Adiabatic fission barriers in superheavy nuclei

Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers $B_{f}$ for 1305 heavy and superheavy nuclei $98\leq Z \leq 126$, including even - even, odd - even, even - odd and odd - odd systems. For odd and odd-odd nuclei, adiabatic potential energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from the 10-th below to the 10-th above the Fermi level. The parameters of the model that have been fixed previously by a fit to masses of even-even heavy nuclei were kept unchanged. A search for saddle points has been performed by the "Imaginary Water Flow" method on a basic five-dimensional deformation grid, including triaxiality. Two auxiliary grids were used for checking the effects of the mass asymmetry and hexadecapole non-axiallity. The ground states were found by energy minimization over configurations and deformations. We find that the non-axiallity significantly changes first and second fission barrier in many nuclei. The effect of the mass - asymmetry, known to lower the second, very deformed barriers in actinides, in the heaviest nuclei appears at the less deformed saddles in more than 100 nuclei. It happens for those saddles in which the triaxiallity does not play any role, what suggests a decoupling between effects of the mass-asymmetry and triaxiality. We studied also the influence of the pairing interaction strength on the staggering of $B_f$ for odd- and even-particle numbers. Finally, we provide a comparison of our results with other theoretical fission barrier evaluations and with available experimental estimates.Comment: submitted to PR

Candidates for Long Lived High-K Ground States in Superheavy Nuclei

On the basis of systematic calculations for 1364 heavy and superheavy nuclei, including odd-systems, we have found a few candidates for high-K ground states in superheavy nuclei. The macroscopic-microscopic model based on the deformed Woods-Saxon single particle potential which we use offers a reasonable description of SH systems, including known: nuclear masses, $Q_{\alpha}$-values, fission barriers, ground state deformations, super- and hyper-deformed minima in the heaviest nuclei. %For odd and odd-odd systems, both ways of including pairing correlations, % blocking and the quasi-particle method, have been applied. Exceptionally untypical high-K intruder contents of the g.s. found for some nuclei accompanied by a sizable excitation of the parent configuration in daughter suggest a dramatic hindrance of the $\alpha$-decay. Multidimensional hyper-cube configuration - constrained calculations of the Potential Energy Surfaces (PES's) for one especially promising candidate, $^{272}$ Mt, shows a $\backsimeq$ 6 MeV increase in the fission barrier above the configuration- unconstrained barrier. There is a possibility, that one such high-K ground- or low-lying state may be the longest lived superheavy isotope.Comment: Accepted in PR

Ground State and Saddle Point: masses and deformations for even-even superheavy nuclei with 98 < Z < 126 and 134< N < 192

We determine ground-state and saddle-point shapes and masses of even-even superheavy nuclei in the range of proton numbers $98\leq Z \leq 126$ and neutron numbers $134\leq N \leq 192$. Our study is performed within the microscopic-macroscopic method. The Strutinsky shell and pairing correction is calculated for the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential energy is taken as a smooth part. We use parameters of the model that were fitted previously to this region of nuclei. A high-dimensional deformation space, including nonaxial and reflection-asymmetric shapes, is used in the search for saddle points. Both ground-state and saddle-point shapes are found with the aid of the minimization procedure, with dynamical programming technique of search for saddle points. The results are collected in two tables. Calculated ground-state mass-excess, Q_{\alpha energies, total and macroscopic energies normalized to the macroscopic energy at the spherical shape, shell corrections (including pairing) and deformations are given for each nucleus in the table one. The second table gives the same properties, but at the saddle-point configuration. The obtained results are discussed and compared with available experimental data for alpha-decay energies ($Q_{\alpha}$) and ground-state masses.Comment: 35 pages, 9 figures, 2 tables, submitted to ADND

Superdeformed Oblate Superheavy Nuclei?

We study stability of superdeformed oblate (SDO) superheavy $Z\geq 120$ nuclei predicted by systematic macroscopic-microscopic calculations in 12D deformation space and confirmed by the Hartree-Fock calculations with the realistic SLy6 force. We include into consideration high-$K$ isomers that very likely form at the SDO shape. Although half-lives $T_{1/2}\lesssim10^{-5}$ s are calclulated or estimated for even-even spin zero systems, decay hindrances known for high-$K$ isomers suggest that some SDO superheavy nuclei may be detectable by the present experimental technique.Comment: 4 pages, 5 figure

Sizes and shapes of very heavy nuclei in high-K states

We have investigated shapes and sizes of selected two- and four-quasiparticle \mbox{high-$K$} states in nobelium and rutherfordium isotopes within the microscopic-macroscopic model with the deformed Woods-Saxon potential. Excited nuclear configurations were obtained by blocking single-particle states lying close to the Fermi level. Their energies and deformations were found by the four-dimensional energy minimization over shape variables. We have selected the most promising candidates for \mbox{$K$-isomers} by analyzing the isotopic dependence of excitation energies, and compared our results to available experimental data. We calculated differences in quadrupole moments and charge radii between nuclei in their \mbox{high-$K$} and ground states and found their quite different pattern for four-quasiparticle states in neighboring No and Rf isotopes. The leading role of the quadrupole and hexadecapole deformations as well as the importance of higher rank symmetries are also discussed. The current development of laser techniques and the resulting ability to measure discussed effects in the near future is the motivation of our study

