scholarly journals On the intensity of total scattering of X-rays

1929 ◽  
Vol 124 (793) ◽  
pp. 119-142 ◽  
Keyword(s):  
High Frequency ◽  
Scattered Radiation ◽  
Wave Length ◽  
Incident Radiation ◽  
Compton Effect ◽  
X Rays ◽  
Free Electrons ◽  
Scattering Angle ◽  
Total Scattering ◽  
Monatomic Gas

We shall here investigate theoretically the intensity of total scattering of X-rays by atoms distributed at random, e. g. , the scattering by the atoms of a monatomic gas. In the scattered radiation we shall not include the characteristic X-rays excited by the incident radiation. The scattered radiation consists then partly of radiation having the same frequency as the incident radiation (coherent scattered radiation) and partly of radiation having other frequencies (incoherent scattered radiation). For sufficiently high frequency of the incident radiation the incoherent scattered radiation is then nearly monochromatic for a given scattering angle, and consists practically entirely of radiation whose wave-length and intensity is given by the formulæ for the Compton effect for the scattering by free electrons. Generally, however, it must be taken into account that several frequencies occur in the scattered radiation for each direction of scattering. The total intensity of the scattered radiation for a given direction has therefore to be taken as a sum of the intensities of the different components, each having a definite frequency. General expressions for the scattered radiation are given by a scattering formula derived by one of us. In this formula “relativity corrections” are neglected; for the intensity of scattering in the Compton effect for free electrons, this approximation, and a further one which we also make, lead to the classical Thomson formula. This means that our intensity formula gives a useful approximation only if the incident radiation is not too hard ( e. g. , has a wave-length not shorter than about 1 Å., in which case the error arising from the approximation just mentioned should not exceed a few per cent.).

scholarly journals The absorption of hard monochromatic γ-radiation

1930 ◽  
Vol 128 (807) ◽  
pp. 345-359 ◽  
Keyword(s):  
Absorption Coefficient ◽  
High Frequency ◽  
Wave Length ◽  
Low Frequency ◽  
Photoelectric Effect ◽  
Fourth Power ◽  
X Rays ◽  
Photoelectric Absorption ◽  
Initial Direction ◽  
Γ Radiation

Energy may be removed from a beam of γ -rays traversing matter by two distinct mechanisms. A quantum of radiation may be scattered by an electron out of its initial direction with change of wave-length, or it may be absorbed completely by an atom and produce a photoelectron. The total absorption coefficient, μ, is defined by the equation d I/ dx = -μI, and is the sum of the coefficients σ and τ referring respectively to the scattering and to the photoelectric effect. For radiation of low frequency, such as X-rays, the photoelectric absorption is very much more important than the absorption due to scattering, and many experiments have shown that the photoelectric absorption per atom varies as the fourth power of the atomic number and approximately as the cube of the wave-length. For radiation of high frequency, such as the more penetrating γ -rays, the photoelectric effect is, even for the heavy elements, smaller than the scattering absorption; and, since the scattering from each electron is always assumed to be independent of the atom from which it is derived, it is most convenient to divide μ. defined above by the number of electrons per unit volume in the material and to obtain μ e the absorption coefficient per electron.

scholarly journals The atomic scattering factor for X-rays in the region of anomalous dispersion

1933 ◽  
Vol 139 (838) ◽  
pp. 459-466 ◽  
Keyword(s):  
Free Electron ◽  
Scattered Radiation ◽  
Wave Length ◽  
Anomalous Dispersion ◽  
X Rays ◽  
Characteristic Frequencies ◽  
X Ray ◽  
Atomic Scattering Factor ◽  
Atomic Scattering ◽  
Scattering Factor

The atomic scattering factor ( f -factor) for X-rays is the ratio of the amplitude of the X-rays scattered by a given atom and that scattered according to the classical theory by one single free electron. It is given as a function of sin ϑ/λ, λ being the wave-length of the X-rays, 2ϑ the angle between the primary and the scattered radiation. It is assumed to be independent of the wave-length so long as sin ϑ/λ remains constant. Recently, however, it has been shown both theoretically and experimentally that the last assumption is no longer valid, when the scattered frequency is in the neighbourhood of one of the characteristic frequencies of the scattering element. The first to show the influence of the anomalous dispersion on the f factor were Mark and Szilard, who reflected strontium and bromine radiations by a rubidium bromide crystal. Theoretically the problem was dealt with by Coster, Knol and Prins in their investigation of the influence of the polarity of zincblende on the intensity of X-ray reflection and later on once more by Gloeker and Schäfer.

