  Inspired by the evidently observed odd-even staggering and the inverted
parabolic-like shape of charge radii along calcium isotopic chain, the ground
state properties of calcium isotopes are investigated by constraining the
root-mean-square (rms) charge radii under the covariant energy density
functionals with effective forces NL3 and PK1. In this work, the pairing
correlations are tackled by solving the state-dependent
Bardeen-Cooper-Schrieffer equations. The calculated results suggest that the
binding energies obtained by constraint method have been reduced less than
$0.1\%$. But for charge radii, the corresponding results deriving from NL3 and
PK1 forces have been increased by about $1.0\%$ and $2.0\%$, respectively. This
means that charge radius is a more sensitive quantity in the calibrated
protocol. Meanwhile, it is found that the reproduced charge radii of calcium
isotopes is attributed to the rather strong isospin dependence of effective
potential. The odd-even oscillation behavior can also be presented in the
neutron skin thickness and proton Fermi energy along calcium isotopic chain,
but keep opposite trends with respect to the corresponding binding energy and
charge radius. As encountered in charge radii, the weakening odd-even
oscillation behavior is still emerged from the proton Fermi energies at the
neutron numbers $N=20$ and $28$ as well, but not in binding energy and neutron
skin thickness.
