Radiat. Phys. Chem. Vol. 41, No. 4/5, pp. 579—630, 1993 0146-5724/93 $6.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1993 Pergamon Press Ltd POLARIZATION EFFECTS ON MULTIPLE SCATTERING GAMMA TRANSPORT J. E. FERNANDEZ,’t J. H. HUBBELL, 2 A. L. HANSON3 and L. V. SPENC& tLaboratorio di Ingegneria Nucleare di Montecuccolino, Università degli Studi di Bologna, via dei Colli 16, 40136 Bologna, Italy, 2National Institute of Standards and Technology, Gaithersburg, MD 20899, U.S.A. and 3Brookhaven National Laboratory, Upton, NY 11973, U.S.A. (Received 8 December 1992; accepted 12 December 1992) Abetract—The scattering of X-rays and v-rays are events that have strong dependencies on the polarization of the incident and scattered photons. Because of this, scattering problems that can be solved without explicit reference to the state of polarization of the incident and scattered radiation are exceptional. This article reviews available information on polarization effects arising when photons in the X-ray and v-ray regime undergo photoelectric effect, coherent (Rayleigh) scattering and incoherent (Compton) scattering by atomic electrons. In addition to descriptions and discussion of these effects, we study the backscattering of y-rays from an infinite thickness target excited with a plane slant monodirec- tional and monochromatic source, using the Boltzmann transport theory and the mathematical represen- tation of polarization introduced by Stokes. Results from this model, for both unpolarized and polarized y-ray sources, are compared with computations performed neglecting or averaging polarization effects, showing the limitations of such approximations. I. INTRODUCTION from certain sequences of collisions, or chains: the X- and y -ray photons interact with matter producing continuous background due to multiple Rayleigh secondary radiation that carries useful information and Compton scattering events (having the classic about the atoms comprising the target. Since X-rays differential cross-sections depending on averaged are penetrating, it is very probable that their sec- polarization states) overlapping the Compton peak ondary radiation may suffer successive interactions (Fernández, 1991; Fernández and Sumini, 1992); with other atoms before leaving the specimen. This Compton and Rayleigh scattering contributions to fact leads to the definition of a “thin” sample as the characteristic photo-peaks (Fernández et aL, having a thickness thin enough that we witness no 1990; Fernández, 1992; Fernández and Molinari, more than one interaction. Because of this a multiple 1992), and higher-order purely photoelectric inter- scattering scheme seems to be necessary to study in actions (Fernández, 1989; Fernández and Molinari, detail the backscattering of X-rays in a dense 1990). The addition of all the contributions of up to material excited with a monochromatic and mono- two (and selected ones of up to three) orders-of-scat- directional source. In a recent work, Fernández and tering obtained with an analytical solution to the Molinari (1991) showed that multiple scattering con- Boltzmann transport equation for photons, allowed tributions due to the three prevailing processes in the the build-up of theoretical X-ray spectra matching X-ray regime (the photoelectric, the Rayleigh and the well experimental data (Fernández and Sumini, Compton effects) can appreciably modify the more 1991). These results confirmed the validity of this intense first-order intensities by contributing a back- approach to get refined solutions in X-ray spec- ground or “multiple scattering spectrum”. This back- trometry. However, the mentioned equations of ground is formed by the overlapping of many single transport do not include, rigorously, the state of contributions—i.e. the possible combinations of the polarization in the description of the radiation field, three types of processes for each number of collisions. although an average polarization state is present in Individually, each process can be more or less prob- the Rayleigh and Compton kernels. able depending on the energy and the geometry In Roentgen’s 1895 “discovery” paper (Roentgen, involved in the scatterings. However, when they are 1895) he conjectured that his newly-revealed radi- combined they become a consistent contribution. Our ation (now called “X-rays”) might be ultraviolet knowledge on the whole background spectrum has light, in which case it should meet a list of four been built, as a mosaic, by studying the contributions criteria including: “It cannot be polarized by any ________________________________________ ordinary polarizing media.” However, in the years tOn leave of absence from the Faculty of Mathematics, following, several attempts were made to find polar- Astronomy and Physics (FaMAF), University of ization effects in X-rays, as the notions of electromag- Cbrdoba, Argentina. Fellow of CONICET, Buenos netic radiation were still in the early stages of Aires, Argentina. development, with the “ether” still a popular medium 579