  An extensive study is carried out for the island of stability in the
superheavy nuclei of Z=120 and N=164-220 within the effective field theory
motivated relativistic mean-field (E-RMF) and the non-relativistic
Skyrme-Hartree-Fock (SHF) approaches. The relativistic G3 and IOPB-I and
non-relativistic SLy4 and SkMP parameter sets are used for the investigations.
Surface properties such as symmetry energy, neutron pressure and the curvature
coefficient of symmetry energy are discussed within the coherent density
fluctuation model (CDFM) using the Skyrme and the Br\"uckner energy density
functionals. The volume and surface contributions of symmetry energy are
evaluated using Danielewicz's liquid drop approximation within the CDFM. The
total nuclear reaction and elastic differential cross-sections are also
obtained for both SHF and E-RMF within the Glauber model. The peaks in the
symmetry energy at N = 182 for SHF and N=184 for E-RMF are seen, which are
absent in the Br\"uckner functional. The shifting of peak in the symmetry
energy with Br\"uckner functional can be correlated to the Coester-band
problem. The enhanced total reaction cross-section for relativistic density of
$^{304}120$ suggests the extra stability of this nucleus. This further confirms
the shell/sub-shell closure of N = 184 in E-RMF force. The differential
cross-section shows its force independent nature and significant increase with
the scattering angle.
