Relativistic Coupled-Cluster Calculations of Isotope Shifts for the Low-Lying States of Ca II in the Finite-Field Approach

We have evaluated the isotope shift (IS) constants of the first five low-lying fine-structure states of the singly charged calcium ion (Ca II) by adopting a finite-field (FF) approach in the relativistic coupled-cluster (RCC), a method developed by us and by using a code also developed by us. A similar previous calculation using singles and doubles approximation RCC theory (RCCSD method), gives results for the individual states in the FF approach that deviate substantially, while the differential values (the shifts of the spectral lines) agree reasonably well with other theoretical results and with experiments. However, we find a contrasting trend from the FF approach using our RCCSD method although calculations with the Dirac-Hartree-Fock (DHF) method shows good agreement. Our results also show that inclusion of partial triple excitations in the perturbative approach (RCCSD(T) method) through energy derivation lessens accuracy, but these results can be improved when triple excitations are included in the wave function that determines the RCC equations. The differences between the RCCSD and RCCSD(T) results demonstrate the importance of triple excitations in evaluating energies and IS constants for Ca II. Finally, we also present ab initio values of IS's between the S-P, S-D, and D-P transitions in the DHF, and RCCSD and RCCSD(T) approximations and this is compared to the previously reported values (theoretical as well as experimental).