogen-deuterium model after large asymmetries are introduced in the densities at the base of the exosphere. This model indicates that in the subsolar region the exospheric temperature is about 640°K and the hydrogen and deuterium densities are about 6 × 10³ and 105 at 6500 km from the center of the planet. The degree of asymmetry is uncertain, but a reduction in the deuterium density by a factor of 10 and in the hydrogen density by a factor of 2 in the antisolar region at 6500 km is suggested by the night-side intensities.