Shielding for the crystalline electric field and for the nuclear quadrupole moments in rare-earth ions

In order to determine the nature of the shielding for the crystalline electric field and the nuclear quadrupole moments in rare earth ions, analytical expressions have been derived for these parameters using hydrogenic orbitals with appropriate screening constants. The dependence of the shielding parameters on the atomic screening constants is clearly indicated. The shielding of the crystalline field parameters A l m corresponding to different values of l is shown to fall off as l increases, and for most of the orbitals the sign of the shielding parameter is such that it acts as a shielding rather than an anti-shielding. Generalized expressions for the shielding of nuclear moment of any order of magnitude have also been derived which show that the radial contributions increase with the increase in the value of l for any particular orbital. There is good agreement with the values of γ[infinity] of Sternheimer for the Pr 3+ ion if Z eff for the outer 5p and 4p orbitals is taken to be about 3 and 11 respectively. In the discussion the inadequacy of the shielding effect in explaining some of the experimentally observed crystalline field parameters has been pointed out.