Mahmoud Yahia Ismail

We study the role of the projectile breakup in the fusion process by example of the 6Li reactions with the 59Co, 144Sm and 209Bi targets in vicinity of the Coulomb barrier. The coupled channel and distorted wave approaches are employed in order to calculate the complete fusion and the breakup cross sections, respectively. The partial cross sections in both the channels are compared in order to estimate the breakup fraction responsible for the suppression of complete fusion. The calculations are compared with available experimental data. The conclusions and recommendations are made.

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.

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%.

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 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 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 structure of some even-even superheavy nuclei with the proton number Z = 98-120 is studied using a semi-microscopic but not self-consistent model. The macroscopic energy part is obtained from the Skyrme nucleon-nucleon interaction in the semi-classical extended Thomas-Fermi approach. A simple but accurate method is derived for calculating the direct part of the Coulomb energy. The microscopic shell plus pairing energy corrections are calculated from the traditional Strutinsky method. Within this semi-microscopic approach, the total energy curves with the quadrupole deformation of the studied superheavy nuclei were calculated. The same approach features the well known 208Pb or 238U nuclei. For each nucleus the model predictions for the binding energy, the deformation parameters, the half-density radii and comparison with other theoretical models are made. The calculated binding energies are in good agreement with the available experimental data. © 2010 Pleiades Publishing, Ltd.

The energy dependence of the real part of the ion-ion interaction potential is studied using an energy density functional derived from the Negele realistic nucleon-nucleon interaction. It is found that the Negele force produces an ion-ion potential which varies slowly with energy compared to that derived using a simple two-body effective interaction. NUCLEAR REACTIONS Antisymmetrization effects, Fermi gas model, momentum density, Negele force, energy dependence of ion-ion potential. © 1982 The 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.

The energy density method was employed to calculate the real part of the 40Ca-40Ca interaction potential in the sudden approximation. A simple effective two-body force as well as the Skyrme and Negele interactions were used to derive the energy density functional. The real part of the 40Ca-40Ca potential calculated using Negele's (1970) force agrees well with the experimental results.

$$\alpha$$decay of 2000 parent heavy and superheavy nuclei, with atomic numbers in the range $$Z=80$$to $$Z=122$$, is considered. We calculated the half-life time, $$T_{\alpha}$$, of each nucleus using the density-dependent cluster model with M3Y-effective nucleon–nucleon interaction. The $$Q_{\alpha}$$values needed for calculation of $$T_{\alpha}$$were extracted from four different mass tables used frequently in $$\alpha$$-decay calculation. These tables are WS4, WS3, FRDM(2012), and DZ tables. The present study shows to what extent the behavior and value of $$T_{\alpha}$$, as the nucleon number varies, depends on choosing the mass table used to extract $$Q_{\alpha}$$values. For this purpose, we studied the variation of log $$T_{\alpha}$$and the corresponding $$1/Q_{\alpha}$$with the neutron number of the daughter nucleus, $$N_{d}$$, using the four different mass tables. The results show that the log $$T_{\alpha}$$variation follows the corresponding $$1/Q_{\alpha}$$variation. The two mass tables WS3 and WS4 predict almost the same log $$T_{\alpha}$$variation and agree in the magic and semi-magic numbers. For FRDM(2012) and DZ tables the variation of log $$T_{\alpha}$$with $$N_{d}$$follows the same $$1/Q_{\alpha}$$variation but the magic numbers deduced from these two tables do not agree with each other and almost differ from those predicted from WS3 and WS4. FRDM(2012) tables predict the main deep minimum at $$N_{d}=128$$instead of the magic neutron number $$N_{d}=126$$.

We systematically investigated the behavior of the α-decay half-lives (Tα) for 20 isotopic chains of even–even nuclei, from 78Pt to 116Lv. Tα is calculated within the preformed cluster model. The α-core potential is determined by the double-folding model based on the M3Y-Reid nucleon–nucleon interaction. The Coulomb potential is also microscopically calculated by the folding procedure. To confirm our results, we used four different parameterizations of the involved proton and neutron densities, which are consistent with extensive microscopic calculations and electron scattering data. The results correlate the logTα behavior for the isotopes of an element with their proton energy levels. We found a clear similarity in the behavior of logTα with the number of neutrons of the daughter nuclei (Nd) for specific isotopic chains. The proton pairs forming the α-particles that emitted from the isotopes of the similar chains belong to the same proton energy level. We pointed out some neutron magic and semi-magic numbers corresponding to characteristic minima in the logTα variation with Nd. We interpreted these magic (semi-magic) numbers as the total number of neutrons filling the upper neutron level in the parent nucleus.

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 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".

Photon production cross sections in 12C-12C and 40Ca-40Ca collisions at Elab=84 and 200 MeV/A are calculated in the framework of the quantum molecular dynamics approach using the medium-dependent NN cross section obtained from the G matrix. Photons are assumed to be produced by incoherent pn bremsstrahlung and a simple classical expression for the production cross section is used. The effects of the equation of state for nuclear matter on the photon production cross section are studied in detail. In the 12C-12C collision, the authors found little difference in the photon cross section due to differences in the equation of state both at 84 and 200 MeV/A. In the 40Ca-40Ca collision, slightly more high-energy photons are produced in the case of the soft equation of state and the difference is slightly larger at higher incident energies.

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.

A fourth-power momentum term is added to a simplified form of Skyrme interaction and the resulting two-body force is used to study the real part of the optical-model potential for the elastic scattering process n+ 40Ca at energies of 10 MeV and 50 MeV. It is found that the k 4 term affects the shape, the magnitude and the energy variation of the optical-model real well.