Background: The reactions with the neutron-rich 48 Ca beam and actinide targets resulted in detection of new super-heavy (SH) nuclides with Z = 104 − 118. The unambiguous identification of the new isotopes, however, still poses a problem because their α-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between α-decay and SF channels in SH nuclei is, therefore, of crucial importance for our ability to map the SH region and assess its extent.Purpose: We perform self-consistent calculations of the competing decay modes of even-even SH isotopes with 108 ≤ Z ≤ 126 and 148 ≤ N ≤ 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 work constitutes the very first 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 seven orders of magnitude in some cases. We predict two competing SF modes: reflection-symmetric and reflection-asymmetric. Conclusions:The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by 280 Hs, 284 Fl, and 284 118 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 Ds with a total half-life of ∼1.5 days. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.

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