The properties of hyperheavy nuclei and the extension of nuclear landscape to hyperheavy nuclei are extensively studied within covariant density functional theory. Axial reflection symmetric and reflection asymmetric relativistic Hartree-Bogoliubov (RHB) calculations are carried out. The role of triaxiality is studied within triaxial RHB and triaxial relativistic mean field + BCS frameworks. With increasing proton number beyond Z ∼ 130 the transition from ellipsoidal-like nuclear shapes to toroidal ones takes place. The description of latter shapes requires the basis which is typically significantly larger than the one employed for the description of ellipsoidal-like shapes. Many hyperheavy nuclei with toroidal shapes are expected to be unstable towards multifragmentation. However, three islands of stability of spherical hyperheavy nuclei have been predicted for the first time in Ref.[1]. Proton and neutron densities, charge radii, neutron skins and underlying shell structure of the nuclei located in the centers of these islands have been investigated in detail. Large neutron shell gaps at N = 228, 308 and 406 define approximate centers of these islands in neutron number. On the contrary, large proton gap appear only at Z = 154 in the (Z ∼ 156, N ∼ 310) island. As a result, this is the largest island of stability of spherical hyperheavy nuclei found in the calculations. The calculations indicate the stability of the nuclei in these islands with respect of octupole and triaxial distortions. The shape evolution of toroidal shapes along the fission path and the stability of such shapes with respect of fission have been studied. Fission barriers in neutron-rich superheavy nuclei are studied in triaxial RHB framework; the impact of triaxiality on the heights of fission barriers is substantial in some parts of this region. Based on the results obtained in the present work, the extension of nuclear landscape to hyperheavy nuclei is provided.

Parametric correlations are studied in several classes of covariant density functional theories (CDFTs) using a statistical analysis in a large parameter hyperspace. In the present manuscript, we investigate such correlations for two specific types of models, namely, for models with density dependent meson exchange and for point coupling models. Combined with the results obtained previously in Ref.[1] for a non-linear meson exchange model, these results indicate that parametric correlations exist in all major classes of CDFTs when the functionals are fitted to the ground state properties of finite nuclei and to nuclear matter properties. In particular, for the density dependence in the isoscalar channel only one parameter is really independent. Accounting for these facts potentially allows one to reduce the number of free parameters considerably.Since the early seventies, analogously to Coulombic quantum mechanical many-body systems, density functional theory (DFT) has played an important role in nuclear physics. In principle, it corresponds to an exact mapping of the complex many-body system to that of an artificial one-body system and therefore one with relatively small computational costs. It is universal in the sense that the form of the energy density functional (EDF) does not depend on the nucleus, nor on the specific region where it is applied, but only on the underlying interaction. Thus there is only one universal functional for the Coulomb interaction in atomic, molecular and condensed matter physics, but another one for nuclear phenomena determined by the strong interaction and the Coulomb force. In Coulombic systems the density functional can be derived in a microscopic way from the Coulomb force. On the contrary in nuclear physics, because of the complexity of the nuclear force such attempts are still in their infancy [2,3]. All the successful functionals are phenomenological. Their various forms obey the symmetries of the system, but in the absolute majority of the cases the parameters are adjusted to experimental data in finite nuclei and in homogeneous nuclear matter.Covariant density functional theories (CDFT) [3-7] are particularly interesting because they obey a basic symmetries of QCD. In particular, Lorentz invariance which not only automatically includes the spin-orbit coupling, but also puts stringent restrictions on the number of phenomenological parameters without loosing the good agreement with experimental data Nonetheless, over the years, the number of phenomenological functionals has grown considerably not only for non-relativistic Skyrme DFTs, but also for CDFTs, so that in recent years, questions have arisen about the reliability and predictive power of such functionals [8,9]. Apart from the systematic uncertainties which are connected with the analytic forms and the various terms in such functionals, there are so-called statistical uncertain-ties, connected with the procedures and strategies to adjust the various parameters to experimental data. Here we investigate whether the para...

Statistical errors in ground state observables and single-particle properties of spherical even-even nuclei and their propagation to the limits of nuclear landscape have been investigated in covariant density functional theory (CDFT) for the first time. In this study we consider only covariant energy density functionals with non-linear density dependency. Statistical errors for binding energies and neutron skins significantly increase on approaching two-neutron drip line. On the contrary, such a trend does not exist for statistical errors in charge radii and two-neutron separation energies. The absolute and relative energies of the single-particle states in the vicinity of the Fermi level are characterized by low statistical errors (σ(ei) ∼ 0.1 MeV). Statistical errors in the predictions of spin-orbit splittings are rather small. Statistical errors in physical observables are substantially smaller than related systematic uncertainties. Thus, at the present level of the development of theory, theoretical uncertainties at nuclear limits are dominated by systematic ones. Statistical errors in the description of physical observables related to the ground state and single-particle degrees of freedom are typically substantially lower in CDFT as compared with Skyrme density functional theory. The correlations between the model parameters are studied in detail. The parametric correlations are especially pronounced for the g2 and g3 parameters which are responsible for the density dependence of the model. The accounting of this fact potentially allows to reduce the number of free parameters of non-linear meson coupling model from six to five.

The study of nuclear limits has been performed and new physical mechanisms and exotic shapes allowing the extension of nuclear landscape beyond the commonly accepted boundaries have been established. The transition from ellipsoidal-to-toroidal shapes plays a critical role in potential extension of nuclear landscape to hyperheavy nuclei. Rotational excitations leading to the birth of particle (proton or neutron) bound rotational bands provide a mechanism for an extension of nuclear landscape beyond spin-zero proton and neutron drip lines.

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A systematic analysis of the ground state and fission properties of actinides and superheavy nuclei important for the r process modeling has been performed within the framework of covariant density functional theory for the first time in Ref. [1]. A brief review of the results related to the heights of primary fission barriers and systematic uncertainties in their prediction is presented. In addition, new results on the potential impact of the isospin dependence of pairing on fission barriers in fission cycling regions is provided for the first time.