Many-body calculation of crystal-field shielding in the Pr3+ion

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Abstract
A discrete basis set consisting of occupied and excited states has been used in conjunction with many-body perturbation theory to calculate the crystal-field shielding parameters sigma k(k=2,4,6) in Pr3+. The shielding-antishielding parameter sigma k measures the modification due to core electrons in the crystal potential at the location of the 4f shell in the rare-earth ions. Obtained values of sigma 2 and sigma 4 correspond to shielding, while that of sigma 6 corresponds to antishielding. Comparison with existing results is made. Contributions to sigma 2 due to the electron-electron correlation effects are also calculated and found to be important (about 17% of the lowest-order contribution, but of opposite sign). Correlation contributions to other parameters reported in earlier work were found to be of similar magnitudes, but of varying signs.