  The relativistic mean-field model, augmented with three types of
center-of-mass corrections and two types of rotational corrections, is employed
to investigate the ground-state properties of helium, beryllium, and carbon
isotopes. The efficacy of the mean-field approach in describing the binding
energies, quadrupole deformations, root-mean-square charge radii,
root-mean-square matter radii, and neutron skins of these light nuclei is
evaluated. By averaging the binding energies obtained from six selected
effective interactions, a mass-dependent behavior of the mean-field
approximation is elucidated. The findings from radii reveal that, unlike in
heavy nuclei, the exchange terms of the center-of-mass correction play an
indispensable role in accurately describing the radii of light nuclei. The
mean-field approximation, when augmented with center-of-mass and rotational
corrections, effectively reproduces the energies and radii of light nuclei.
However, due to the absence of many-body correlations between valence neutrons,
the mean-field approximation falls short in describing the deformations and
shell evolutions of the helium and beryllium isotopic chains.