8Dim calculations of the third barrier in 232^{232}Th and a conflict between theory and experiment on uranium nuclei

We find the height of the third fission barrier $B_{III}$ and energy of the third minimum $E_{III}$ in $^{232}$Th using the macroscopic - microscopic model, very well tested in this region of nuclei. For the first time it is done on an 8-dimensional deformation hypercube. The dipole distortion is included among the shape variables to assure that no important shapes are missed. The saddle point is found on a lattice containing more than 50 million points by the immersion water flow (IWF) method. The shallow third minimum, $B_{III}-E_{III}\approx 0.36$ MeV, agrees with experimetal data of Blons et al. This is in a sharp contrast with the status of the IIIrd minima in $^{232-236}$U: their experimental depth of $\geq3$ MeV contradicts all realistic theoretical predictions. We emphasize the importance of repeating the experiment on $^{232}$Th, by a technique similar to that used in the uranium nuclei, for settling the puzzle of the third minima in actinides

Static fission properties of actinide nuclei

Fission barriers heights and excitation energies of superdeformed isomeric minima are calculated within the microscopic - macroscopic Woods - Saxon model for 75 actinide nuclei for which the experimental data are known. State - of - the - art methods were used: minimization over many deformation parameters for minima and the imaginary water flow on many - deformation energy grid for saddles, including nonaxial and reflection-asymmetric shapes. We obtain 0.82 - 0.94 MeV rms deviation between the calculated and experimental barriers and 0.53 MeV rms error in the excitation of superdeformed minima (SD). Experimental vs theory discrepancies seem to be of various nature and not easy to eliminate, especially if one cares for more than one or two observables. As an example, we show that by strengthening pairing in odd systems one can partially improve agreement in barriers, while spoiling it for masses. We also discuss the "thorium anomaly" and suggest its possible relation to a different way in which the Ac and Th barriers are derived from experimental data.Comment: Submitted to PR

Properties of heaviest nuclei with 98≤Z≤12698\leq Z \leq 126 and 134≤N≤192134 \leq N \leq 192

We systematically determine ground-state and saddle-point shapes and masses for 1305 heavy and superheavy nuclei with $Z=98-126$ and $N=134-192$, including odd-$A$ and odd-odd systems. From these, we derive static fission barrier heights, one- and two-nucleon separation energies, and $Q_\alpha$ values for g.s. to g.s transitions. Our study is performed within the microscopic-macroscopic method with the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy taken as the smooth part. We use parameters of the model that were fitted previously to masses of even-even heavy nuclei. For systems with odd numbers of protons, neutrons, or both, we use a standard BCS method with blocking. Ground-state shapes and energies are found by the minimization over seven axially-symmetric deformations. A search for saddle-points was performed by using the "imaginary water flow" method in three consecutive stages, using five- (for nonaxial shapes) and seven-dimensional (for reflection-asymmetric shapes) deformation spaces. The results are collected in two main tables. Calculated ground-state mass excess, nucleon separation- and $Q_\alpha$ energies, total, macroscopic(normalized to the macroscopic energy at the spherical shape) and shell corrections energies, and deformations are given for each nucleus in \mbox{Table 1}. \mbox{Table 2} contains calculated properties of the saddle-point configurations and the fission barrier heights. In \mbox{Tables 3-7}, are given calculated ground-state, inner and outer saddle-point and superdeformed secondary minima characteristics for 75 actinide nuclei, from Ac to Cf, for which experimental estimates of fission barrier heights are known. These results are an additional test of our model.Comment: Submitted to ADNDT. arXiv admin note: text overlap with arXiv:1203.501

Hindered alpha decays of heaviest high-K isomers

To find candidates for long-lived high-K isomers in even-even Z=106-112 superheavy nuclei we study dominant alpha-decay channel of two- and four-quasi-particle configurations at a low excitation. Energies are calculated within the microscopic - macroscopic approach with the deformed Woods-Saxon potential. Configurations are fixed by a standard blocking procedure and their energy found by a subsequent minimization over deformations. Different excitation energies of a high-K configuration in parent and daughter nucleus seem particularly important for a hindrance of the alpha-decay. A strong hindrance is found for some four-quasi-particle states, particularly $K^{\pi} = 20^{+}$ and/or $19^{+}$ states in $^{264-270}$Ds. Contrary to what was suggested in experimental papers, it is rather a proton configuration that leads to this strong hindrance. If not shortened by the electromagnetic decay, alpha half-lives of $\sim$ 1 s could open new possibilities for studies of chemical/atomic properties of related elements

Level-density parameters in superheavy nuclei

We systematically study the nuclear level densities of superheavy nuclei, including odd systems, using the single-particle energies obtained with the Woods-Saxon potential diagonalization. Minimization over many deformation parameters for the global minima - ground states and the "imaginary water flow" technique on many deformation energy grids for the saddle points, including nonaxial shapes has been applied. The level density parameters are calculated by fitting the obtained results with the standard Fermi gas expression. The total potential energy and shell correction dependencies of the level-density parameter are analyzed and compared at the ground state and saddle point. These parameters are compared with the results of the phenomenological expression. As shown, this expression should be modified for the saddle points, especially for small excitation energy. The ratio of the level-density parameter at the saddle point to that at the ground state is shown to be crucial for the survival probability of the heavy nucleus.Comment: submitted to PR