In the present paper some quantitative estimations of Using a nonintegral expansion method of screened potentials the screening effect of the crystal-field potential generated about a displaced center (by a) the intrinsic crystal-field terms by the three basic multipoles (monopole, dipole, and quadgenerated by the point charge, dipole, and quadrupole moments rupole), within the frame of the Thomas-Fermi model, of a ligand have been quantitatively estimated. The calculation are presented using a nonintegral expansion method ( 6) has been performed within the Thomas-Fermi model for the of f (R)Y M L (, ) functions about a displaced center. The screening radius 1/ Ն a/3. In contrast to an almost total results are given directly in the real coordinate space which attenuation of the monopole component (of no contribution to is convenient from the crystal-field theory point of view the crystal-field splitting) the screening efficiency for higher whereas the approaches preferred by the solid state physicrystal-field terms regularly drops. The screening factor for the cists, based on the dielectric constant formalism, are given fourth-order terms does not exceed 0.5 and that for the sixthin the Fourier representation (7, 8).
order, 0.3. In the case of the second-order crystal-field terms
The estimation has been carried out for the screening a particular situation is observed. Their screening factor for the point-charge potential reaches 0.6 for a ؍ 3 but contributions radius 1/ Ն a/3, where is the screening constant and a generated by the dipole and quadrupole components are several the distance between the neighboring lattice sites or betimes enhanced. This fact may explain some interpretation tween the central atom (ion) and its ligand. For the smallest difficulties occurring often in the case of the second-order pavalue of the considered screening radius (1/ ϭ a/3) an rameters and concerning both their magnitude and sign.