MCDHF Calculations of Isotope Shifts for Be-like Ions Using Perturbation Theory and Finite-Field Method

In this work, we implement the finite-field (FF) method for isotope shift (IS) calculations within the relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) framework of the GRASPG program package. The implementation is benchmarked using the ten lowest-lying fine-structure levels of B II by comparing FF results for the IS parameters with first-order perturbation theory (PT) results obtained using the RIS4 program. The relative deviations for the IS parameters are within 0.03%, and the computed transition isotope shifts agree with previous theoretical predictions and experimental measurements within the reported experimental uncertainties. Additional calculations for Ar XV further confirm the consistency between the FF and PT methods for heavier ions, and the resulting isotope shifts are consistent with the experimental values. This implementation therefore provides GRASPG with two equivalent and reliable approaches for isotope shift calculations.