Investigation on the 48Ca+249-252Cf reactions synthesizing isotopes of the superheavy element 118

The study of the $^{48}$Ca+$^{249,250,251,252}$Cf reactions in a wide energy interval around the external barrier has been achieved with the aim of investigating the dynamical effects of the entrance channel via the $^{48}$Ca induced reactions on the $^{249-252}$Cf targets and to analyze the influence of odd and even neutron composition in target on the capture, quasifission and fusion cross sections. Moreover, we also present the results of the individual evaporation residue excitation functions obtained from the de-excitation cascade of the various even-odd and even-even $^{297-300}$118 superheavy compound nuclei reached in the studied reactions, and we compare our results of the $^{294}$118 evaporation residue yields obtained in the synthesis process of the $^{48}$Ca+$^{249,250}$Cf reactions with the experimental data obtained in the $^{48}$Ca+$^{249}$Cf experiment carried out at the Flerov Laboratory of Nuclear Reactions of Dubna.Comment: 10 pages, 14 figures, Accepted for publication in Phys. Rev.

Relativistic Energy Density Functional Description of Shape Transition in Superheavy Nuclei

Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. A modern semi-empirical functional, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, is applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison of calculated masses, quadrupole deformations, and potential energy barriers to available data on actinide isotopes. Self-consistent mean-field calculations predict a variety of spherical, axial and triaxial shapes of long-lived superheavy nuclei, and their alpha-decay energies and half-lives are compared to data. A microscopic, REDF-based, quadrupole collective Hamiltonian model is used to study the effect of explicit treatment of collective correlations in the calculation of Q{\alpha} values and half-lives.Comment: 23 pages, 10 figure

Relativistic mean field study of the properties of Z=117 nucleus and the decay chains of 293,294^{293,294}117 isotopes

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 $\alpha$-decay $Q_\alpha$ and the half-lives $T_{\alpha}$ are calculated for the $\alpha$-decay chains of $^{293}$117 and $^{294}$117, supporting the magic numbers at N=172 and/ or 184.Comment: 6 Pages and 8 Figure

Analytical relationship for the cranking inertia

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the $^{240}$Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.Comment: 12 pages, 4 figure

Superheavy Nuclei in the Relativistic Mean Field Theory

We have carried out a study of superheavy nuclei in the framework of the Relativistic Mean-Field theory. Relativistic Hartree-Bogoliubov (RHB) calculations have been performed for nuclei with large proton and neutron numbers. A finite-range pairing force of Gogny type has been used in the RHB calculations. The ground-state properties of very heavy nuclei with atomic numbers Z=100-114 and neutron numbers N=154-190 have been obtained. The results show that in addition to N=184 the neutron numbers N=160 and N=166 exhibit an extra stability as compared to their neighbors. For the case of protons the atomic number Z=106 is shown to demonstrate a closed-shell behavior in the region of well deformed nuclei about N=160. The proton number Z=114 also indicates a shell closure. Indications for a doubly magic character at Z=106 and N=160 are observed. Implications of shell closures on a possible synthesis of superheavy nuclei are discussed.Comment: 29 pages Latex, 13 ps figures, to appear in Nucl. Phys.

Alpha decay chains study for the recently observed superheavy element Z=117 within the Isospin Cluster Model

The recently observed $\alpha$-decay chains $^{293-294}117$ were produced by the fusion reactions with target $^{249}Bk$ and projectile $^{48}Ca$ at Dubna in Russia. The reported cross-sections for the mentioned reaction are $\sigma=0.5(+1.1,-0.4)$pb and $\sigma$=1.3(+1.5,-0.6)$pb$ at $E^{*}=35MeV$ and $E^{*}=39MeV$, respectively. The Q-values of $\alpha$-decay and the half-lives $Log_{10}T^{\alpha}_{1/2}$(s) are calculated for the $\alpha$-decay chains of $^{293-294}117$ nuclei, within the framework of Isospin Cluster Model (ICM). In the ICM model the proximity energy is improved by using the isospin dependent radius of parent, daughter and alpha particle. The binding energy $B(A_{i}, Z_{i})$ (i=1,2) of any nucleus of mass number A and atomic number Z was obtained from a phenomenological and more genaralized BW formula given by \cite{samanta02}. The calculated results in ICM are compared with the experimental results and other theoretical Macro-Microscopic(M-M), RMF(with NL3 and SFU Gold forces parameter) model calculations. The estimated values of $\alpha$-decay half-lives are in good agreement with the recent data. The ICM calculation is in favor of the persence of magic number at N=172

