A systematic study of 160 heavy and super-heavy nuclei is performed in the Hartree-Fock-Bogoliubov approach with the finite range and density dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflexion symmetric wave functions, with axially symmetric and non-reflexion symmetric wave functions and finally some representative examples with triaxial wave functions are also discussed. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, Q$_\alpha$-factors and lifetimes with respect to fission and $\alpha$-decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.

M. Warda J. L. Egido

This is a short review of methods and results of calculations of fission barriers and fission half-lives of even-even superheavy nuclei. An approvable agreement of the following approaches is shown and discussed: The macroscopic-microscopic approach based on the stratagem of the shell correction to the liquid drop model and a vantage point of microscopic energy density functionals of Skyrme and Gogny type selfconsistently calculated within Hartree-Fock-Bogoliubov method. Mass parameters are calculated in the Hartree-Fock-Bogoliubov cranking approximation. A short part of the paper is devoted to the nuclear fission dynamics. We also discuss the predictive power of Skyrme functionals applied to key properties of the fission path of $^{266}$Hs. It applies the standard techniques of error estimates in the framework of a $\chi^2$ analysis.

A. Baran M. Kowal P. -G. Reinhard L. M. Robledo A. Staszczak M. Warda

The microscopic studies on nuclear fission require the evaluation of the potential energy surface as a function of the collective coordinates. A reasonable choice of constraints on multipole moments should be made to describe the topography of the surface completely within a reasonable amount of computing time. We present a detailed analysis of fission barriers in the self-consistent Hartree-Fock-Bogoliubov approach with the D1S parametrization of the Gogny nucleon-nucleon interaction. Two heavy isotopes representing different spontaneous fission modes - $^{252}$Cf (asymmetric) and $^{258}$No (bimodal) - have been chosen for the analysis. We have shown the existence of complicated structures on the energy surface that can not be fully described in two-dimensional calculations. We analyze apparent problems that can be encountered in this type of calculations: multiple solutions for given constraints and transitions between various potential energy surfaces. We present possible solutions on how to deal with these issues.

A. Zdeb M. Warda L. M. Robledo

The calculations of the potential energy surface are essential in the theoretical description of the fission process. In the constrained self-consistent approach, the smooth evolution of nuclear shape is described from the ground state until a very elongated one with a narrow neck. In all microscopic calculations, the rupture of the neck at scission is associated with a substantial change of nuclear matter density distribution and rapid energy decrease. In this paper, we show that there is no discontinuity of the potential energy surface at scission when multi-constrained calculations are applied with the neck constraint. An early rupture of the neck at lower quadrupole and octupole moments is discussed as competitive with the conventional fission path. We discuss the neck properties in the scission configuration. We find that the neck radius in the asymmetric fission mode cannot decrease below 2 fm, and the nuclear matter density cannot decrease below the saturation density. In the compact fission mode, nuclear density may go down to half of the saturation density before the rupture of the neck.

R. Han M. Warda A. Zdeb L. M. Robledo

Cluster radioactivity is the emission of a fragment heavier than $\alpha$ particle and lighter than mass 50. The range of clusters observed in experiments goes from $^{14}$C to $^{32}$Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic $^{208}$Pb nucleus. Cluster radioactivity is described in this paper as a very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment as the parameter driving the system to fission. The mean-field HFB theory with the phenomenological Gogny interaction has been used to compute the cluster emission properties of a wide range of even-even actinide nuclei from $^{222}$Ra to $^{242}$Cm, where emission of the clusters has been experimentally observed. Computed half-lives for cluster emission are compared with experimental results. The noticeable agreement obtained between the predicted properties of cluster emission (namely, clusters masses and emission half-lives) and the measured data confirms the validity of the proposed methodology in the analysis of the phenomenon of cluster radioactivity. A continuous fission path through the scission point has been described using the neck parameter constraint.

