[en] Calculations of the alpha-decay and the spontaneous-fission of the heaviest nuclei are described. Main attention is given to the presentation of the results of the author, obtained in recent few years. One of the important modification, with respect to earlier studies, is the use of a multidimensional deformation space, which is especially important for the calculation of the fission barrier. Even-even nuclei with atomic number Z=92-110 are considered. Much attention is paid to the description of shell effects in the half-lives. These effects are especially important for the heaviest nuclei as they decide the question of their existence. (author)

[en] Theoretical results of calculation for lifetime of trans-Es nuclei at spontaneous fision and alpha-decay are presented

[en] We test the importance of non-axial nuclear shapes in spontaneous fission of heavy and superheavy even-even nuclei from the region around a hypothetical doubly magic nucleus ²⁹⁸114. Fission half-lives are calculated by finding dynamical fission paths as dictated by the least WKB action principle with the macroscopic-microscopic energy and the cranking inertial parameters. Results show that the effects of non-axial shapes on the fission process are weakened by the inertia tensor and become important only for the heaviest elements with Z ≥ 120

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[en] Shell effects are extracted in the following experimental quantities: Mass, alpha-decay energy and half-life, spontaneous-fission barrier and lifetime. The heaviest even-even nuclei known experimentally, with Z=92-108 are considered. This extraction is based on the Yukawa-plus-exponential model, used for the description of the macroscopic part of nuclear mass. The effects are found to be large: e.g. they increase the spontaneous-fission half-life of some nuclei by about 15 orders of magnitude. The sensitivity of these effects to changing the macroscopic model is discussed. (orig.)

[en] Ground-state collective properties of heaviest nuclei, such as deformations and rotational energies, are studied. In particular, the role of deformations of various multipolarities in the rotational energies is discussed. A large region of even-even nuclei with proton, Z=82-126, and neutron, N=126-190, numbers is considered. (author)