The Compton and photoelectric spectroscopy of multiply scattered photons

An analysis is made of the pulse height spectra of multiply scattered γ-rays having energies between 0.01 and 0.7 MeV, whose interactions with matter are described by their Compton scattering and photoelectric absorption cross sections. It is shown that multiply scattered photon spectra generated in nonuniform media contain more than two significant spectral components. It is demonstrated that the variability of the spectra is due in part to the spatially nonuniform sampling of the medium by such devices. The most significant spectral components are displayed. A spectral sensitivity matrix that quantitatively relates the linear variations of the material properties to those of the spectra is defined. Analysis of this sensitivity matrix makes it possible to define a set of independent, characteristic spectroscopic components, each of which is uniquely related to a particular mode of cross section variation. The analysis is carried out for an ensemble of empirical data from a γ-γ device similar to those employed for borehole logging