Background: The reactions with the neutron-rich ${}^{48}\mathrm{Ca}$ beam and actinide targets resulted in the detection of new superheavy (SH) nuclides with $Z=104–118$. The unambiguous identification of the new isotopes, however, still poses a problem because their $\alpha$-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between $\alpha$-decay and SF channels in SH nuclei is, therefore, of crucial importance for our ability to map the SH region and to assess its extent.

Purpose: We perform self-consistent calculations of the competing decay modes of even-even SH isotopes with $108\le Z\le 126$ and $148\le N\le 188$.

Methods: We use the state-of-the-art computational framework based on self-consistent symmetry-unrestricted nuclear density functional theory capable of describing the competition between nuclear attraction and electrostatic repulsion. We apply the SkM* Skyrme energy density functional. The collective mass tensor of the fissioning superfluid nucleus is computed by means of the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (HFB) approach. This paper constitutes a systematic self-consistent study of spontaneous fission in the SH region, carried out at a full HFB level, that simultaneously takes into account both triaxiality and reflection asymmetry.

Results: Breaking axial symmetry and parity turns out to be crucial for a realistic estimate of collective action; it results in lowering SF lifetimes by more than 7 orders of magnitude in some cases. We predict two competing SF modes: reflection symmetric modes and reflection asymmetric modes.

Conclusions: The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by ${}^{280}\mathrm{Hs}$, ${}^{284}\mathrm{Fl}$, and ${}_{118}^{284}\mathrm{Uuo}$ that separates the regions of SH nuclei synthesized in “cold-fusion” and “hot-fusion” reactions. The region of long-lived SH nuclei is expected to be centered on ${}^{294}\mathrm{Ds}$ with a total half-life of $\sim 1.5\mathrm{days}$. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.

• Received 26 July 2012

DOI:https://doi.org/10.1103/PhysRevC.87.024320