scholarly journals A critical-absorption photometer for the study of the Compton effect

1928 ◽  
Vol 119 (783) ◽  
pp. 526-530
Keyword(s):  
Absorption Coefficient ◽  
Wave Length ◽  
Light Element ◽  
Compton Effect ◽  
X Rays ◽  
X Ray ◽  
X Ray Scattering ◽  
Length Changes ◽  
Absorption Measurements ◽  
Ray Scattering

That a change of wave-length occurs in X-ray scattering was first indicated by absorption measurements with the ionisation chamber, which showed that the absorption coefficient of a light element like aluminium was slightly greater for the scattered than for the primary X-rays. Later more conclusive and direct evidence was obtained when spectrometric analysis of the scattered X-rays was made first by the ionisation and afterwards by the photographic method. This analysis disclosed the existence of an unshifted as well as the shifted line, and showed also that the latter becomes relatively more prominent with diminishing wave-length and lower atomic number of the scattering element. After the main features of the Compton effect were established by means of spectrometric measurements, however, absorption measurements with the ionisation method have again been employed for a detailed study of the phenomenon, for such measurements are much quicker than the spectrum experiments, where the final energy available is much smaller on account of the double scattering involved. As mentioned above, the absorption measurements were based on the slight increase in the absorption coefficient of a light element when the wave-length changes from the unmodified to the modified value. The much larger and sudden diminution in absorption of X-rays when the frequency is altered from the short to the long wave-length side of the critical K-absorption limit of the element used as a filter, furnishes us with an easy and convenient method of exhibiting the wave-length change in X-ray scattering. In the present paper will be described a photographic wedge photometer based on this principle, which enables the characteristics of the Compton effect to be readily observed. It may be pointed out that the same idea could no doubt be utilised also in connection with the ionisation measurements of the Compton effect.

scholarly journals XII. On the scattering and absorption of light in gaseous media, with applications to the intensity of sky radiation

1913 ◽  
Vol 212 (484-496) ◽  
pp. 375-433 ◽  
Keyword(s):  
Scattered Radiation ◽  
Gaseous Medium ◽  
Wave Length ◽  
Incident Radiation ◽  
Continuous Change ◽  
Small Particles ◽  
Absorption Of Light ◽  
Original Direction ◽  
Gaseous Media ◽  
Parallel Radiation

1. On the Scattering of Parallel Radiation by Molecules and Small Particles . The effect of small particles in scattering incident radiation was first worked out by Lord Rayleigh. When a stream of parallel radiation falls on a particle whose dimensions are small compared with the wave-length the resulting secondary disturbance travels in all directions at the expense of the intensity in the original direction. In a later paper Lord Rayleigh gave reasons for believing that the molecules of a gas are themselves able to scatter radiation in this way. In a gaseous medium it is legitimate to sum up the intensities of the scattered radiation due to each molecule in an element of volume without a consideration of phase-difference in consequence of the continuous change in the relative positions of a molecule in a gas. The same remark applies to the case where the scattering is due to small particles of dust since these partake, to some extent at least, of the molecular agitation of the gas in which they are held in suspension.

scholarly journals The differential action of X-rays on tissue, growth and vitality.—Part III. The biological reaction to X-radiation in relation to the area of tissue irradiated

1930 ◽  
Vol 107 (751) ◽  
pp. 302-307 ◽  
Keyword(s):  
Early Stage ◽  
Wave Length ◽  
Incident Radiation ◽  
Tissue Growth ◽  
X Rays ◽  
Selective Action ◽  
Imperfect Crystal ◽  
Biological Reaction ◽  
Embryo Chick ◽  
Differential Action

