Mahmoud Yahia Ismail

{We present a systematic calculation of α-decay half-lives of even-even heavy and superheavy nuclei in the framework of the preformed α model. The microscopic α-daughter nuclear interaction potential is calculated by double-folding the density distributions of both α and daughter nuclei with a realistic effective Michigan three-Yukawa nucleon-nucleon interaction, and the microscopic Coulomb potential is calculated by folding the charge density distributions of the two interacting nuclei. The half-lives are found to be sensitive to the density dependence of the nucleon-nucleon interaction and the implementation of the Bohr-Sommerfeld quantization condition inherent in the Wentzel-Kramers-Brillouin approach. The α-decay half-lives obtained agree reasonably well with the available experimental data. Moreover, the study has been extended to the newly observed superheavy nuclei. The interplay of closed-shell effects in α-decay calculations is investigated. The α-decay calculations give the closed-shell effects of known spherical magicities

The interaction potential for a deformed-spherical pair of nuclei is calculated using the folding model derived from different range nucleon-nucleon (NN) interactions. Five spherical projectiles of different mass numbers scattered on the 238U deformed target are considered. The error in the heavy ion (HI) potential by using the truncated multipole density expansion is evaluated for each case. We find systematic trends of the percentage error in the HI potential depending on the number of multipoles considered; this percentage decreases if the mass number of the projectile or the range of the NN force increases, and it becomes smaller for small values of the separation distance between two nuclei or when higher deformation parameters vanish. The maximum error in using the truncated density expansion is estimated in the case of two deformed interacting nuclei. © 2008 IOP Publishing Ltd.

The azimuthal angle variation of the Coulomb and nuclear heavy ion (HI) potentials is studied in the framework of the double folding model, which is derived from realistic nuclear density distributions and a nucleon-nucleon (NN) interaction. The present calculation shows that the variation of HI potentials with the azimuthal angle depends strongly on the range of the NN forces. For the long-range Coulomb force, the maximum variation with is about 0.9%, and for HI potential derived from zero-range NN interaction the variation can reach up to 90.0%. Our calculations are compared with the recent dependence of the HI potential derived from proximity method. The present realistic dependence calculations of the HI potential is completely different from the results of the proximity calculations. © 2007 The American Physical Society.

The reaction cross section (σ R) is calculated using the optical limit of the Glauber theory. A density-dependent effective nucleon-nucleon (NN) cross section σ NN is considered. Finite and zero range NN interactions are studied. The effect of finite range and an appropriate local density can increase σ R up to 20% compared to the zero range at constant density (0.16 fm -3), while a zero range calculation with free NN cross section increases σ R up to 13%. These factors affect the values of the rms radii for neutron rich nuclei extracted from σ R. ©2005 The American Physical Society.

The deformation and orientation dependence of the real part of the interaction potential is studied for two heavy deformed nuclei using the Hamiltonian energy density approach derived from the well-known Skyrme NN interaction with two parameter sets SIII and SkM*. We studied the real part of the heavy ion (HI) potential for U238+U238 pair considering quadrupole and hexadecapole deformations in both nuclei and taking into consideration all the possible orientations, coplanar and noncoplanar, of the two interacting nuclei. We found strong orientation dependence for the physically significant region of the HI potential. The orientation dependence increases with adding the hexadecapole deformation. The azimuthal angle dependence is found to be strong for some orientations. This shows that taking the two system axes in one plane produces a large error in calculating the physical quantities. © 2005 The American Physical Society.

A method is described to calculate the heavy ion reaction cross section σ R when one of the two nuclei is deformed. This method is based on both the double folding model and the optical limit approximation to Glauber theory. Both finite range of the nucleon-nucleon (NN) interaction and in-medium effects of NN cross section are included. The interacting pair 12C -238U is taken to study orientation, energy, and deformation dependence of σ R. The finite range force increases the value of σ R by about 5%. In-medium NN cross section decreases σ R by about 1.9% compared to the free NN cross section.

