Application of the coherent density fluctuation model to study the nuclear matter properties of finite nuclei within the relativistic mean-field formalism

We obtained a density-dependent analytical expression of binding energy per nucleon for different neutron-proton asymmetry the nuclear matter (NM) with polynomial fitting, which manifests results effective-field theory motivated relativistic mean-field (E-RMF) model. This has edge over Br\"uckner density functional [Phys. Rev. 171, 1188 (1968)] since it resolves Coster-Band problem. The NM parameters like incompressibility, neutron pressure, symmetry energy, and its derivatives are calculated using acquired nucleon. Furthermore, weight function by E-RMF densities folded within coherent fluctuation model to find properties closed or semiclosed-shell even-even $^{16}\mathrm{O}, ^{40}\mathrm{Ca}, ^{48}\mathrm{Ca}, ^{56}\mathrm{Ni}, ^{90}\mathrm{Zr}, ^{116}\mathrm{Sn}$, $^{208}\mathrm{Pb}$ nuclei. values pressure ${P}^{A}$, ${S}^{A}$, derivative ${L}_{\mathrm{sym}}^{A}$ known as slope parameter lie narrow domain whereas there is large variation in isoscalar incompressibility ${K}^{A}$ surface ${K}_{\mathrm{sym}}^{A}$ while moving from light heavy sizable nuclei depicts their structural dependence due peculiar distribution each nucleus. A comparison quantities present work also been made ones via functional.