Exotic clustering in heavy and superheavy nuclei within the relativistic and non-relativistic mean field formalisms
The clustering phenomenon in heavy and superheavy nuclei is studied within the relativistic mean field (RMF) approach using axially deformed basis and the non-relativistic Skyrme?Hartree?Fock (SHF) formalism. The calculated ground and intrinsic excited state properties, and the total matter densities as well as the neutron?proton asymmetry distributions are analysed to look for the cluster configurations and/or exotic clusters in the known cluster emitting 222Ra, 232U, 236Pu and 242Cm nuclei, and the superheavy nuclei with Z = 114, N = 172?184. Both the theories predict N ? Z, ?-like matter or clustering in the ground states, and both N ? Z matter and N ? Z clustering in the excited intrinsic states of radioactive actinides, though this result is more apparent and universal for the RMF approach. For superheavy nuclei, the detailed analysis shows a non-clustering, 'bubble'-like structure for Z = 114, N = 184 nucleus in the RMF method and Z = 114, N = 176 or 180 nucleus in the SHF method, as the signatures of doubly closed shell nuclei. Our earlier similar calculations for Z = 120 nuclei predicted the same for Z = 120, N = 172 nucleus in the RMF model. Also, in contrast to radioactive actinides, in superheavy nuclei the two fragments, N ? Z cluster configurations at the centre of ground superdeformed states in the RMF approach, and the same for at least some of the excited superdeformed states in the SHF method, are some of the interesting results obtained. Thus, new possibilities of exotic clusters at the centre of superheavy nuclei are indicated as ground or excited intrinsic superdeformed state configurations, more so as ground superdeformed states in the RMF theory. The N/Z ratios of the clusters are also calculated on the basis of the (average value of) colour code of the contours, which give a reasonable correspondence with the experimental data on cluster decay of radioactive nuclei.

title: Nuclear symmetry energy effects in finite nuclei and neutron star
abstract: Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of 208Pb and the neutron star masses and radii with kaon condensation has been studied. We find that 208Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.

title: Clustering in superheavy nuclei within the relativistic mean field approach
abstract: 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: Nuclear symmetry energy effects on liquid-gas phase transition in hot asymmetric nuclear matter
abstract: The liquid-gas phase transition in hot asymmetric nuclear matter is investigated within the relativistic mean-field model using the density dependence of nuclear symmetry energy constrained from the measured neutron skin thickness of finite nuclei. We find symmetry energy has a significant influence on several features of liquid-gas phase transition: the boundary and area of the liquid-gas coexistence region, the maximal isospin asymmetry, and the critical values of pressure and isospin asymmetry, all of which systematically increase with increasing softness in the density dependence of symmetry energy. The critical temperature below which the liquid-gas mixed phase exists is found higher for a softer symmetry energy.

title: Axially-symmetric Neutron stars: Implication of rapid rotation
abstract: Models of relativistic rotating neutron star composed of hyperon rich matter is constructed in the framework of an effective field theory in the mean-field approach. The gross properties of compact star is calculated at both static and the mass-shedding limit in the axially symmetric basis. The effect of appearance and abundance of hyperons on equation of state of dense matter and stellar properties is lineated with particular emphasis on the underlying nuclear interactions. We find that the models can explain fast rotations, which supports the existence of millisecond pulsars. An important offshoot of the present investigation is that, irrespective of the model parameters and interaction taken, the star seems to sustain faster rotations (an increase in rotational frequency up to $\approx$ 50%) without any further deformation.

title: NUCLEON–NUCLEUS OPTICAL POTENTIAL FROM HARD- AND SOFT-CORE INTERNUCLEON POTENTIALS
abstract: We have compared the binding energy of nuclear matter and the nucleon–nucleus optical potential, calculated in Brueckner theory starting from both the soft-core Urbana V-14 and the hard-core Hamada–Johnston internucleon potentials. Our results show that the real central part of the optical potential calculated from V-14 is about 10 MeV deeper than from the hard-core potential in the energy region 1–200 MeV. This greater depth mainly comes from the internucleon S- and D-states. In these states, the V-14 and Hamada–Johnston potentials give different phase shifts, the V-14 being in better agreement with experimental data. This difference is further enhanced by the Pauli principle in the calculation of the optical potential. Our analysis of proton–40Ca differential cross-section and polarization data, in the energy region 30–200 MeV, shows that the optical potential calculated using V-14 is in better agreement with the data as compared with the Hamada–Johnston potential.

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.

