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.

💡 Research Summary

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The present work investigates the competition between α‑decay and spontaneous fission (SF) for even‑even superheavy nuclei with atomic number Z = 120 and mass numbers 256 ≤ A ≤ 304. The authors employ a fully microscopic framework that couples relativistic mean‑field (RMF) calculations (using the NL3 parameter set) with the pre‑formed cluster‑decay model (PCM). From self‑consistent RMF solutions they obtain binding energies, nucleon density distributions, and mean‑field potentials, which are then used to calculate Qα values and to construct the α‑daughter interaction potentials. Two nucleon‑nucleon (NN) forces are considered: the traditional phenomenological M3Y interaction and the recently derived relativistic R3Y interaction, both folded with the RMF densities to produce the nuclear part of the α‑daughter potential.

In the PCM the α‑particle is assumed to be pre‑formed inside the parent nucleus with a probability P₀ estimated from an empirical formula that depends on mass, charge, and Qα. The assault frequency ν₀ is taken as the classical frequency of the α‑particle inside the nuclear radius, while the barrier penetration probability P is obtained via the Wentzel‑Kramers‑Brillouin (WKB) approximation between the inner turning point (including a neck‑length correction ΔR) and the outer turning point defined by V(R) = Qα. The decay constant λ = ν₀ P₀ P yields the half‑life T₁/₂ = ln 2 / λ.

Spontaneous fission half‑lives are evaluated with the semi‑empirical formula of Xu et al., and the competition between the two decay modes is quantified by the branching ratio b = T_SF / T_α. A value b < 1 indicates α‑decay dominance, whereas b > 1 signals fission dominance.

The RMF calculations produce Qα values that decrease slowly with increasing neutron number, remaining relatively high (≈10–12 MeV) for isotopes with A ≈ 296–304 (N ≈ 166–182). Using both M3Y and R3Y potentials, the authors find that the α‑decay half‑lives are of the same order, but the R3Y interaction systematically yields slightly shorter half‑lives (by about 10–20 %). This reflects the stronger intermediate‑range attraction of R3Y, which lowers the barrier height.

Spontaneous fission half‑lives show a dramatic increase for A ≥ 296, reaching values up to 10⁶ s, while for lighter isotopes (A < 280) they remain extremely short (10⁻³–10⁻⁶ s). Consequently, the branching ratio b falls well below unity in the region 296 ≤ A ≤ 304, indicating that α‑decay dominates. The calculated log₁₀ T₁/₂ exhibits pronounced maxima around N ≈ 166–182, suggesting a new “island of stability” centred on Z = 120 and neutron numbers near 172–184.

The authors attribute this enhanced stability to three intertwined effects: (i) shell closures that open sizable neutron gaps at N ≈ 172 and N ≈ 184, (ii) reduced quadrupole deformation (β₂ ≈ 0.1 or less) in the same isotopes, as obtained from the RMF solutions, and (iii) strong pairing correlations that increase the pre‑formation probability P₀. The combined impact of these factors lowers the fission barrier and raises the α‑decay Q‑value, thereby extending the α‑decay chains toward the known fermium region.

A detailed comparison with experimental data (where available) and with other theoretical approaches—such as macroscopic‑microscopic models, Skyrme‑Hartree‑Fock calculations, and empirical formulas like the Universal Decay Law (UDL) and the Horoi relation—shows that the present RMF‑PCM predictions agree within 0.5–1.5 dex. This level of agreement validates the self‑consistent microscopic treatment and demonstrates that the R3Y interaction can serve as a reliable alternative to M3Y for superheavy decay studies.

Finally, the study identifies the isotopes ^296120, ^298120, ^300120, ^302120, and ^304120 as the most promising candidates for experimental synthesis, because they possess the longest α‑decay half‑lives and the smallest spontaneous fission probabilities within the examined range. The work provides quantitative guidance for future experiments aiming to reach the Z = 120 region and contributes to the broader understanding of how shell effects, deformation, and pairing shape the stability landscape of the heaviest elements.