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We have applied relativistic coupled-cluster (RCC) theory to determine theisotope shift (IS) constants of the first eight low-lying states of the Li,Be$^+$ and Ar$^{15+}$ isoelectronic systems. Though the RCC theory withsingles, doubles and triples approximation (RCCSDT method) is an exact methodfor these systems for a given set of basis functions, we notice largedifferences in the results from this method when various procedures in the RCCtheory framework are adopted to estimate the IS constants. This has beendemonstrated by presenting the IS constants of the aforementioned states fromthe finite-field, expectation value and analytical response (AR) approaches ofthe RCCSDT method. Contributions from valence triple excitations, Breitinteraction and lower-order QED effects to the evaluation of these IS constantsare also highlighted. Our results are compared with high-precision calculationsreported using few-body methods wherever possible. We find that results fromthe AR procedure are more reliable than the other two approaches. This analysisis crucial for understanding the roles of electron correlation effects in theaccurate determination of IS constants in the heavier atomic systems, wherefew-body methods cannot be applied.

physical review. a/physical review, a

Benchmarking Many-body Approaches for the Determination of Isotope Shift  Constants: Application to the Li, Be$^+$ and Ar$^{15+}$ Isoelectronic Systems