Analytical relationship for the cranking inertia

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the $^{240}$Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.Comment: 12 pages, 4 figure

Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory

The magic proton and neutron numbers are searched in the superheavy region with proton number $Z$=100 - 140 and neutron number $N$= ($Z$+30) - (2$Z$+32) by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with interactions NL1, NL3, NLSH, TM1, TW99, DD-ME1, PK1, and PK1R. Based on the two-nucleon separation energies $S_{2p}$ and $S_{2n}$, the two-nucleon gaps $\delta_{2p}$ and $\delta_{2n}$, the shell correction energies $E_{shell}^{p}$ and $E_{shell}^{n}$, the pairing energies $E_{pair}^{p}$ and $E_{pair}^{n}$, and the pairing gaps $\Delta_{p}$ and $\Delta_{n}$, $Z$=120, 132, and 138 and $N$=172, 184, 198, 228, 238, and 258 are suggested to be the magic numbers within the present approach. The $\alpha$-decay half-lives are also discussed. In addition, the potential energy surfaces of possible doubly magic nuclei are obtained by the deformation-constrained relativistic mean field (RMF) theory, and the shell effects stabilizing the nuclei are investigated. Furthermore, the formation cross sections of $^{292}_{172}$120 and $^{304}_{184}$120 at the optimal excitation energy are estimated by a phenomenological cold fusion reactions model with the structure information extracted from the constrained RMF calculation.Comment: 37 pages, 14 figure

Shell Structure of the Superheavy Elements

Ground state properties of the superheavy elements (SHE) with Z from 108 to 128 and N from 150 to 192 are investigated using both the Skyrme-Hartree-Fock method with a density-independent contact pairing interaction and the macroscopic-microscopic approach with an average Woods-Saxon potential and a monopole pairing interaction. Detailed analysis of binding energies, separation energies, shell effects, single proton and neutron states, equilibrium deformations, alpha-decay energies, and other observables is given.Comment: 27 RevTeX pages, 22 figures available upon request to [email protected]

New Outlook on the Possible Existence of Superheavy Elements in Nature

A consistent interpretation is given to some previously unexplained phenomena seen in nature in terms of the recently discovered long-lived high spin super- and hyper-deformed isomeric states. The Po halos seen in mica are interpreted as due to the existence of such isomeric states in corresponding Po or nearby nuclei which eventually decay by gamma- or beta-decay to the ground states of 210Po, 214Po and 218Po nuclei. The low-energy 4.5 MeV alpha-particle group observed in several minerals is interpreted as due to a very enhanced alpha transition from the third minimum of the potential-energy surface in a superheavy nucleus with atomic number Z=108 (Hs) and atomic mass number around 271 to the corresponding minimum in the daughter.Comment: 8 pages, 8 figures, 5 tables. Paper presented at VII Int. School-Seminar on Heavy Ion Physics, May 27 - June 1, 2002, Dubna, Russi

Fusion cross sections for superheavy nuclei in the dinuclear system concept

Using the dinuclear system concept we present calculations of production cross sections for the heaviest nuclei. The obtained results are in a good agreement with the experimental data. The experimentally observed rapid fall-off of the cross sections of the cold fusion with increasing charge number $Z$ of the compound nucleus is explained. Optimal experimental conditions for the synthesis of the superheavy nuclei are suggested.Comment: 16 pages, LaTeX, including 3 postscript figure

Cluster Interpretation of Properties of Alternating Parity Bands in Heavy Nuclei

The properties of the states of the alternating parity bands in actinides, Ba, Ce and Nd isotopes are analyzed within a cluster model. The model is based on the assumption that cluster type shapes are produced by the collective motion of the nuclear system in the mass asymmetry coordinate. The calculated spin dependences of the parity splitting and of the electric multipole transition moments are in agreement with the experimental data.Comment: 29 pages, 10 figure

Shell structure of superheavy nuclei in self-consistent mean-field models

We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models -- the Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a large number of parameterizations. Results obtained with the Folded-Yukawa potential are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. While all relativistic models give a reasonable description of spin-orbit splittings, all non-relativistic models show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%-80%. Spherical doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or (Z=126,N=184) depending on the parameterization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in Pb208. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for (Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.Comment: 22 pages REVTeX, 16 eps figures, accepted for publication in Phys. Rev.

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

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.Comment: 30 pages RevTeX, 7 tables, 12 low resolution Gif figures (high resolution PostScript versions are available at http://www.th.physik.uni-frankfurt.de/~bender/nucl_struct_publications.html or at ftp://th.physik.uni-frankfurt.de/pub/bender

Shell Corrections of Superheavy Nuclei in Self-Consistent Calculations

Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and Relativistic Mean-Field theories. Due to the presence of low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of single-particle level density. To cure the pathological behavior of shell correction around the particle threshold, the method based on the Green's function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for Z=124, and 126, and for N=184. On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for Z=120 and N=172. This difference has probably its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent on the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrisation used. That is, the A and Z dependence of mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties.Comment: 14 pages REVTeX, 8 eps figures, submitted to Phys. Rev.

Mean-field description of ground-state properties of drip-line nuclei. (I) Shell-correction method

A shell-correction method is applied to nuclei far from the beta stability line and its suitability to describe effects of the particle continuum is discussed. The sensitivity of predicted locations of one- and two-particle drip lines to details of the macroscopic-microscopic model is analyzed.Comment: 22 REVTeX pages, 13 uuencoded postscript figures available upon reques