Global improvement of covariant energy density functionals.

The nucleus is described as a system of nucleons which interact via the exchange of mesons in covariant density functional theory (CDFT) [1]. Unfortunately, because of numerical considerations the absolute majority of covariant energy density functionals (CEDFs) have been fitted only to spherical nuclei and infinite basis corrections to binding energies due to finite sizes of fermionic and mesonic bases have been neglected. To alleviate the former problem an anchor-based optimization approach (ABOA) of defining the energy density functionals (EDFs) to global set of data which includes all even-even nuclei was proposed by us in [2,3]. In this approach, the optimization of the parameters of EDF is carried out for the selected set of spherical anchor nuclei the physical observables of which are modified by the correction function which takes into account the global performance of EDF. It is shown that the use of this approach leads to a substantial improvement in global description of binding energies for several classes of covariant EDFs. The computational cost of defining a new functional within this approach is drastically lower as compared with the one for the optimization which includes the global experimental data on spherical, transitional and deformed nuclei directly into the optimization. For the first time, the numerical errors in the calculation of binding energies related to the truncation of bosonic and fermionic bases have been globally investigated with respect of asymptotic values corresponding to the infinite bases in the CDFT framework in [3]. The reduction of the errors in binding energies due to the truncation of the fermionic basis in CDFT is significantly more numerically costly than in mesonic sector [3]. Finally, the fit of a new generation of CEDFs is in progress [4]. For the first time, these functionals take into account the infinite basis corrections to binding energies for fermionic and mesonic bases, total electron binding energies (including those of superheavy ions) in conversion of experimental atomic binding energies to the nuclear ones, and relativistic corrections in the calculation of charge radii.