Parametric correlations in energy density functionals*

Density functional theories (DFT) are defined by underlying functionals. Some of those functionals depend on substantial number of parameters. However, the parametric correlations between them have not been studied before. Using covariant DFT as an example and statistical tools, we study such correlations for major classes of covariant energy density functionals. These include the non-linear meson-nucleon coupling (NL) model, the density dependent meson-exchange (DD-ME) model and point coupling (PC) model. Their functionals are defined by properties of spherical nuclei and nuclear matter properties. It turn out that parametric correlations exist between a number of parameters in all of those functionals. For example, linear parametric correlations exist between the $g_2$ and $g_3$ parameters which are responsible for the density dependence in the NL model [1]. Observed correlations effectively reduce the number of independent parameters to five or six dependent on the structure and the underlying physics of the functional. Thus, this is how many independent parameters could be defined in the CDFT using fitting protocols based on ground state and nuclear matter properties. \\[1][1] S. E. Agbemava, A.V. Afanasjev, A. Taninah, Phys. Rev. C 99, 014318 (2019).