Clustering in superheavy nuclei within the relativistic mean field approach
The clustering phenomenon in superheavy nuclei is studied within the relativistic mean field approach by using the axially deformed harmonic oscillator basis. The standard BCS pairing scheme is adopted for taking the pairing interaction into account. The calculated ground and intrinsic excited state properties, and the nucleon and total matter densities, as well as the proton–neutron asymmetry distributions, are analysed to look for cluster configurations and/or exotic clusters in superheavy nuclei. We have applied our method to Z = 120, N = 172–184 nuclei. A new 'bubble'-like structure for the Z = 120, N = 172, 292120 nucleus as signatures of doubly closed shells and a two-cluster configuration for the Z = 120, N = 184, 304120 nucleus are some of the interesting results obtained. New possibilities of exotic clusters at the centre of superheavy nuclei are also indicated.

title: Phase transition and properties of a compact star
abstract: We investigate the phase transition to a deconfined phase and the consequences in the formation of neutron stars. We use the recently proposed effective-field-theory-motivated relativistic mean-field theory for the hadrons and the MIT bag model and color-flavor locked (CFL) phase for the quark matter to get the appropriate equation of state. The properties of the stars are then calculated. The differences between unpaired and CFL quark matter are discussed.

title: Role of isospin physics in supernova matter and neutron stars
abstract: We investigate the liquid-gas phase transition of hot protoneutron stars shortly after their birth following supernova explosion and the composition and structure of hyperon-rich (proto)neutron stars within a relativistic mean-field model where the nuclear symmetry energy was constrained from the measured neutron skin thickness of finite nuclei. Light clusters are abundantly formed with increasing temperature well inside the neutrino-sphere for a uniform supernova matter. Liquid-gas phase transition is found to suppress the cluster yield within the coexistence phase as well as decrease considerably the neutron-proton asymmetry over a wide density range. We find symmetry energy has a modest effect on the boundaries and the critical temperature for the liquid-gas phase transition, and the composition depends more sensitively on the number of trapped neutrinos and temperature of the protoneutron star. The influence of hyperons in the dense interior of stars makes the overall equation of state soft. However, neutrino trapping distinctly delays the appearance of hyperons because of an abundance of electrons. We also find that a softer symmetry energy further makes the onset of hyperon less favorable. The resulting structures of the (proto)neutron stars with hyperons and with liquid-gas phase transition are discussed.

title: Superheavy nuclei in a relativistic effective Lagrangian model
abstract: Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z= 82 and N= 126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N= 172 and Z= 120 and N= 258 and Z= 120 as spherical doubly magic superheavy nuclei, whereas N= 184 and Z= 114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

title: Nuclear reaction studies of unstable nuclei using relativistic mean field formalisms in conjunction with the Glauber model
abstract: We study nuclear reaction cross sections for stable and unstable projectiles and targets within Glauber model, using densities obtained from various relativistic mean-field formalisms. The calculated cross sections are compared with the experimental data in some specific cases. We also evaluate the differential scattering cross sections at several incident energies and observe that the results found from various densities are similar at smaller scattering angles, whereas a systematic deviation is noticed at large angles. In general, these results agree fairly well with the experimental data.

title: DECREASE OF THE SPIN-ORBIT INTERACTION IN DRIP-LINE NUCLEI, USING RELATIVISTIC MEAN FIELD MODELS
abstract: The spin-orbit potential and the energy splitting of spin-orbit partners in nuclei towards the neutron drip-line are found to show the decreasing behavior with the increase of neutron number, in both the spherical and deformed versions of the standard relativistic mean field model, the SRMF and DRMF, and its extended version for spherical case, the effective field theory motivated relativistic mean field model, the E-RMF. The calculations are presented for nuclei in different mass regions, which include the isotopes of F, Mg, Sb, Pb and Bi nuclei.

title: Basic Mechanics of Planet-Satellite Interaction with special reference to Earth-Moon System
abstract: In1879 George Howard Darwin theoretically analyzed the outward spiraling orbit of Moon and the subsequent lengthening of the Mean Solar Day. The author redid the same analysis based on the fact that Moon was receding at the rate of 3.8 cm per annum. Basic Mechanics of Earth-Moon is worked out and various system parameters are optimized to fit the given boundary condition obtained by Apollo Mission and other modern means of observations. Based on this theoretical formulation the theoretical graph of the lengthening of the Mean Solar Day with respect to time is drawn and is compared with the observational graph of the same based on pale ontological data, paleo tidal data and iron-banded formation. The observational data on Mean Solar Day is found to follow the theoretical smooth curve in post-Cambrian Era but is found to deviate in the remote past. This deviation is corrected by taking the evolving form of Moment of Inertia of Earth. The deviation of the observed data prompts the Author to suggest that the lengthening of the Mean Solar Day curve could possibly be used as an analytical seismograph for the impending earthquakes and sudden volcanic eruptions. The Basic Mechanics of E-M system is generalized to lay the foundation of simulation software for any Planet-Satellite pair in our Solar System.

title: Theoretical Formulation of the Origin of Cataclysmic Late Heavy Bombardment Era based on the New Perspective of Birth & Evolution of Solar Systems
abstract: Based on the planet-satellite dynamics, a new perspective on the birth and evolution of the Solar System was proposed in 2004. This new perspective has 1:2 Mean Motion Resonance (1:2 MMR, that is Ps/Pj = 2) implicit in itself . This paper has shown that if we assume the sequential birth of the planets with the heaviest, i.e. Jupiter, being born the earliest and this axiom is central to the new perspective then there is an unique initial condition for which 1:2 MMR crossing occurs exactly 300My after the birth of Jupiter. It is shown that 25 My time gap between the birth of Jupiter and Saturn results in the 300 My time delay in the occurrence of 1:2 MMR. Because the process by which Late Heavy Bombardment is triggered involves the movement of Neptune over enormous distances hence almost 200 My time delay occurs between 1:2MMR crossing and the actual spike in the Meteoritic Shower on all the terrestrial planets as evidenced by the petrology record on the Moon. The analytical derivation of the time delay in the spike is a vindication of this new perspective of the application of planet-satellite dynamics to the birth and evolution of Solar Systems.