The Thomas-Fermi statistical theory of the free atom is used to calculate the momentum distribution and the shape of the Compton profile for X-ray scattering, the results being expressed in dimensionless form applicable to all atoms. The mean momentum, which varies as Z 2/3 , where Z is the atomic number, agrees well with more accurate wave-mechanical calculations. Numerical results are also reported for argon and krypton using the Dirac modification of the original theory, in which exchange effects are taken into account and the atom has a finite radius. Agreement with experiment is not noticeably better with these refinements.
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Coulson et al. (1950) studied this question.
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