The effect of hexacontatetrapole deformation parameter on both the fusion cross-section and the barrier distribution have been studied for U238 + O16 nuclear pair using microscopically derived heavy ion (HI) potential. A method was described to extend the calculation of HI potential between two spherical nuclei using density dependent finite range NN forces to the spherical-deformed interacting pair. Density dependent and density independent effective NN forces were used in the generalized double folding model to derive the HI potential. We found that positive β6 has large effect on both the fusion cross-section and the barrier distribution in the presence of a small value of hexadecapole deformation parameter β4. In this case the fusion cross-section is less sensitive to the negative value of β6. In the presence of a large value of β4, negative and positive β6 values affect the fusion cross-section and have a small effect on the barrier distribution.

The reaction cross section (σ R) for a deformed target nucleus and spherical projectile is calculated using the optical-limit approximation of the Glauber-Sitenko theory. A method is presented to include both the density-dependent N N interaction and the higher order deformations of the target nucleus in the collision process. We studied both the orientation and the deformation dependence of σ R within the energy range 30-900 MeV/A We found that the orientation of the heavy target nucleus (A ≥ 120) can produce a difference in the calculated σ R up to 30%. The averaged σ R over all directions of the symmetry axis of the deformed nucleus differs by less than 1 % compared with σ R calculated for a spherical target with the same rms matter radius as the deformed nucleus. For certain orientation, it was found that σ R is highly dependent on the hexadecapole deformation. The orientation-averaged cross sections show almost no variation with either the sign or the value of the hexadecapole deformation. We compared the average cross section with the experimental data for several mass numbers; fair agreement is obtained. © 2003 MAIK "Nauka/Interperiodica".

A method is presented to calculate the exact HI Coulomb potential between spherical and deformed nuclei in the framework of the double folding model. We used realistic density distributions taking the deformations of the target into account. We have compared between our calculations and one of the more recent analytical expressions based on assuming sharp surface of the interacting nuclei. We have found that the finite surface diffuseness affects strongly the HI Coulomb interaction in the inner region and has a smaller effect in the tail region. Moreover, neglecting non-linear higher order terms in the analytical expressions produces errors in the outer region of the Coulomb interaction. © 2003 Published by Elsevier Science B.V.

The optical limit approximation to Glauber theory was used to calculate the reaction cross-section, σ R, for a deformed target nucleus. A method is presented to include both density dependence of NN reaction cross-section and higher order deformations of the target nucleus. We studied orientation, energy and deformation dependence of σ R for C 12-N 17 and C 12-U 238 interacting pairs. We found that the orientation dependence of σ R for the heavy target U 238 depends on the value and sign of hexadecapole deformation and it is more than 2.2 times compared to the light deformed target nucleus N 17. The presence of hexadecapole deformation does not affect the value of σ R averaged over all orientation of the target nucleus. A geometrical model was proposed to account for the orientation dependence of σ R. We found that the error in this model is less than 10%.

The interaction potential for a deformed-spherical pair is calculated, and the error in using the truncated multipole expansion is evaluated for different numbers of terms of the expansion considered. It was found for the internal region of the nuclear part that three terms are sufficient, but for the surface and tail region up to five terms are necessary, while for the Coulomb potential three terms were found to be sufficient.

A method has been advised to calculate the interaction potential between deformed-spherical nuclear pair using density dependent nucleon-nucleon (NN) effective interaction. We performed our study on 16O- 238U nuclear pair using four types of recently derived density dependent NN forces. These forces correspond to different values of nuclear matter compressibility coefficient (K). The orientation and density dependence on the heavy ion potential is studied at different nuclear matter compressibility. The fusion cross-section and the fusion barrier distribution have been calculated for the pair considered. We found that density dependence affects the fusion cross-section and the barrier distribution at low values of compressibility and no effect for high compressibility case. © 2002 Elsevier Science Ltd. All rights reserved.

The energy dependence of the ion-ion reaction cross section has been investigated using the eikonal approximation to study the effects of the Pauli blocking and surface contribution to the optical potential. This leads to theoretical cross sections lower than the data. If the collective surface contribution is added to the volume part, one obtains reasonable agreement with experiment at higher energies.

The authors have investigated proximity scaling for Pb+U and U+U potentials calculated recently from the collision of two infinite nuclear matters flowing through each other. They have found that the proximity theorem is satisfied to a good extent for the Pb+U system. for the U+U system a deviation between the proximity approach and the energy-density method has been found.