Competing decay modes and stability analysis of superheavy nuclei with Z = 120 using relativistic mean-field approach

We systematically study the competition between α-decay and spontaneous fission in even-even superheavy nuclei with (Z=120) and 256 \leq A \leq 304 within the preformed cluster-decay model using microscopic inputs from relativistic mean-field calculations with the NL3 parameter set. The α-decay half-lives are obtained from WKB barrier penetration with empirically determined preformation factors, self-consistent Q_α values from RMF, and nuclear interaction potentials constructed using both M3Y and relativistic R3Y nucleon-nucleon forces, and are benchmarked against standard semi-empirical formulas. Our results predict reduced spontaneous fission probabilities and extended α-decay chains toward the fermium region for isotopes with 296 \leq A \leq 304, with enhanced stability reflected in maxima of log_{10} T_{1/2} around neutron numbers N \approx 166-182. In particular, the nuclei 296,298,300,302,304_{120} are identified as the most favorable candidates for survival against fission, demonstrating the crucial role of shell effects, deformation, and pairing correlations and providing quantitative guidance for future experimental searches of Z=120 nuclei.