The Shape of the Compton Line for Helium and Molecular Hydrogen

Abstract

By using variation functions which take into consideration the instantaneous interaction of the electrons, mementum distribution functions and intensity distributions in the Compton line are computed for helium and molecular hydrogen, neglecting small relativity and binding corrections. The half-value breadths are expressed in terms of $\frac{l}{2{\lambda }^{*}}$ where $l$ is the wave-length displacement from the center of the shifted line and $2{\lambda }^{*}={({{\lambda }_1}^2+{{\lambda }_c}^2-2\mathrm{}{\lambda }_1{\lambda }_{c}cos\chi )}^{\frac{1}{2}}$. ${\lambda }_1$ and ${\lambda }_c$ are the primary and scattered wave-lengths and $\chi$ the scattering angle. The absolute breadth of the line may therefore be computed for any ${\lambda }_1$ and $\chi$. For helium and molecular hydrogen the values of $\frac{l}{2{\lambda }^{*}}$ at half-maximum are 10.8 and 8.5, respectively.