Single-scattering Approximation Research Articles

Validity of Ray-Optics Calculations in a Turbulent Atmosphere

The restrictions on the applicability of ray optics in the turbulent atmosphere are investigated. Within the single-scatter approximation, the requirement that amplitude fluctuations have negligible effect compared to phase fluctuations leads to the condition linner11/3louter1/3/λ2≫(L/27)2 where linner, louter are the inner and outer turbulence scales and L is the range. This criterion is a considerable relaxation of the criterion which has been employed (linner2/λ≫L).

A Simple Calculation for Air-Scattered Gamma-Rays

A simple formula for air-scattered γ-rays is proposed. The proposed formula is derived using a single-scattering approximation, with exponential attenuation and buildup factor for scattered γ-ray energy. The results of calculation obtained with the formula are compared with those by Monte Carlo method, and by single-scattering calculation without exponential attenuation and buildup, for line beams of mono-energetic γ-rays emitted from a point source. For higher energies, the air-scattered flux and dose rate given by this simple approximation agree fairly well with the Monte Carlo calculations at all beam angles and source-detector distances. The accuracy is within about 10%. The flux and dose rate for γ-rays emitted isotropically from the point source have also been calculated, and are presented as a function of distance.

Multiple Scattering and the Method of Rytov*

Rytov’s method (method of smooth perturbations) has been used extensively to solve problems involving wave propagation in weakly inhomogeneous media. Critics of the method have questioned the closure procedure employed in the Rytov theory and have expressed doubt as to the range of validity of the solution. Some of the criticisms have claimed the method fails because it does not treat multiple scattering and that it is limited in applicability to precisely the same region as the Born single-scattering approximation. These criticisms are shown herein to be at fault. A multiple-scattering interpretation of the Rytov solution is given, thus lending support to those proponents of Rytov who claimed an extended range of applicability relative to the Born approximation.

Attempt to Fix the Nucleon-Nucleon Parameters by Examining Nucleon-Nucleus Scattering

The scattering of protons and neutrons from carbon at 142, 210, and 310 MeV is calculated using an optical potential obtained from nucleon-nucleon scattering amplitudes with the impulse, single-scattering, and energy-shell approximations. The integral scattering equation in momentum space is solved numerically using this potential. The present calculation is compared to previous approximate solutions and to the data. An attempt is made to choose among the currently available nucleon-nucleon phase-shift sets.

Determination of the coefficient of diffuse scattering for a medium of variable reflection coefficient

The single-scattering approximation is applied to give the coefficient of diffuse scattering for a set of plane-parallel layers of variable reflection coefficient.

Effect of multiple scattering on line-of-sight propagation

This paper deals with the effect of small random variations in the atmosphere's refractive index upon electromagnetic waves propagated along a line-of-sight path. These fluctuations are considered to be due only to the turbulent character of the medium, and the effect of the earth and other bodies is taken to be negligible. Previous analyses of this problem have utilized the first Born or single-scattering approximation. This method, however, assumes that each part of the scattering region is illuminated by the incident wave, i.e., that any incident wave is scattered at most once. The applicability of this approximation in the microwave region is questionable since the mean free path for scattering at high frequencies decreases as the square of the frequency. If at microwave frequencies the transmission distance is large compared to the mean free path length multiple-scattering effects are of importance. It is these effects which are considered here. Multiple-scattering analysis is used to determine expressions for the mean value, mean-square value, and variance of the field at a single receiver. Also determined is the correlation function for zero time difference for the fields at two spaced receivers, as well as the mean value, mean square, and variance of the difference of the fields at two spaced receivers.

Radio Waves in Turbulent Magnetoplasmas

The Ewald-Oseen extinction theorem is generalized to account for electromagnetic propagation in a turbulent magneto-ionic medium. Using the Born (single-scatter) approximation, the effective dielectric constant for the medium is determined. The scattered field is derived and a general expression for the second-order term in the Born series for the mean-square amplitude of the scattered field is obtained.

The Single-Scattering Approximation to the Solution of the Gamma-Ray Air-Scattering Problem

The results of a calculation using the single-scattering approximation, with no exponential attenuation or buildup, is compared tc results of a Monte Carlo calculation of the dose rate and number flux in air from a monoenergetic gamma-ray source. The comparison shows that the simple approximation is generally adequate for unshielded detectors. (auth)

Line-of-site wave propagation in a randomly inhomogeneous medium

Theoretical calculations have been made, using the single-scattering approximation, for propagation in a randomly inhomogeneous medium in which the deviations of refractive index from the mean are small. The statistical quantities considered were the variance, correlation function, and power spectrum for the phase and relative amplitude of the field at a point and their differences at two points. The emphasis in this paper is in indicating the transition from the ray treatment results to the scattering cross section results. The correlation function for the refractive index is taken to be time as well as space dependent so that the power spectrum can be computed from the original formulation.

Wave Propagation in a Randomly Inhomogeneous Medium. II

The region of validity of the single-scattering approximation used in Part I is found by considering the next higher approximation; it is valid for k02arα2≪1, where k0 is the wave number of the incident sound, r is the range from source to observer, a is the mean size of the inhomogeneities, and α is the rms value of the refractive index variations. Some approximate results are given for the case of wavelength large compared with inhomogeneity size. By consideration of the intensity variations, it is found that ray theory is valid for (k0a2/r)≫1, as has been found for plane waves.