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