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A very simple relationship between momentum density and the Fourier transform of the population matrix is derived, valid for the representation of the electronic structure of a solid in a given atom-like basis set. This expression allows for the direct refinement of experimental anisotropic Compton profiles: the parameters are the coupling coefficients between various atomic functions and adjustable constants describing the radial part of atomic functions. In the case of unfilled bands, the shape of the Fermi surface can be refined as well. A simple ionocovalent model is proposed for LiH crystals, for which many anisotropic Compton profiles have been measured. The result of the refinement is very satisfactory, leading to a fair description of the anisotropies of the momentum density. The agreement between theory and experiment is as good for this simple model (with any four parameters) as for a sophisticated band-structure calculation. Possible extensions are presented.
