Accurate determination of H2, He, and D2 Compton profiles by high energy electron impact spectroscopy

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Abstract
The effective nonrelativistic Compton profiles J (q,K) of H2 and He {defined in terms of the absolute generalized oscillator strength (GOS), df (K,E)/dE, as J (q,K) = (2K3/E)[df (K,E)/dE], where q is (E−K2)/2K, with K the momentum transfer and E the energy loss} have been studied as a function of scattering angle by means of high energy electron impact spectroscopy (HEEIS) with an incident energy of 25 keV over an angular range of 3°–10°. It was found that the binary encounter limit is not reached until the x‐ray incoherent scattering factor reaches its large K asymptotic limit N, the number of target electrons. At 10° , the results of the Compton profiles of He and H2 were fitted by least squares to a polynomial of the form Σmn=1{an/[1+(q/ζn)2]n+2}, which leads to analytic expressions for the one electron momentum density and its integer powered moments. The fits proved to be radically different for He and H2. The experimental values for the moments of the momentum density function were found to be in excellent agreement with the best available theoretical results. In addition, the Compton profile of D2 at 8° was measured and no significant deviations from the Compton profile for H2 were observed. The new results reported here for H2 clear up a disagreement between theory and experiment and suggest that quoted uncertainties in the previous studies were unrealistically small owing to improper analysis of systematic experimental errors.