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On the basis of systematic calculations for 1364 heavy and superheavy nuclei, including odd-systems, we have found a few candidates for high-K ground states in superheavy nuclei. The macroscopic-microscopic model based on the deformed Woods-Saxon single particle potential which we use offers a reasonable description of SH systems, including known: nuclear masses, $Q_{alpha}$-values, fission barriers, ground state deformations, super- and hyper-deformed minima in the heaviest nuclei. %For odd and odd-odd systems, both ways of including pairing correlations, % blocking and the quasi-particle method, have been applied. Exceptionally untypical high-K intruder contents of the g.s. found for some nuclei accompanied by a sizable excitation of the parent configuration in daughter suggest a dramatic hindrance of the $alpha$-decay. Multidimensional hyper-cube configuration - constrained calculations of the Potential Energy Surfaces (PESs) for one especially promising candidate, $^{272}$ Mt, shows a $backsimeq$ 6 MeV increase in the fission barrier above the configuration- unconstrained barrier. There is a possibility, that one such high-K ground- or low-lying state may be the longest lived superheavy isotope.
Negative results obtained in AMS searches by Dellinger et al. on mostly unrefined ores have led them to conclude that the very heavy long-lived species found in chemically processed samples with ICP-SFMS by Marinov et al. are artifacts. We argue that
We have investigated shapes and sizes of selected two- and four-quasiparticle mbox{high-$K$} states in nobelium and rutherfordium isotopes within the microscopic-macroscopic model with the deformed Woods-Saxon potential. Excited nuclear configuration
We systematically study the nuclear level densities of superheavy nuclei, including odd systems, using the single-particle energies obtained with the Woods-Saxon potential diagonalization. Minimization over many deformation parameters for the global
Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers $B_{f}$ for 1305 heavy and superheavy nuclei $98leq Z leq 126
A fully systematic study of even and odd isotopes (281 $leq$ A $leq$ 380) of Z = 121 superheavy nuclei is presented in theoretical frameworks of Relativistic mean-field plus state dependent BCS approach and Macroscopic-Microscopic approach with triax