We investigate the systematics of fission barriers in superheavy elements in the range $Z=108\char21{}120$ and $N=166\char21{}182$. Results from two self-consistent models for nuclear structure, the relativistic mean-field (RMF) model as well as the nonrelativistic Skyrme-Hartree-Fock approach are compared and discussed. We restrict ourselves to axially symmetric shapes, which provides an upper bound on static fission barriers. We benchmark the predictive power of the models examining the barriers and fission isomers of selected heavy actinide nuclei for which data are available. For both actinides and superheavy nuclei, the RMF model systematically predicts lower barriers than most Skyrme interactions. In particular, the fission isomers are predicted too low by the RMF, which casts some doubt on recent predictions about superdeformed ground states of some superheavy nuclei. For the superheavy nuclei under investigation, fission barriers drop to small values around $Z=110$, $N=180$, and increase again for heavier systems. For most of the forces, there is no fission isomer for superheavy nuclei, as superdeformed states are in most cases found to be unstable with respect to octupole distortions.

Systematics of fission barriers in superheavy elements

The symmetric and asymmetric fission path for 240Pu, 232Th, and 226Ra is investigated within the relativistic mean field model. Standard parametrizations which are well fitted to nuclear ground state properties are found to deliver reasonable qualitative and quantitative features of fission, comparable to similar nonrelativstic calculations. Furthermore, stable octupole deformations in the ground states of Radium isotopes are investigated. They are found in a series of isotopes, qualitatively in agreement with nonrelativistic models. But the quantitative details differ amongst the models and between the various relativsitic parametrizations.

Fission barriers and asymmetric ground states in the relativistic mean field theory

We carry out the study of finite nuclei, infinite nuclear matter, and neutron star properties with the newly developed relativistic force, the Institute of Physics Bhubaneswar-I (IOPB-I). Using this force, we calculate the binding energies, charge radii, and neutron-skin thickness for some selected nuclei. From the ground-state properties of superheavy nuclei ($Z=120$), it is noticed that considerable shell gaps appear at neutron numbers $N=172$, 184, and 198, manifesting the magicity at these numbers. The low-density behavior of the equation of state for pure neutron matter is compatible with other microscopic models. Along with the nuclear symmetry energy, its slope and curvature parameters at the saturation density are consistent with those extracted from various experimental data. We calculate the neutron star properties with the equation of state composed of nucleons and leptons in $\ensuremath{\beta}$-equilibrium, which are in good agreement with the x-ray observations by Steiner [Astrophys. J. 722, 33 (2010)] and N\"attil\"a [Astron. Astrophys. 591, A25 (2016)]. Based on the recent observation of GW170817 with a quasi-universal relation, Rezzolla et al. [Astrophys. J. Lett. 852, L25 (2018)] have set a limit for the maximum mass that can be supported against gravity by a nonrotating neutron star in the range $2.01\ifmmode\pm\else\textpm\fi{}0.04\ensuremath{\lesssim}M({M}_{\ensuremath{\bigodot}})\ensuremath{\lesssim}2.16\ifmmode\pm\else\textpm\fi{}0.03$. We find that the maximum mass of the neutron star for the IOPB-I parametrization is $2.15{M}_{\ensuremath{\bigodot}}$. The radius and tidal deformability of a canonical neutron star of mass $1.4{M}_{\ensuremath{\bigodot}}$ are 13.2 km and $3.9\ifmmode\times\else\texttimes\fi{}{10}^{36}\phantom{\rule{0.16em}{0ex}}\mathrm{g}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{2}$, respectively.

New relativistic effective interaction for finite nuclei, infinite nuclear matter, and neutron stars

Superheavy magic structures in the relativistic Hartree–Fock–Bogoliubov approach

We investigate the ground state properties of the nuclei with proton number $Z=94--110$ within the framework of deformed relativistic mean-field (RMF) theory. A systematic comparison between calculated binding energies and experimental data is made. The calculated binding energies are in good agreement with experimental ones. The reliability of the RMF model for superheavy nuclei has been tested by this comparison. The experimental data of alpha-decay energies and half-lives are reasonably reproduced by calculations. Calculated results further show that a prolate deformation is important for the ground state of these nuclei. The properties of some unknown nuclei are predicted and these are useful for future experimental researches of superheavy nuclei.

Systematic calculations of the ground state properties of superheavy nuclei

A systematic study of superheavy nuclei for Z = 114 and beyond using the relativistic mean field approach

Using axially symmetric deformed relativistic mean field model, we calculate the proton, neutron and matter distributions radii, the quadrupole moments, the binding energies and the single particle energies of 7Be, 8B, 9B and 10B. Analysis of the single particle energies and the calculated density distributions of protons and neutrons of these nuclei show the existence of a thick proton-skin in 8B. For 7Be and 9B the skins are less pronounced; while for 10B the neutron and proton distributions are almost identical.

Proton-skin in 8b-nucleus

The dynamical symmetries of the fermion dynamical symmetry model are used as a principle of truncation for the spherical shell model. Utilizing the usual principle of energy-dictated truncation to select a valence space, and symmetry-dictated truncation to select a collective subspace of that valence space, we are able to reduce the full shell model space to one of manageable dimensions with modern supercomputers, even for the heaviest nuclei. The resulting shell model then consists of diagonalizing an effective Hamiltonian within the restricted subspace. This theory is not confined to any symmetry limits, and represents a full solution of the original shell model if the appropriate effective interaction of the truncated space can be determined. As a first step in constructing that interaction, we present an empirical determination of its matrix elements for the collective subspace with no broken pairs in a representative set of nuclei with . We demonstrate that this effective interaction can be parametrized in terms of a few quantities varying slowly with particle number, and is capable of describing a broad range of low-energy observables for these nuclei. Finally we give a brief discussion of extending these methods to include a single broken collective pair.

Solution of the nuclear shell model by symmetry-dictated truncation

In the framework of relativistic mean-field theory, we study the structural properties of Yb and Hf isotopes over a wide mass range. We find an oscillatory nature of hexadecapole moments from positive to negative, and from negative to positive values, again with an increase of mass number in an isotopic chain. A quadrupole shape change from prolate to oblate shape is predicted in our calculations. For each isotope, a low-lying intrinsic excited state of an opposite quadrupole deformation is noticed. The trends in rms charge radii are studied.

http://iopscience.iop.org/article/10.1088/0954-3899/25/3/003/pdf

Cheng-Li Wu

Papers

A systematic study of superheavy nuclei for Z = 114 and beyond using the relativistic mean field approach

Proton-skin in 8b-nucleus

Solution of the nuclear shell model by symmetry-dictated truncation

Oscillations in deformation properties of heavy rare-earth nuclei