Covariant density functional theory (CDFT) is a modern theoretical tool for the description of nuclear structure phenomena. The current investigation aims at the global assessment of the accuracy of the description of the ground state properties of e
ven-even nuclei. We also estimate {it theoretical uncertainties} defined here as the spreads of predictions within four covariant energy density functionals (CEDF) in known regions of the nuclear chart and their propagation towards the neutron drip line. Large-scale axial relativistic Hartree-Bogoliubov (RHB) calculations are performed for all $Zleq 104$ even-even nuclei between the two-proton and two-neutron drip lines with four modern covariant energy density functionals such as NL3*, DD-ME2, DD-ME$delta$ and DD-PC1. The physical observables of interest include the binding energies, two-particle separation energies, charge quadrupole deformations, isovector deformations, charge radii, neutron skin thicknesses and the positions of the two-proton and two-neutron drip lines. The predictions for the two-neutron drip line are also compared in a systematic way with the ones obtained in non-relativistic models. As an example, the data set of the calculated properties of even-even nuclei obtained with DD-PC1 CEDF is provided as Supplemental Material with this article (file ddpc1.pdf).
The transition quadrupole moments, $Q_{t}$, of rotational bands in the neutron-rich, even-mass $^{102-108}$Mo and $^{108-112}$Ru nuclei were measured in the 8 to 16 $hbar $ spin range with the Doppler-shift attenuation method. The nuclei were populat
ed as fission fragments from $^{252}$Cf fission. The detector setup consisted of the Gammasphere spectrometer and the HERCULES fast-plastic array. At moderate spin, the $Q_{t}$ moments are found to be reduced with respect to the values near the ground states. Attempts to describe the observations in mean-field-based models, specifically cranked relativistic Hartree-Bogoliubov theory, illustrate the challenge theory faces and the difficulty to infer information on $gamma $ softness and triaxiality from the data.
The neutron and proton drip lines represent the limits of the nuclear landscape. While the proton drip line is measured experimentally up to rather high $Z$-values, the location of the neutron drip line for absolute majority of elements is based on t
heoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the covariant density functional theory has been performed by employing a set of the state-of-the-art parametrizations. Calculated theoretical uncertainties in the position of two-neutron drip line are compared with those obtained in non-relativistic DFT calculations. Shell effects drastically affect the shape of two-neutron drip line. In particular, model uncertainties in the definition of two-neutron drip line at $Zsim 54, N=126$ and $Zsim 82, N=184$ are very small due to the impact of spherical shell closures at N=126 and 184.
The cranked relativistic Hartree-Bogoliubov (CRHB) theory has been applied for a systematic study of pairing and rotational properties of actinides and light superheavy nuclei. Pairing correlations are taken into account by the Brink-Booker part of f
inite range Gogny D1S force. For the first time in the covariant density functional theory (CDFT) framework the pairing properties are studied via the quantities (such as three-point $Delta^{(3)}$ indicators) related to odd-even mass staggerings. The investigation of the moments of inertia at low spin and the $Delta^{(3)}$ indicators shows the need for an attenuation of the strength of the Brink-Booker part of the Gogny D1S force in pairing channel. The investigation of rotational properties of even-even and odd-mass nuclei at normal deformation, performed in the density functional theory framework in such a systematic way for the first time, reveals that in the majority of the cases the experimental data are well described. These include the evolution of the moments of inertia with spin, band crossings in the $Ageq 242$ nuclei, the impact of the particle in specific orbital on the moments of inertia in odd-mass nuclei. The analysis of the discrepancies between theory and experiment in the band crossing region of $Aleq 240$ nuclei suggests the stabilization of octupole deformation at high spin, not included in the present calculations. The evolution of pairing with deformation, which is important for the fission barriers, has been investigated via the analysis of the moments of inertia in the superdeformed minimum. The dependence of the results on the CDFT parametrization has been studied by comparing the results of the calculations obtained with the NL1 and NL3* parametrizations.
Neutron-proton (np-) pairing is expected to play an important role in the N Z nuclei. In general, it can have isovector and isoscalar character. The existence of isovector np-pairing is well established. On the contrary, it is still debated whether t
here is an isoscalar np-pairing. The review of the situation with these two types of pairing with special emphasis on the isoscalar one is presented. It is concluded that there are no substantial evidences for the existence of isoscalar np-pairing.
Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial deformations. In t
he second part we discuss a microscopic theory of quantum phase transitions (QPT) based on the relativistic generator coordinate method.
The systematic investigation of hyperdeformation (HD) at high spin in the $Z=40-58$ part of the nuclear chart has been performed in the framework of the cranked relativistic mean field theory. The properties of the moments of inertia of the HD bands,
the role of the single-particle and necking degrees of freedom at HD, the spins at which the HD bands become yrast, the possibility to observe discrete HD bands etc. are discussed in detail.
The additivity principle of the extreme shell model stipulates that an average value of a one-body operator be equal to the sum of the core contribution and effective contributions of valence (particle or hole) nucleons. For quadrupole moment and ang
ular momentum operators, we test this principle for highly and superdeformed rotational bands in the A~130 nuclei. Calculations are done in the self-consistent cranked non-relativistic Hartree-Fock and relativistic Hartree mean-field approaches. Results indicate that the additivity principle is a valid concept that justifies the use of an extreme single-particle model in an unpaired regime typical of high angular momenta.
