Experimental definition of valence-shell and cumulative-shell Compton profiles from 25-keV electron-impact studies onN2, Ne, and Ar

The maximum and high-energy loss side of the Bethe ridge, obtained from high-energy electron-impact spectroscopic observations with 25-keV electrons, has been interpreted in terms of an effective Compton profile, $J_{\mathrm{eff}}(q, K)$ defined in terms of the absolute generalized oscillator strength (GOS) $f(K, E)$ as $J_{\mathrm{eff}}(q, K)=\left(\frac{2K^3}{E}\right)f(K, E)$, where $q$ is $\frac{(E-K^2)}{2K}$ with $K$ the momentum transfer and $E$ the energy loss. It is well known that for He and ${\mathrm{H}}_2$ this effective profile for constant $q$ approaches the x-ray Compton profile in the limit of large $K$ for fixed but large incident-electron energy. We report here the discovery of plateaus in the envleope of $J_{\mathrm{eff}}(q, K)$ for constant $q$ with increasing $K$, in addition to the x-ray profile limit, for target systems containing more than one shell. In the cases of ${\mathrm{N}}_2$ and Ne, an additional plateau is observed which is associated with the outer-shell electrons because the maximum of the Bethe ridge has not yet reached the energy-loss region of core or $K$-shell excitations. This additional plateau makes it possible to define an effective outer-shell Compton profile. In the case of argon, two plateau regions are observed before the Bethe ridge reaches the $K$-shell contributions and effective profiles are defined for the $M$ and $M$- plus-$L$ shells. Comparisons with theory suggest that the cumulative-shell Compton profiles agree with direct theoretical computations utilizing the x-ray formula but including only contributions from the shell(s) in question at the 5% accuracy level. On the other hand, computations of the GOS using explicit final-state ion wave functions agree with our experiments at the (1-2)% level.