LAUSR

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