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: Irregularly Shaped Satellites-Phobos & Deimos- moons of Mars, and their evolutionary history
abstract: Phobos, a moon of Mars, is below the Clarke synchronous orbit and due to tidal interaction is losing altitude. With this altitude loss it is doomed to the fate of total destruction by direct collision with Mars. On the other hand Deimos, the second moon of Mars is in extra-synchronous orbit and almost stay put in the present orbit. The reported altitude loss of Phobos is two meter per century by wikipedia and sixty ft per century according to ozgate url . The reported time in which the destruction will take place is fiftyMy and fortyMy respectively. The authors had proposed a planetary-satellite dynamics based on detailed study of Earth-Moon. Based on this planetary satellite dynamics, two meter/century approach velocity leads to the age of Phobos to be twenty three Gyrs which is physically untenable since our Solar System age is four and a half Gyrs. Hence the present altitude loss is assumed to be twenty meter per century. This leads to the age of Phobos to be two decimal three Gyrs and age of Deimos to be two decimal two six Gyrs which is an acceptable result and from this analysis it is predicted that the travel time from the present orbital radius of nine thousand three hundred and eighty km to the Martian surface at three thousand, three hundred and ninety seven km is ten decimal and four Myrs. Hence doomsday of Phobos is at ten decimal and fourMyrs from now. Mars Express studies have confirmed that Phobos is indeed trapped in a death spiral.

title: The Architectural Design Rules of Solar Systems Based on the New Perspective
abstract: In this paper I present a new perspective of the birth and evolution of Planetary Systems. This new perspective presents an all encompassing and self consistent Paradigm of the birth and evolution of the solar systems. In doing so it redefines astronomy and rewrites astronomical principles. Kepler and Newton defined a stable and non-evolving elliptical orbits. While this perspective defines a collapsing or expanding spiral orbit of planets except for Brown Dwarfs. Brown Dwarfs are significant fraction of the central star. Hence they rapidly evolve from non-Keplerian state to the end point which is a Keplerian state where it is in stable elliptical orbits. On the basis of the Lunar Laser Ranging Data released by NASA on the Silver Jubilee Celebration of Man’s Landing on Moon on 21st July 1969–1994, theoretical formulation of Earth-Moon tidal interaction was carried out and Planetary Satellite Dynamics was established. It was found that this mathematical analysis could as well be applied to Star and Planets system and since every star could potentially contain an extra-solar system, hence we have a large ensemble of exo-planets to test our new perspective on the birth and evolution of solar systems. Till date 403 exo-planets have been discovered in 390 extra-solar systems by radial velocity method, by transiting planet method, by gravitational lensing method, by direct imaging method and by timing method. I have taken 12 single planet systems, four Brown Dwarf—Star systems and two Brown Dwarf pairs. Following architectural design rules are corroborated through this study of exo-planets. All planets are born at inner Clarke’s Orbit what we refer to as inner geo-synchronous orbit in case of Earth-Moon System. The inner Clarke’s Orbit is an orbit of unstable equilibrium. By any perturbative force such as cosmic particles or radiation pressure, the planet gets tipped long of aG1 or short of aG1. Here aG1 is inner Clarke’s Orbit. If planet is long of aG1 then it is said to be in extra-synchronous orbit. Here Gravitational Sling Shot effect is in play. In gravity assist planet fly-by maneuver in space flights, gravitational sling shot is routinely used to boost the space craft to its destination. The exo-planet can either be launched on death spiral as CLOSE HOT JUPITERS or can be launched on an expanding spiral path as the planets in our Solar System are. In death spiral, exo-planet less than 5 mJ will get pulverized and vaporized in close proximity to the host star. If the mass is between 5 and 7.5 mJ then it will be partially vaporized and partially engulfed by the host star and if it is greater than 7.5 mJ, then it will be completely ingested by the host star. In the process the planet will deposit all its material and angular momentum in the Host Star. This will leave tell-tale imprints of ingestion: in such cases host Star will have higher 7Li, host star will become a rapidly rotating progenitor and the host star will have excess IR. All these have been confirmed by observations of Transiting Planets. It was also found that if the exo-planet are significant fraction of the host star then those exo-planets rapidly migrate from aG1 to aG2 and have very short Time Constant of Evolution as Brown Dwarfs have. But if exo-planets are insignificant fraction of the host star as our terrestrial planets are then they are stay put in their original orbit of birth. By corollary this implies that Giant exo-planets reach nearly Unity Evolution Factor in a fraction of the life span of a solar system. This is particularly true for brown dwarfs orbiting main sequence stars. In this study four star systems hosting Brown Dwarfs, two Brown Dwarf pairs and 12 extrasolar systems hosting Jupiter sized planets are selected. In Brown Dwarfs evolution factor is invariably UNITY or near UNITY irrespective of their respective age and Time Constant of Evolution is very short of the order of year or tens of years. In case of 12 exo-planets system with increasing mass ratio evolution factor increases and time constant of evolution shortens from Gy to My though there are two exceptions. TW Hydrae is a special case. This Solar System is newly born system which is only 9 million years old. Hence its exo-planet has just been born and it is very near its birth place just as predicted by my hypothesis. In fact it is only slightly greater than aG1. This vindicates our basic premise that planets are always born at inner Clarke’s Orbit. This study vindicates the design rules which had been postulated at 35th COSPAR Scientific Assembly in 2004 at Paris, France, under the title “New Perspective on the Birth & Evolution of Solar Systems”.