  The ground state and first intrinsic excited state of superheavy nuclei with
Z=120 and N=160-204 are investigated using both non-relativistic
Skyrme-Hartree-Fock and the axially deformed Relativistic Mean Field
formalisms. We employ a simple BCS pairing approach for calculating the energy
contribution from pairing interaction. The results for isotopic chain of
binding energy, quadrupole deformation parameter, two neutron separation
energies and some other observables are compared with the FRDM and some recent
macroscopic-microscopic calculations. We predict superdeformed ground state
solutions for almost all the isotopes. Considering the possibility of magic
neutron number, two different mode of \alpha-decay chains (292)120 and (304)120
are also studied within these frameworks. The Q_{\alpha}-values and the
half-life T^{\alpha}_{1/2} for these two different mode of decay chains are
compared with FRDM and recent macroscopic-microscopic calculations. The
calculation is extended for the \alpha-decay chains of 292120 and 304120 from
their exited state configuration to respective configuration, which predicts
long half-life T^{\alpha}_{1/2}(sec.).