M. Warda L. M. Robledo

Background: Recent experiments on beta-delayed fission in the mercury-lead region and the discovery of asym- metric fission in 180 Hg [1] have stimulated theoretical interest in the mechanism of fission in heavy nuclei. Purpose: We study fission modes and fusion valleys in 180 Hg and 198 Hg to reveal the role of shell effects in pre-scission region and explain the experimentally observed fragment mass asymmetry and its variation with A. Methods: We use the self-consistent nuclear density functional theory employing Skyrme and Gogny energy density functionals. Results: The potential energy surfaces in multi-dimensional space of collective coordinates, including elongation, triaxiality, reflection-asymmetry, and necking, are calculated for 180 Hg and 198 Hg. The asymmetric fission valleys - well separated from fusion valleys associated with nearly spherical fragments - are found in in both cases. The density distributions at scission configurations are studied and related to the experimentally observed mass splits. Conclusions: The energy density functionals SkM\ast and D1S give a very consistent description of the fission process in 180 Hg and 198 Hg. We predict a transition from asymmetric fission in 180 Hg towards more symmetric distribution of fission fragments in 198 Hg. For 180 Hg, both models yield 100 Ru/80 Kr as the most probable split. For 198 Hg, the most likely split is 108 Ru/90 Kr in HFB-D1S and 110 Ru/88 Kr in HFB-SkM\ast.

M. Warda A. Staszczak W. Nazarewicz

Assuming a~simple spherical relativistic mean field model of the nucleus, we estimate the width of the antiproton--neutron annihilation ($\Gamma_n$) and the width of antiproton--proton ($\Gamma_p$) annihilation, in an antiprotonic atom system. This allows us to determine the halo factor $f$, which is then discussed in the context of experimental data obtained in measurements recently done on LEAR utility at CERN. Another quantity which characterizes the deviation of the average nuclear densities ratio from the corresponding ratio of the homogeneous densities is introduced too. It was shown that it is also a good indicator of the neutron halo. The results are compared to experimental data as well as to the data of the simple liquid droplet model of the nuclear densities. The single particle structure of the nuclear density tail is discusssed also.

Andrzej Baran Krzysztof Pomorski Michal Warda

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass-yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass-yields of considered nuclei are evaluated within a 3D collective model using the Born-Oppenheimer approximation.

Krzysztof Pomorski Jose M. Blanco Pavel V. Kostryukov Artur Dobrowolski Bozena Nerlo-Pomorska Michal Warda Zhigang Xiao Yongjing Chen Lile Liu Jun-Long Tian Xinyue Diao Qianghua Wu

An effective Fourier nuclear shape parametrization which describes well the most relevant degrees of freedom on the way to fission is used to construct a 3D collective model. The potential energy surface is evaluated within the macroscopic-microscopic approach based on the Lublin-Strasbourg Drop (LSD) macroscopic energy and Yukawa-folded single particle potential. A phenomenological inertia parameter is used to describe the kinetic properties of the fissioning system. The fission fragment mass yields are obtained by using an approximate solution of the underlying Hamiltonian. The predicted mass fragmentations for even-even Pt to Ra isotopes are compared with available experimental data. Their main characteristics are well reproduced when the neck rupture probability dependent on the neck radius is introduced.

Krzysztof Pomorski Artur Dobrowolski Rui Han Bozena Nerlo-Pomorska Michal Warda Zhigang Xiao Yongjing Chen Lilie Liu Jun-Long Tian

Potential energy surfaces of even-even superheavy nuclei are evaluated within the macroscopic-microscopic approximation. A very rapidly converging analytical Fourier-type shape parametrization is used to describe nuclear shapes throughout the periodic table, including those of fissioning nuclei. The Lublin Strasbourg Drop and another effective liquid-drop type mass formula are used to determine the macroscopic part of nuclear energy. The Yukawa-folded single-particle potential, the Strutinsky shell-correction method, and the BCS approximation for including pairing correlations are used to obtain microscopic energy corrections. The evaluated nuclear binding energies, fission-barrier heights, and Q-alpha energies show a relatively good agreement with the experimental data. A simple one-dimensional WKB model a la Swiatecki is used to estimate spontaneous fission lifetimes, while alpha-decay probabilities are obtained within a Gamow-type model.

Krzysztof Pomorski Artur Dobrowolski Bozena Nerlo-Pomorska Michal Warda Johann Bartel Zhigang Xiao Yongjing Chen Lile Liu Jun-Long Tian Xinyue Diao