In this theoretical study, we establish a correlation between the neutron skin thickness and the nuclear symmetry energy for the even−even isotopes of Fe, Ni, Zn, Ge, Se and Kr within the framework of the axially deformed self-consistent relativistic mean field for the non-linear NL3 * and density-dependent DD-ME1 interactions. The coherent density functional method is used to formulate the symmetry energy, the neutron pressure and the curvature of finite nuclei as a function of the nuclear radius. We have performed broad studies for the mass dependence on the symmetry energy in terms of the neutron-proton asymmetry for mass 70 ≤ A ≤ 96. From this analysis, we found a notable signature of a shell closure at N = 50 in the isotopic chains of Fe, Ni, Zn, Ge, Se and Kr nuclei. The present study reveals a interrelationship between the characteristics of infinite nuclear matter and the neutron skin thickness of finite nuclei.

The mean field properties and equation of state for asymmetric nuclear matter are studied by using a simple effective interaction which has a single finite range Gaussian term. The study of finite nuclei with this effective interaction is done by means of constructing a quasilocal energy density functional for which the single particle equations take the form of Skryme-Hartree-Fock equations. The predictions of binding energies and charge radii of spherical nuclei are found to be compatible with the results of standard models as well as experimental data.

We calculate the binding energy, root-mean-square radius and quadrupole deformation parameter for the recent, possibly discovered superheavey element Z=122, using the axially deformed relativistic mean field (RMF) and non-relativistic Skyrme Hartree-Fock (SHF) formalisms. The calculation is extended to include various isotopes of Z=122 element, strarting from A=282 to A=320. We predict highly deformed structures in the ground state for all the isotopes. A shape transition appears at about A=290 from a highly oblate to a large prolate shape, which may be considered as the superdeformed and hyperdeformed structures of Z=122 nucleus in the mean field approaches. The most stable isotope (largest binding energy per nucleon) is found to be 302 122, instead of the experimentally observed 292 122.

In this theoretical study, we report an investigation on the behavior of two-neutron separation energy, a differential variation of the nucleon separation energy, the nuclear charge radii and the single-particle energy levels along the isotopic chains of transitional nuclei. We have used the relativistic mean field formalism with NL3 and NL3 * forces for this present analysis. The study refers to the even-even nuclei such as Zr, Mo, Ru and Pd for N = 42−86, where a rich collective phenomena such as proton radioactivity, cluster or nucleus radioactivity, exotic shapes, Island of Inversion and etc. are observed. We found that there are few non-monotonic aspects over the isotopic chain, which are correlated with the structural properties like shell/sub-shell closures, the shape transition, clustering and magicity etc. In addition to these, we have shown the internal configuration of these nuclei to get a further insight into the reason for these discrepancies.

We have calculated the binding energy, root-mean-square radius and quadrupole deformation parameter for the recently synthesized superheavy element Z=117, using the axially deformed relativistic mean field (RMF) model. The calculation is extended to various isotopes of Z=117 element, strarting from A=286 till A=310. We predict almost spherical structures in the ground state for almost all the isotopes. A shape transition appears at about A=292 from prolate to a oblate shape structures of Z=117 nucleus in our mean field approach. The most stable isotope (largest binding energy per nucleon) is found to be the 288 117 nucleus. Also, the Q-value of α-decay Qα and the half-lives Tα are calculated for the α-decay chains of 293 117 and 294 117, supporting the magic numbers at N=172 and/ or 184.

An extensive theoretical search for the proton magic number in the superheavy valley beyond Z =82 and 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. Keywords:After the discovery of artificial transmutation of elements by Sir Ernest Rutherford in 1919 [1], the search for new elements is an important issue in nuclear science. The existence of elements beyond the last heaviest naturally occurring 238 U, i.e., the discovery of Neptunium, Plutonium and other 14 elements (transuranium elements), which make a separate block in Mendeleev ′ s periodic table was a revolution in the Nuclear Chemistry. This enhancement in the periodic table raises a few questions in our mind:• Whether there is a limited number of elements that can co-exist either in nature or can be produced from artificial synthesis by using modern technique ?• What is the maximum number of protons and neutrons that of a nucleus ?• What is the next double shell closure nucleus beyond 208 Pb ?To answer these questions, first we have to understand the agent which is responsible to rescue the nucleus against Coulomb repulsion. The obvious reply is the shell energy, which stabilises the nucleus against Coulomb disintegration [2]. Many theoretical models, like the macroscopic−microscopic (MM) calculations to explain involve some prior knowledge of densities, single-particle potentials and other bulk properties which may accumulate serious error in the largely extrapolated mass region of interest. They predict the magic shells at Z=114 and N=184 [3,4,5,6] which could have surprisingly long life time even of the order of a million years [7,8,9,5,10]. Some other such predictions of shell-closure for the superheavy region within the relativistic and non-relativistic theories depend mostly on the force parameters [11,12].Experimentally, till now, the quest for superheavy nuclei has been dramatically rejuvenated in recent years owing to the emergence of hot and cold fusion reactions. In cold fusion reactions involving a doubly magic spherical target and a deformed projectile were used by GSI [13,14,15,16,17] to produce heavy elements upto Z = 110−112. In hot fusion evaporation reactions with a deformed transuranium target and a doubly magic spherical projectile were used in the synthesis of superheavy nuclei Z = 112−118 at Dubna [18,19,20,21,22,23,24]. At the production time of Z = 112 nucleus at GSI the fusion cross section was extremely small (1pb), which led to the conclusion that reaching still heavier elements will be very difficult. At this time, the emergence of hot fusion reactions usi...

In this theoretical study, we establish an interrelationship between the nucleon-nucleon interaction potential and the nuclear fusion reaction cross-sections at low energies. The axially deformed self-consistent relativistic mean field with non-linear NL3 * force is used to calculate the density distribution of the projectile and target nuclei for fusion. The Wong formula is used to estimate the fusion cross-section and barrier distribution from the nucleus-nucleus optical potential for Nibased systems, which are known for fusion hindrance phenomena. The results of the application of the so obtained nucleus-nucleus optical potential for the fusion cross-section from the recently developed relativistic N N −interaction (R3Y) are compared with the well-known, phenomenological M3Y effective N N potential. We found a relatively good results from R3Y interactions below the barrier energies as compare to the M3Y potential concerning the experimental data. We also observe the density dependence on the nuclear interaction potential in terms of nucleon-nucleon optical potentials.

A microscopic nucleon-nucleon (NN) interaction is derived from the popular relativistic-mean-field (RMF) theory Lagrangian and used to obtain the optical potential by folding it with the RMF densities of cluster and daughter nuclei. The NN-interaction is remarkably related to the inbuilt fundamental parameters of RMF theory, and the results of the application of the so obtained optical potential, made to exotic cluster radioactive decays and α+α scattering, are found comparable to that for the well-known, phenomenological M3Y effective NN-interaction. The RMF-based NN-interaction can also be used to calculate a number of other nuclear observables.