The allantoic membrane of the embryo chick was exposed to homogeneous X-radiation obtained by crystal diffraction and a selective action was observed (Moppett, 1929). A particular wave-length 0·53 Å. produced a hypertrophic reaction with an exposure of ½ hour and an atrophic reacion in 1¼ hours and this was adopted as a standard in the investigation of problems other than selective action (Moppett, 1929 and 1930). The Effect of Irradiating a Large or Small Area . A variation in effect with the area irradiated was suggested because at an early stage reactions were readily produced with an imperfect crystal and it was found that the results could be imitated by placing he specimen at an oblique angle to the incident radiation. It appears that the imperfect crystal was "convex," spreading the rays out to a greater extent than usual and various aspects of the problem are illustrated by the following typical experiments.

Excitation of Plasmons with X-rays

1973 ◽  
Vol 28 (5) ◽  
pp. 550-553 ◽  
Author(s):  
Kessar D. Alexopoulos
Keyword(s):  
Dielectric Constant ◽  
Surface Plasmons ◽  
Scattered Radiation ◽  
Energy Shift ◽  
Short Review ◽  
X Rays ◽  
Scattering Angle ◽  
X Ray ◽  
Second Category ◽  
Colloidal Materials

A short review is given of plasma phenomena produced in solids by impinging X-rays. The first category refers to bulk plamons due to X-ray photons scattered on solids. They are observed through the appearance of a new component in the spectrum of the scattered radiation. The energy shift increases slightly with scattering angle but eventually the dispersion stops. A second category of phenomena consists in the light emitted by decaying surface plasmons. They are excited by photoelectrons produced in colloidal materials by X-rays. The spectrum shifts with the dielectric constant of the stabilizing medium.

Evaluation of Soft and Hard Scarttered X-Rays as an Internal Standard for Light Element Analysis

1969 ◽  
Vol 13 ◽  
pp. 80-93
Author(s):  
David L. Taylor ◽  
George Andermann
Keyword(s):  
Matrix Effects ◽  
Wave Length ◽  
Internal Standard ◽  
Light Element ◽  
X Rays ◽  
Element Analysis ◽  
Scattering Angle ◽  
Wide Range ◽  
The Matrix ◽  
Internal Standardization

In the research described, the use of scattered x-rays has been successfully applied as an internal standard for the analysis of calcium in aqueous specimens containing a wide range of matrix components. In addition to the demonstration of the utility of scattered x-rays for light element analysis, some comments are offered on the fundamental aspects of this technique, since to date the method has not been explained thoroughly. The present research represents a continued effort to determine the fundamental importance of various parameters intrinsic to any collection of atoms undergoing scattering, such as the Rayleigh-Compton ratio, the scattering angle, the wave length utilized, and the presence or absence of discontinuities in the matrix absorption coefficient. It has been concluded that large values of the scattering angle coupled with short wavelength tend to yield improved internal compensation. The results also indicate that for light matrices the Compton component of the scattered continuum is of particular importance in achieving good internal standardization for matrix effects.

scholarly journals On the scattering and absorption of light in gaseous media, with applications to the intensity of sky radiation

1913 ◽  
Vol 88 (601) ◽  
pp. 83-89 ◽  
Keyword(s):  
Refractive Index ◽  
Scattered Radiation ◽  
Unit Volume ◽  
Solid Angle ◽  
Wave Length ◽  
Incident Radiation ◽  
Small Particles ◽  
Absorption Of Light ◽  
Original Direction ◽  
Gaseous Media

Sections 1 and 2.—Lord Rayleigh showed, in 1871, that when radiation travels through a medium containing small particles whose dimensions are small compared with the wave-length, each of these sets up a secondary disturbance which travels in all directions at the expense of the energy in the original direction. Various hypotheses of the æther and of the molecule agree in giving for the scattered radiation near an element of volume an expression of the form I (0, θ ) - μ ( θ ) E = ½ π 2 ( n 2 ─ 1) 2 λ -4 (1+cos 2 θ ) E/N, (1) where ω I (0, θ ) is the intensity contained in a small solid angle ω in a direction θ with the direction of the original beam E; n is the refractive index of the gas, N the number of molecules per unit volume, and λ the wave-length of the incident radiation.

Sign in / Sign up

Export Citation Format

Share Document