Narrow Results

Encouraged by the success of relativistic mean-field plus BCS (RMF + BCS) approach for the description of the ground state properties of the chains of isotopes of proton magic nuclei with proton number Z = 8, 20, 28, 50 and 82 as well as those of proton sub-magic nuclei with Z = 40, we have further employed it, in an analogous manner, for a detailed calculations of the ground state properties of the neutron magic isotones with neutron number N = 8, 20, 28, 50, 82 and 126 as well as those of neutron sub-magic isotones with N = 40 using the TMA force parametrizations in order to explore low lying resonance and other exotic phenomenon near drip-lines. The results of these calculations for wave function, single particle pairing gaps etc. are presented here to demonstrate the general validity of our RMF + BCS approach. It is found that, in some of the proton-rich nuclei in the vicinity of the proton drip-line, the main contribution to the pairing correlations is provided by the low-lying resonant states, in addition to the contributions coming from the states close to the Fermi surface, which results extended proton drip-line for isotonic chain.

This paper refers to another attempt to search for spherical double shell closure nuclei beyond Z = 82, N = 126. All calculations and results are based on a newly developed approach entitled as simple effective interaction (SEI). Our results predict that the combination of magic nucleus occurs at N = 182 (Z = 114, 120, 126). All possible evidences for the occurrence of magic nuclei are discussed systematically. And, the obtained results for all observables are compared with the relativistic mean field theory for NL3 parameter.

In this paper, breaking of Cooper pairs in ${}^{108}$Pd is investigated within the canonical ensemble framework and the BCS model. Our results show an evidence of two phase transitions, which are related to neutron and proton systems. Also, with consideration of pairing interaction, the role of neutron and proton systems in entropy, spin cutoff parameter and as a result in the moment of inertia are investigated. The results show minor role for the proton system at low temperatures and approximately equal roles for both neutron and proton systems after the critical temperature. Good agreement was observed between obtained results and the experimental data.

In this paper, we have taken the effect of small size of nucleus and static fluctuations into account in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity calculations of ${}^{45}$Ti nucleus. Thermodynamic quantities of ${}^{45}$Ti have been extracted within the BCS model with the inclusion of the average value of the pairing gap square, extracted by the modified Ginzburg–Landau (MGL) method for small systems. Calculated values of the excitation energy and entropy within the MGL+BCS method improve the extracted results within the usual BCS model and show a smooth behavior around the critical temperature with a very good agreement with the semi-empirical values. The result of using MGL+BCS method for the heat capacity of ${}^{45}$Ti is compared with the corresponding semi-empirical values and the calculated values within the BCS, static path approximation (SPA) and Modified Pairing gap BCS (MPBCS) which is a method that was proposed in our previous publications. Both MGL+BCS and MPBCS avoid the discontinuity of the heat capacity curve, which is observed in the usual BCS method, and lead to an S-shaped curve with a good agreement with the semi-empirical results.

The effect of using a temperature dependent pairing term in back-shifted Fermi-gas (BSFG) formula of nuclear level density has been studied. We have used the mean order parameter formula of modified Ginzburg–Landau (MGL) theory as a simple possible choice for temperature dependency of the pairing term. The level density and heat capacity of ${}^{98}$Mo have been calculated with this formalism and compared with the experimental data. We observed good agreement between the heat capacity of this model and the experimental data.

The systematic search of axial ground state and the emergence of new gaps in neutron-rich ${}^{44-52}$Ar isotopes are the challenging of current calculations of relativistic and nonrelativistic mean field models. For this purpose, we have employed the model based on Relativistic Hartree–Bogoliubov (RHB) with the density-dependent effective interaction of point coupling DD-PCX type. However, the nonrelativistic mean field calculations based on Hartree-Fock model were carried out with Skyrme SV-min parametrization. All the present calculations were performed within axial symmetries. The results provide that most of isotopes show an oblate-deformed ground state. In particular, ${}^{50}$Ar and ${}^{52}$Ar display a spherical shape in their ground states with SV-Min calculations. There is a notable signature of the sub-shell closure at neutron number $N=32$, whereas $N=34$ is expected to be nearly quenched in the spherical ground. Furthermore, coexistence features are predicted in the neutron-rich ${}^{44}$Ar isotope. We have also studied the neutron axial densities and its central depletion in the well-deformed grounds for the first time. In addition to these, the proton single-particle evolution and bubble-like structure at ${}^{46}$Ar are very well reproduced with DD-PCX calculations.

This study is an investigation of the effect of the pairing strength using different types of pairing (surface, volume and mixed surface–volume pairing) on the ground state properties of even and odd Mg isotopes. The Hartree–Fock–Bogoliubov (HFB) theory and two types of Skyrme forces, SKI3 and SLY6, were employed in our calculations. The pairing strength values are modified at each execution of the HFBTHO code to obtain the experimental values of binding energy for the investigated even and odd isotopes separately. Then a new formula for pairing strength for each even and odd isotope independently for all the pairing, surface, volume and mixed surface–volume types is developed by fitting the pairing strength values to the mass number. Based on the newly generated formulas for pairing strength, some of the calculated ground state properties are found to depend strongly on the pairing strength values and the pairing type also plays an essential role in providing accurate results.