  We have carried out theoretical investigations of electron correlation
effects on the atomic properties of the Ca atom trapped inside an attractive
spherically symmetric potential well of an endohedral fullerene C$_{60}$
cluster. Relativistic coupled-cluster (RCC) theory has been employed to obtain
electron correlation energy, ionization potential and dipole polarizability of
this atom. We have also performed calculations using the Dirac-Hartree-Fock
(DF), relativistic second-order many-body perturbation theory (RMBPT(2) method)
and relativistic random phase approximation (RRPA) to demonstrate propagation
of the correlation effects in these properties. Our results are compared with
the reported calculations employing multi-configuration Hartree-Fock (MCHF)
method in Phys. Rev. A {\bf 87}, 013409 (2016). We found trends in correlation
energy with respect to the potential depth are same, but magnitudes are very
large in the relativistic calculations. We have also determined the
differential and total cross-sections for elastic scattering of electrons from
the free and confined Ca atoms using the electronic charge densities from the
Dirac-Hartree core-potential (DFCP) and RCC methods to demonstrate role of
potential depth in these properties.
