Profiles of the Compton Band from Lithium

Measurements are reported on the Compton profile from Li for the Cr $K\beta$ radiation for scattering angles 10°, 18°, 32°, and 45°. As the momentum transferred to the recoil electron depends on the scattering angle $\varphi$, a critical value ${\varphi }_0$ is found beyond which all the valence electrons contribute to the scattering. For the case $\varphi >{\varphi }_0$ the profile is known to be parabolic, while for $\varphi <{\varphi }_0$ the elementary theory predicts that the profile consists of a parabolic part which is continued by an inclined straight line terminating at the position of the unmodified line. Our effort was mainly concentrated on scattering angles below ${\varphi }_0$. Because of experimental errors and also the nonmonochromatic nature of the primary radiation, it is difficult to determine the exact shape of the profile. But there is a discrepancy with the profiles calculated both by the Hartree-Fock approximation (noninteracting free-electron gas) and in the random-phase approximation (with Coulomb interaction). For scattering angle 45°, i.e., larger than ${\varphi }_0$, the measured half-width is 28±5 eV, of the same order of magnitude as the value obtained by theory.