Mahmoud Yahia Ismail

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.

In view of the role of nuclear deformations in the fusion between spherical and deformed nuclei to form super-heavy elements, we try to understand how a cancellation of the different nuclear deformations could arise. We first investigated the correlation between the orientation variation of the deformed nucleus radius and the orientation Coulomb barrier distribution in presence of the higher order deformation components, β 6 and β 8, in addition to the lower order ones. This correlation has been reported in our previous work (Ismail and Seif, 2010) [1] in presence of the lower order (β 2, β 3 and β 4) deformations. Even if there are higher deformations, we found here that the simple expression which describes the deformed target nucleus can be used to predict with good accuracy the behavior of the fusion Coulomb barrier with both orientation and deformation as well as the optimum (cold or hot) fusion configurations. It can predict the orientations of compact and elongated configurations of the interaction and whether they are equatorial or polar or none of them. The value and sign of the deformation parameters ratios with respect to one of them have been used to classify these configurations. We applied the same correlation to predict successfully the mutual cancellation effects between the different deformation components up to β 8. Illustrative examples are given in which the cancellation, at some orientations, brings the fusion barrier back to the spherical case or keeps only the effect of quadrupole deformation, or the effects of both β 2 and β 4. © 2011 Elsevier B.V.

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 Coulomb and nuclear heavy ion (HI) potentials are derived for an interacting pair of deformed nuclei assuming sharp surface model for each nucleus. The orientation and separation dependences of the Coulomb and nuclear interactions are studied. It is assumed 238U + 238U as an example, and the effect of quadrupole term is investigated. For the nuclear potential part based on M3Y nucleonnucleon interaction, the sharp surface model shows much difference compared with the more accurate frequently used multipole expansion method while the success of this model in calculating the Coulomb potential between this deformed pair of nuclei exists in the physically important surface region. © 2010 World Scientific Publishing Company.

A simple straightforward method has been presented to predict the dependence of barrier distributions at arbitrary orientations on different deformations. The proposed interpretation is developed independently of the complicated numerical calculations. It is related to the change of half-density radius of the deformed nucleus, in the direction of the separation vector. The microscopic calculations of Coulomb barrier are carried out by using a realistic density dependent nucleon-nucleon (NN) interaction, BDM3Y, for the interaction between spherical, Ca48, and deformed, Pu244, nuclei, as an example. To do so, the double-folding model for the interaction of spherical-deformed nuclei is put in a suitable computational form for the calculation of the potential at several separation distances and orientation angles using the density dependent NN force without consuming computational time. We found that the orientation distributions of the Coulomb barrier parameters show similar patterns to those of the interacting deformed nucleus radius. It is found that the orientation distribution of the Coulomb barrier radius follows the same variation of the deformed nucleus radius while the barrier height distribution follows it inversely. This correlation (anticorrelation) allows a simple evaluation of the orientation barrier distribution which would be very helpful to estimate when the barrier parameters will increase or decrease and at which orientations they will be independent of the deformation. This also allows us to estimate the compact and elongated configurations of the interacting nuclei which lead to hot and cold fusion, respectively. © 2010 The American Physical Society.

{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 effect of octupole deformation, β 3, and the higher multipole deformations, β 6 and β 8, on the distribution of barriers in orientation degrees of freedom, is studied. Coulomb barriers are derived in the frame work of the double folding model with the realistic M3Y nucleon-nucleon interaction and its density dependent version. 48Ca + 244Pu spherical-deformed nuclear interacting pair is considered, as an example, to study the effect of deformation parameters on the height and position of the Coulomb barrier. Although the dependence of the Coulomb barrier parameters on the higher deformations is complicated, numerically, if it is treated in microscopic way, we found a simple linear variation of barrier parameters with the different orders of deformation. We found that the variation of the barrier parameters with deformation exactly follows the change of the half density radius of the deformed nucleus in the direction of the separation vector between the centers of mass of the interacting nuclei. This suggests a simple and straightforward way to predict the behavior of the barrier parameters with different orders of deformations. We compared the results of present work with a similar recent study of the same quantities based on simple expression derived by Wong for the Coulomb part and proximity approach for the nuclear part of heavy ion potential, respectively. © 2009 Elsevier B.V. All rights reserved.

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 Coulomb interaction for a spherical-deformed interacting pair is derived assuming realistic nuclear charge distributions. The effect of a finite diffuseness parameter is described either by the folding product of spherical or deformed sharp-surface distribution and a spherical short-range function or by using a Fermi two-parameter distribution function. The approximate solutions obtained using these categories of charge distributions are then compared to the numerical solution obtained within the framework of the double-folding model. We found that the finite surface diffuseness parameter affects slightly the inner region of the total Coulomb potential, while it produces large errors in calculating the Coulomb form factors used frequently in nuclear reactions and fusion numerical codes. © Nauka/Interperiodica 2006.

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".

The effect of both rotation and vibration of a deformed target nucleus on the fusion cross-section and barrier distributions was studied. This was done in the framework of the microscopically derived heavy-ion (HI) potential. Moreover, the effect of target deformation up to β6 and the density dependence of the NN force on the fusion process was studied in the presence of vibrational excitations of the target. The results obtained were compared with experimental data.

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.