Nuclear Half-Lives for Alpha Radioactivity of Elements with 100 ≤\leq Z ≤\leq 130

Theoretical estimates for the half lives of about 1700 isotopes of heavy elements with Z from 100 to 130 are tabulated using theoretical Q-values. The quantum mechanical tunneling probabilities are calculated within a WKB framework using microscopic nuclear potentials. The microscopic nucleus-nucleus potentials are obtained by folding the densities of interacting nuclei with a density dependent M3Y (DDM3Y) effective nucleon-nucleon interaction. The alpha-decay half lives calculated in this formalism using the experimental Q-values were found to be in good agreement over a wide range of experimental data spanning about twenty orders of magnitude. The theoretical Q-values used for the present calculations are extracted from three different mass estimates viz. Myers-Swiatecki [MS], Muntian-Hofmann-Patyk-Sobiczewski [M] and Koura-Tachibana-Uno-Yamada [KUTY].Comment: 57 pages, 2 tables, 1 figur

Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory

The magic proton and neutron numbers are searched in the superheavy region with proton number $Z$=100 - 140 and neutron number $N$= ($Z$+30) - (2$Z$+32) by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with interactions NL1, NL3, NLSH, TM1, TW99, DD-ME1, PK1, and PK1R. Based on the two-nucleon separation energies $S_{2p}$ and $S_{2n}$, the two-nucleon gaps $\delta_{2p}$ and $\delta_{2n}$, the shell correction energies $E_{shell}^{p}$ and $E_{shell}^{n}$, the pairing energies $E_{pair}^{p}$ and $E_{pair}^{n}$, and the pairing gaps $\Delta_{p}$ and $\Delta_{n}$, $Z$=120, 132, and 138 and $N$=172, 184, 198, 228, 238, and 258 are suggested to be the magic numbers within the present approach. The $\alpha$-decay half-lives are also discussed. In addition, the potential energy surfaces of possible doubly magic nuclei are obtained by the deformation-constrained relativistic mean field (RMF) theory, and the shell effects stabilizing the nuclei are investigated. Furthermore, the formation cross sections of $^{292}_{172}$120 and $^{304}_{184}$120 at the optimal excitation energy are estimated by a phenomenological cold fusion reactions model with the structure information extracted from the constrained RMF calculation.Comment: 37 pages, 14 figure

Shell Structure of the Superheavy Elements

Ground state properties of the superheavy elements (SHE) with Z from 108 to 128 and N from 150 to 192 are investigated using both the Skyrme-Hartree-Fock method with a density-independent contact pairing interaction and the macroscopic-microscopic approach with an average Woods-Saxon potential and a monopole pairing interaction. Detailed analysis of binding energies, separation energies, shell effects, single proton and neutron states, equilibrium deformations, alpha-decay energies, and other observables is given.Comment: 27 RevTeX pages, 22 figures available upon request to [email protected]

Skyrme mean-field study of rotational bands in transfermium isotopes

Self-consistent mean field calculations with the SLy4 interaction and a density-dependent pairing force are presented for nuclei in the Nobelium mass region. Predicted quasi-particle spectra are compared with experiment for the heaviest known odd N and odd Z nuclei. Spectra and rotational bands are presented for nuclei around No252,4 for which experiments are either planned or already running.Comment: 13 pages LATEX, elsart style, 6 embedded eps figure