Mahmoud Yahia Ismail

The influence of nuclear deformation on α -decay half-lives is taken into account in the deformed density-dependent cluster model. The microscopic potential between the spherical α particle and the deformed daughter nucleus is evaluated numerically from the double-folding model by the multipole expansion method. A realistic density-dependent nucleon-nucleon (NN ) interaction with finite-range exchange part, which produces the nuclear matter saturation curve and the energy dependence of the nucleon-nucleus optical potential model is used. The ordinary zero-range exchange NN force, which is commonly used in α decay, is also considered in the present work. We systematically investigate the influence of nuclear deformations on the α -particle preformation probability of the deformed medium and heavy nuclei from the ground state to ground-state α transitions within the framework of the Wentzel-Kramers-Brillouin method by considering the Bohr-Sommerfeld quantization condition. Taking the deformation of daughter nuclei into account changes the behavior of the preformation probability, S α , by an amount depending on the Q value, the order, values, and signs of deformation parameters. Calculations have been conducted for the spherical nuclei in order to present clearly the effect of the deformation on the preformation probability. The combined effect of both finite-range force and deformation can reduce the value of S α by about an order of magnitude.

The interactions of 48Ca spherical nucleus are considered with the deformed targets 224Ra and 244Pu to form the super heavy elements 272Hs and 292114 (292Fl), respectively. The double folding model with effective density dependent M3Y-NN force, and the energy density functional method based on Skyrme force are used to derive the nucleus–nucleus interaction. The effect of deformation and orientation on the Coulomb barrier parameters is studied, and the results are compared with the corresponding quantities derived from a simple model based on the proximity approach for the nuclear part and simple analytical formula for the Coulomb interaction. Consistent behavior of the results is obtained at certain ranges for deformation parameters and orientations.

The preformation probability of an α cluster inside radioactive parent nuclei is investigated. The calculations are employed in the framework of the density-dependent cluster model for both even-even and odd-A isotopes with 74≤Z≤83 . A realistic density-dependent nucleon-nucleon (NN ) interaction with a finite-range exchange part is used to calculate the microscopic α -nucleus potential in the well-established double-folding model. The main effect of antisymmetrization under exchange of nucleons between the α and daughter nuclei has been included in the folding model through the finite-range exchange part of the NN interaction. The calculated potential is then implemented to find both the assault frequency and the penetration probability of the α particle by means of the Wentzel-Kramers-Brillouin approximation in combination with the Bohr-Sommerfeld quantization condition. We investigated the correlation between the α -particle preformation probability, S α , and the energy levels of the parent nucleus for α emitters with atomic number 74≤Z≤83 . Based on the similarity in the behavior of S α with the neutron number for two nuclei, we try to predict or confirm the unknown or doubted nuclear spins and parities in this mass region.

We assume a simple model to describe the ion-ion potential with dynamical change in its surface diffuseness. In particular, this model is used to calculate the heavy-ion fusion cross-section using different values of the surface diffuseness. Both the static and dynamic nuclear Woods-Saxon potentials with diffuseness values ranging between 0.65 fm and 1.3 fm are used to reproduce the fusion cross-sections data of the 19F+208Pb and 16O+154Sm reactions. The results estimate that there are different physical processes which could contribute to the fusion cross-section with different weights at each energy value. Each of these processes has its own nuclear potential. © 2013 World Scientific Publishing Company.

The study show the effect of the local density and the accuracy of neglecting s-dependence on direct part of α-α interaction potential. The large error in neglecting s-dependence produced at (R<2 fm) for BDM3Y3 -Ried force. In the surface and tail region (R≥3) the error is less than 50%.

A new averaging process of the calculation of α-decay half-lives for heavy and superheavy nuclei is studied in the framework of a deformed density-dependent cluster model. The potential between a spherical α particle and a deformed daughter nucleus is calculated numerically from the double-folding model by the multipole expansion method. The nuclear potential is calculated at each α-particle emission angle applying the Bohr-Sommerfeld condition at each case. The penetration factors and the half-lives for all the emission angles are evaluated with the new averaging process and compared with older values based on a fixed value of the nuclear potential depth. Finally, the half-lives of 83 even-even heavy nuclei in the atomic-number range 82-118 are calculated by the two methods and compared with their experimental values and the corresponding half-lives of the spherical daughter nuclei. © 2012 American Physical Society.

In the present paper we discuss the differences between the fusion barrier parameters (the height of Coulomb barrier V B and its radius R B) computed by two methods namely; the proximity approach for coplanar and non-coplanar systems of interacting nuclei and double folding model. The minimum separation distance, s, between the deformed surfaces of interacting nuclei was determined exactly from numerical calculations and the results of Coulomb parameters were compared with previous calculations based on approximate determination of s. We considered the three interaction systems 48Ar+ 238Pu, 150Nd+ 150Nd and 86Kr+ 180Hf and found that V B and R B, evaluated by using the proximity approach, have too strong Φ-dependence for the system 150Nd+ 150Nd at relative orientation angles of the nuclei symmetry axes θ 1=θ 2=90°. © 2012 Elsevier B.V.

