Propagation of statistical uncertainties in covariant density functional theory: Ground state observables and single-particle properties

Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in covariant density functional theory (CDFT) for the first time. In this study we consider only covariant energy density functionals with nonlinear density dependency. Statistical errors for binding energies and neutron skins significantly increase on approaching the two-neutron drip line. On the contrary, such a trend does not exist for statistical errors in charge radii and two-neutron separation energies. The absolute and relative energies of the single-particle states in the vicinity of the Fermi level are characterized by low statistical errors [sigma(e(i) ) similar to 0.1 MeV]. Statistical errors in the predictions of spin-orbit splittings are rather small. Statistical errors in physical observables are substantially smaller than related systematic uncertainties. Thus, at the present level of the development of theory, theoretical uncertainties at nuclear limits are dominated by systematic ones. Statistical errors in the description of physical observables related to the ground state and single-particle degrees of freedom are typically substantially lower in CDFT as compared with Skyrme density functional theory. The correlations between the model parameters are studied in detail. The parametric correlations are especially pronounced for the g(2) and g(3) parameters which are responsible for the density dependence of the model. The accounting of this fact potentially allows us to reduce the number of free parameters of the nonlinear meson coupling model from 6 to 5.