Elucidate the non-relativistic and relativistic energy density functional from momentum space to coordinate space within local density approximation

In this paper, we have developed relativistic and nonrelativistic energy density functionals within the local density approximation, transitioning from momentum space to coordinate space. Utilizing the Coherent Density Fluctuation Model, these functionals predict shell and sub-shell closures across isotopic and isotonic chains. Our focus has been on refining fitting procedures and testing these functionals on selected nuclei. Previously, we compared our energy density functionals for E-RMF forces G3 and IOPB-I with the Brückner energy density functional. Our results highlighted significant advantages, particularly in accurately predicting peaks in the symmetry energy curve at magic neutron numbers within heavy and superheavy regions. This success motivates us to extend our fitting procedure for both the relativistic mean field (E-RMF) and nonrelativistic Skyrme–Hartree–Fock (SHF) parameter sets. To further ensure the reliability of our newly fitted functionals, we establish Pearson-type correlations between the symmetry energy and its derivatives.