Multiple scattering in the Compton effect

In the experimental study of the spectral distribution of x-radiation scattered by light elements it has always, up to the present, been assumed that multiple scattering could be neglected. Recent improvements in experimental technique however make it possible to suppose that multiple (especially double) scattering may now be detectable from large scattering bodies. Multiple scattering may (1) affect the breadth of the modified line, (2) change the structure of the modified line, (3) distort the background in such a way as to render measurements of shift unreliable. It is therefore valuable to analyze the effect of multiple scattering in case some of the recent mutually discordant experimental results may be explained and harmonized in this way. Assuming initially monochromatic radiation, scattering of any degree of multiplicity contributes a spectral band whose wave-length limits are here determined and discussed. The Breit, Compton, Jauncey formula taking polarization into account is adopted for the purposes of calculation of modified intensity. The results are thus fairly accurate for hard radiation scattered from very light elements. For softer radiation modified scattering at small scattering angles is greatly reduced below the values given by the Breit, Compton, Jauncey formula and unmodified scattering appears. The effect of this on the results of this paper is discussed in a qualitative way. The case of double scattering from a spherical scatterer is computed in complete detail and a formula for the ratio of double to single scattering is derived. Curves of the spectral distributions due to double scattering are shown. The dependence of the total doubly scattered intensity on the primary scattering angle is plotted. The natural width of the modified line is neglected throughout these calculations. Absorption in the scatterer is also neglected. The ratio of double to single scattering for a spherical scatterer observed under any given angle is proportional to the radius of the scatterer (neglecting absorption) and is given by Doubly scattered energy /Singly scattered energy =9/32σrR(θ) where σ is the linear scattering coefficient for the material of the scattering sphere, r the radius of the sphere, θ the angle under which single scattering occurs. R(θ) never differs greatly from 2.5. Triple scattering is negligible in comparison to single scattering. Twice modified doubly scattered radiation may contribute a faint asymmetric line or edge at the shifted position Δλ=2(h/mc)(1+cos1/2θ) For hard radiation when the Thompson formula (with Breit correction) applies with fair accuracy to modified scattering alone twice modified doubly scattered radiation contributes a spectral band of breadth 4(h/mc) cos1/2θ Once modified doubly scattered radiation may cause a slight broadening of the Compton line except in regions near θ=0 and θ=180°