Spontaneous fission modes and lifetimes of superheavy elements in the nuclear density functional theory

Abstract

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 $\ensuremath{\alpha}$-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between $\ensuremath{\alpha}$-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 $108\ensuremath{\le}Z\ensuremath{\le}126$ and $148\ensuremath{\le}N\ensuremath{\le}188$.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 $\ensuremath{\sim}1.5\phantom{\rule{0.28em}{0ex}}\mathrm{days}$. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.