MAGIC NUCLEI IN SUPERHEAVY VALLEY

An extensive theoretical search for the proton magic number in the superheavy valley beyond Z = 82 and the corresponding neutron magic number after N = 126 is carried out. For this we scanned a wide range of elements Z = 112–130 and their isotopes. The well-established non-relativistic Skryme–Hartree–Fock and Relativistic Mean Field formalisms with various force parameters are used. Based on the calculated systematics of pairing gap, two-neutron separation energy and the shell correction energy for these nuclei, we find Z = 120 as the next proton magic and N = 172, 182/184, 208 and 258 the subsequent neutron magic numbers.

DYNAMICAL SHELL EFFECT IN THE FUSION REACTIONS

Dynamical nuclear shell effect is introduced to the improved quantum molecular dynamics model in interaction potential energy in the process of fusion reactions. The dynamical shell correction energy of the system is calculated and applied to dynamical process of fusion reactions with a switch function employed to connect the shell correction energy of the projectile and target with that of the compound nucleus. It is found that the shell effect enhances the fusion barrier and the calculated fusion (capture) cross-sections decrease for subbarrier fusion reactions which both projectile and target are doubly magic nuclei. The experimental data of the fusion cross-sections for four systems 40 Ca + 48 Ca , 48 Ca + 48 Ca , 16 O + 208 Pb and 48 Ca + 208 Pb can be reproduced better with the shell effect being considered by using the ImQMD model.

MICROSCOPIC ENERGY CORRECTIONS AT THE SCISSION CONFIGURATION

The Strutinsky shell correction and the pairing correlations at deformations close to scission point are studied. It is shown that the shell correction energy of the nuclear system at scission is simply the sum of the shell-correction energies of the two nascent fragments while this is not the case for the pairing corrections when the reflection symmetry of the system is broken. To study this effect the use of a δ-pairing force or of the Gogny interaction is recommended. It is also shown that the strength of the pairing correlations should grow with increasing deformation of the fissioning nucleus in order to obtain the correct properties of the fragments.

REMARKS ON THE NUCLEAR SHELL-CORRECTION METHOD

The shell-correction energy is calculated using the single-particle levels obtained with the folded-Yukawa mean-field potential. Three different ways of evaluation of the shell-correction are compared: the traditional Strutinsky method, the modified prescription by the smearing of the total energy sum in the nucleon number space, and the smoothing of the single-particle energies of occupied states and summing them up. The dependence of these three energies on nuclear elongation is investigated.

SHELL CORRECTION ENERGY AND THE ENTRANCE CHANNEL EFFECT ON THE FORMATION OF SUPERHEAVY NUCLEI

Based on the improved isospin dependent molecular dynamics model in which the shell correction energy of the system is calculated by using deformed two-center shell model and the surface energy of the system is improved by introducing a switch function that combines the surface energies of projectile and target with the one of the compound nucleus. The effects of the shell correction energy on synthesis of superheavy nuclei and the fusion cross sections in asymmetric and nearly symmetric reaction systems leading to the same compound nuclei 62 Zn , 76 Kr , and 202 Pb are studied. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, Coulomb barriers and fusion cross sections. The experimental data are described quantitatively by the present model. It is found that the compound nucleus formation is favorable for the systems with larger mass asymmetry.

WHAT CAN WE LEARN FROM THE FISSION TIME OF THE SUPER-HEAVY ELEMENTS?

Recent experiments performed at GANIL with a crystal blocking technique have shown direct evidences of long fission times in the Super-Heavy Elements (SHE) region. Aimed to localize the SHE island of stability, can these experiments give access to the fission barrier and then to the shell-correction energy? In this paper, we calculate the fission time of heavy elements by using a new code, KEWPIE2, devoted to the study of the SHE. We also investigate the effect of potential structure beyond the saddle on the fission time.

IMPORTANCE OF SHELL CORRECTION ENERGY ON SYNTHESIS OF SUPERHEAVY NUCLEI

Based on the improved isospin dependent molecular dynamics model in which the shell correction energy of the system is calculated by using deformed two-center shell model and the surface energy of the system is improved by introducing a switch function that combines the surface energies of projectile and target with the one of the compound nucleus. The importance of shell correction energy on synthesis of superheavy nuclei is studied systematically. For reaction systems induced by of 16 O and 40,48 C at low energies near Coulomb barrier, it is found that the calculated fusion cross sections show a strong enhancement for the neutron-rich combinations, which can regenerate the experimental data quantitatively.

SHELL CORRECTION ENERGIES IN CALCULATIONS OF THE SURVIVAL PROBABILITY

Analysis of existing data on experimental fission barriers for about 90 nuclei shows that the shell correction energy practically vanishes at the barrier configuration. Statistical model calculations, with shell effects accounted for by the Ignatyuk formula, were carried out for the decay of the 248 Cf compound nucleus assuming the ground state shell corrections of Möller et al., and the vanishing shell correction energy at the barrier. The results are consistent with existing experimental data on fusion- and xn evaporation-residue cross sections in the 12 C +236 U reaction.