Electronic shielding of the crystalline electric field in rare earth ions

The effect of electronic shielding on the A 2 0 term of the crystal field potential of the Pr 3+ and the Tm 3+ ion has been estimated from the numerical solution of the first-order perturbation equation. The shielding factor σ 2 is 0.59 and 0.70 for Tm 3+ and Pr 3+ respectively. The results stress the importance of electronic shieldings in rare-earth ions in agreement with the experimental findings of Barnes et al.