  In this theoretical study, we have derived a simplified analytical expression
for the binding energy per nucleon as a function of density and isospin
asymmetry within the relativistic mean-field model. We have generated a new
parameterization for the density-dependent DD-ME2 parameter set using the
Relativistic-Hartree-Bogoliubov approach. Moreover, this work attempts to
revisit the prior polynomial fitting in [Phy. Rev. C 103, 024305 (2021)] for
the non-linear NL3 force parameter to provide a simplified set of equations for
the energy density functional which is used for calculating the surface
properties of finite nuclei. The current study improves the existing fitting
procedure by effectively proposing a simpler model that provides comparably
precise results while lowering the computational expense. To study the surface
properties of finite nuclei with these parameterizations, we have adopted the
coherent density fluctuation model, which effectively translates the quantities
of nuclear matter from momentum space to coordinate space at local density. The
isospin properties, such as symmetry energy and its surface and volume
components, slope parameter, finite nuclear incompressibility, and surface
incompressibility for even-even nuclei, are calculated for different mass
regions. Moreover, we have studied the effect of density, weight function, and
choice of relativistic force parameters on the surface properties. The
consequence of this work will help to determine the properties of nuclei along
the nuclear landscape and can facilitate an improved understanding of the
island of stability, heavy-ion collision, and nucleosynthesis, among others.
