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A correction is shown for the Compton scattering intensity that is calculated theoretically for free atoms, if the loosely bound outer electrons of the atoms construct the conduction or valence band in crystals, typically in the case of aluminium and silicon. The correction originates from the Pauli exclusion principle forbidding the electron in the band to make a transition to a filled state inside the band. The corrected figures satisfactorily explain the observed intensity at low scattering angles. The correction should be taken into account in analyses of diffuse scattering such as that caused by thermal vibration of crystals or by short-range order in alloys, particularly in the range of low scattering angles.