Narrow Results

Based on a relativistic mean field (RMF) framework, we analyze the BCS approximation to the relativistic Hartree–Bogoliubov (RHB) approach for the case of nuclei close to the drip line. In the BCS calculations the single particle continuum corresponding to RMF is replaced by a set of discrete positive energy states generated by enclosing the nucleus in a box. It is found that the main contribution to the pairing correlations for the neutron-rich nuclei is given by the low-lying resonant states, in addition to the contributions coming from the states close to the Fermi surface. Towards this end we present the results of our calculations for the entire chain of even–even ^48–98Ni isotopes. Results for the neutron-rich nucleus ⁸⁴Ni is discussed in detail as a prototype. A detailed comparison of our results for the nucleus ⁸⁴Ni with those obtained in similar studies using RHB, nonrelativistic Hartree–Fock–Bogoliubov (HFB), and a recently proposed resonant continuum HF+BCS method provides strong evidence for the applicability of the RMF+BCS approach for the treatment of neutron-rich nuclei as well. Additional results of extensive calculations for the isotopes of O, Ca, Zr, Sn and Pb nuclei further reinforce our conclusions. From amongst these calculations, the results of the even–even ^32–76Ca isotopes with two different RMF force parametrizations, and their agreement with the recent continuum relativistic Hartree–Bogoliubov (CRHB) results are discussed briefly for illustration purposes.

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.

The variation of the two-neutron separation energy (S_2N), as a function of the neutron number N, is studied using a microscopic model that includes the pairing effects rigorously within the Fixed-Sharp-BCS method. The model was first tested on "ordinary" nuclei and allowed one to suitably reproduce the experimental data and to confirm the results of previous studies. The model was then applied to the even–even neutron-rich isotopes in the rare-earth region and showed, on the one hand, a relatively important variation of S_2N, when N = 100, that could lead to the assumption of the existence of a new magic number in this region, and on the other hand, a weak variation of S_2N when N > 100. These findings corroborate the previously obtained results for the charge mean square radius and the quadrupole and hexadecapole moments within the same model.

We investigate isovector pygmy dipole resonance (IVPDR) for the case of neutron-rich soft nuclei ⁶⁸Ni, and heavy nuclei such as ¹¹²Sn and ²⁰⁸Pb using effective nucleon–nucleon Skyrme interaction. We use the mean-field theory and employ the random phase approximation (RPA). We observe that our results for the pygmy dipole resonance (PDR) for neutron-rich nuclei are in reasonable agreement with their experimental results. We also predict PDR for very neutron-rich heavy nuclei. We then study two-neutron separation Skyrme energies (S_2n) using the Hartree–Fock + BCS with and without tensor interaction in the same nucleus and compare our results with their experimental values. We see that the total binding energies of nuclei ²⁰⁸Pb are not extremely sensitive to the tensor interaction.

We propose to study the thermal two-neutron separation energy in the case of Erbium isotopes: 80 ≤ N ≤ 108. In this aim, one used the finite temperature Bardeen Cooper Schrieffer (FTBCS) method where the statistical fluctuations are treated as a part of Landau prescription. The behavior of this quantity according to the neutron number and temperature provides indication about the nuclear shape transition, and disappearance of shell effects. The obtained results allow to show that the inclusion of statistical fluctuations in the calculation have a nonnegligible effect. Indeed, the fact that this kind of fluctuations effect is important at high temperatures induces a smooth decrease of pairing gap parameter. As a consequence, the persistence of pairing effect at high temperature leads a change on the shell effect. Indeed, when statistical fluctuations are considered, the shell effect persists at high temperature which is not the case of the usual FTBCS approach.