A realistic density-dependent nucleon-nucleon (NN) interaction with a finite-range exchange part which produces the nuclear matter saturation curve and the energy dependence of the nucleon-nucleus optical potential model is used to calculate the preformation probability, S α, of α decay from Po isotopes to superheavy nuclei. The variation of S α with the neutron number for the isotopes of Po, Rn, Ra, Th, and U elements is studied below and above the magic neutron number N=126. We found a strong correlation between the behavior of S α and the energy levels of the parent nucleus at and just below the Fermi level. S α has a regular behavior with the neutron number if the neutron pair of α particles, emitted from adjacent isotopes, comes from the same energy level or from a group of levels, assuming that the order of levels in this group is not changed. Irregular behavior of S α with the neutron number occurs if the levels of the adjacent isotopes change or holes are present in lower levels. © 2012 American Physical Society.

The role of neutron transfer is investigated in the fusion process near and below the Coulomb barrier within the empirical channel coupling approach. The possibility of neutron transfer with positive Q-values considerably increases the barrier penetrability. The enhancement of fusion cross sections for 58Ni+ 64Ni, 32S+ 64Ni, 40Ca+ 48Ca, and 40Ca+ 124Sn is well reproduced at subbarrier energies by the empirical channel coupling approach including the coupling to the neutron-transfer channels. The predictions of the fusion cross sections for several combinations of colliding nuclei are also proposed which may shed additional light on the effect of neutron transfer in fusion processes. A huge enhancement of deep subbarrier fusion probability was found for light neutron-rich weakly bound nuclei. This may be quite important for astrophysical primordial and supernova nucleosynthesis. © 2012 Elsevier B.V..

{The shell and pairing correction energies are calculated for heavy and superheavy nuclei (SHN) by means of the Strutinsky's method. The single-particle (s.p.) energy levels are obtained from the diagonalization of the WoodsSaxon s.p. Hamiltonian in the deformed harmonic oscillator basis for both neutrons and protons. The residual pairing interaction is calculated by means of the usual BardeenCooperSchrieffer (BCS) approximation. A two-dimensional deformation space describing axially and reflection-symmetric shapes of nuclei has been used. Based on the shell and pairing correction energies, the signatures of the magic numbers appear at the spherical shell closures Z = 82, 114, 164 and N = 126, 184, 228 and 308. There are also signatures for some other shell closures at, e.g.

The study show the effect of the local density and the accuracy of neglecting s-dependence on the exchange part of α-α interaction potential. This effect is bout 30% for the force BDM3Y2-Ried while it is less than 7% for BDM3Y1 -Reid. For BDM3Y3 force which corresponds to large value of compressibility coefficient, the corresponding error is too large at separation distance R=0.

The accuracy of multipole expansion of density distribution for deformed nuclei is tested. The interaction potential for a deformed-spherical pair of nuclei was calculated using the folding model derived from zero-range nucleonnucleon (NN) interaction. We considered two spherical projectiles Ca 40 and Pb 208 scattered on U 238 deformed target nucleus. The error in the heavy ion (HI) potential resulting from using a truncated multipole density expansion is evaluated for each case in the presence of octupole deformation δ 3 besides quadrupole δ 2. We are interested in the value of error for R < R T (touching distance). We found that for values of |δ 3|≤0.1 the error at R = R T reaches reasonable values when six terms expansion is used. For |δ 3| = 0.2, we calculated the Coulomb barrier parameters using realistic NN force and found that the large error present in six terms for zero range force decreases strongly to less than 1% when the zero range is added to finite range forces and Coulomb interaction to form the Coulomb barrier. It is noted that the negative value of octupole deformation parameters δ 3 = -0.1 produce error at orientation angle θ equal in value to that produced at angle (180°-θ) for the positive values δ 3 = 0.1. We also found that the error decreases as the mass number of the projectile nucleus increases. © 2011 World Scientific Publishing Company.

The azimuthal angle (φ) dependence of the Coulomb barrier parameters (height V b and position R b) are studied in the framework of the double-folding model with the realistic M3Y nucleon-nucleon interaction. Different pairs of axially symmetric, deformed nuclei are considered. For the interaction between medium and heavy nuclei, the maximum percentage of φ dependence is studied as a function of relative orientations of the interacting nuclei. It appreciably increases as the values of the deformation parameters increase and is sensitive to the hexadecapole deformation. The smallest φ variation is found for the relative orientations θ P= θ T=90. The φ variation of the Coulomb barrier parameters, as calculated in the present paper, is completely different in both magnitude and behavior from those deduced in the widely used proximity approach. © 2011 American Physical Society.

The Coulomb barrier parameters (radius, Rb, and height, Vb) for the interaction between two deformed nuclei are calculated in phenomenological way in the framework of the double folding model with the realistic M3Y nucleon-nucleon (NN) interaction. The variations of Rb and Vb for the reactions Ar48+Pu238, Mg26+Cm248, Mg26+U238, and Ne22+U238 in the orientation degrees of freedom are investigated. It is found that the distribution of the Coulomb barrier parameters in the orientation degrees of freedom shows almost the same patterns as the sum of the nuclear radii of the interacting nuclei along the direction of the separation vector joining their two centers of mass. The orientation Coulomb barrier radius distribution follows the same variations as the sum of radii while the barrier height distribution follows it inversely. This correlation (anticorrelation) between Rb (Vb) and the nuclear radii of the deformed nuclei dose not give the values of Rb and Vb. This suggests a simple and straightforward way to predict the behavior of the barrier parameters with different orders of deformations without performing the heavy numerical calculations necessary when the two nuclei are being deformed. It also allows us to estimate, with reasonable accuracy, the compact and elongated configurations of the interacting nuclei which lead to hot and cold fusion reactions, respectively. © 2011 Elsevier B.V.