  With increasing demand for accurate calculation of isotope shifts of atomic
systems for fundamental and nuclear structure research, an analytic energy
derivative approach is presented in the relativistic coupled-cluster theory
framework to determine the atomic field shift and mass shift factors. This
approach allows the determination of expectation values of atomic operators,
overcoming fundamental problems that are present in existing atomic physics
methods, i.e. it satisfies the Hellmann-Feynman theorem, does not involve any
non-terminating series, and is free from choice of any perturbative parameter.
As a proof of concept, the developed analytic response relativistic
coupled-cluster theory has been applied to determine mass shift and field shift
factors for different atomic states of indium. High-precision isotope-shift
measurements of $^{104-127}$In were performed in the 246.8-nm (5p $^2$P$_{3/2}$
$\rightarrow$ 9s $^2$S$_{1/2}$) and 246.0-nm (5p $^2$P$_{1/2}$ $\rightarrow$ 8s
$^2$S$_{1/2}$) transitions to test our theoretical results. An excellent
agreement between the theoretical and measured values is found, which is known
to be challenging in multi-electron atoms. The calculated atomic factors
allowed an accurate determination of the nuclear charge radii of the ground and
isomeric states of the $^{104-127}$In isotopes, providing an
isotone-independent comparison of the absolute charge radii.
