Determination of the Energy Gap of LiD by Small-Angle Compton Scattering

Abstract

X rays incoherently scattered by electrons at angles of a few degrees transfer energies to them which amount to only a few eV. If the electrons have binding energies of the same order of magnitude, interesting effects are expected which will change the usual form of the Compton spectrum. Theoretical considerations show that in the case of a conductor the spectrum starts from the position of the primary line with the form of a straight line and continues as an inverse parabola. In the case of an insulator the spectrum will show an abrupt limit on the side towards the primary radiation. The energy transfer corresponding to the edge is equal to the energy gap. The present paper describes experiments which allow the determination of the energy gap of LiD by this method. $\mathrm{Cu} K\beta$ rays scattered by polycrystalline LiD at 18° were analyzed in a spectrometer employing a Soller slit and a (22¯43) quartz crystal as an analyzer. At this scattering angle the intense diffraction peaks are avoided so that the spectrum of the scattered radiation consists only of thermal diffuse scattering and Compton scattering. By comparing it with the spectrum produced in copper by fluorescence, the two components were separated. The experiment was then repeated with metallic lithium, in which the Compton component starts exactly at the wavelength of the primary radiation. The two Compton profiles show a shift which is put equal to the energy gap. The resulting value is 5.4±0.8 eV.