Hoda M. Abou Shady

A relativistic version of the two colliding nuclear matter approach together with the eikonal approximation are used to calculate the reaction cross-section σr for the spherically deformed pair C12-N17. Both the energy and the orientation dependence of the σr are studied. A maximum variation of 13% was found in σr due to all possible orientations of the deformed nucleus.

The optical limit to Glauber theory is used to calculate the reaction cross section, σR, for neutron rich nuclei. In-medium and iso-spin dependence of the effective nucleon-nucleon (NN) reaction cross-section, σNN, are treated correctly assuming both finite and zero range NN interaction. We find that the combined effect of iso-spin dependence and finite range of NN force can increase up to 20% for neutron rich nuclei compared to σR calculated using zero range approximation and constant matter density value 0.16 fm-3 in σNN. The maximum percentage increase is reduced to 13% compared with σR based on 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 β 6 has large effect on both the fusion cross-section and the barrier distribution in the presence of a small value of hexadecapole deformation parameter β 4. In this case the fusion cross-section is less sensitive to the negative value of β 6. In the presence of a large value of β 4, negative and positive β 6 values affect the fusion cross-section and have a small effect on the barrier distribution.

The optical limit approximation to Glauber theory was used to calculate the reaction cross-section, σR, 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 σR for C12–N17 and C12–U238 interacting pairs. We found that the orientation dependence of σR for the heavy target U238 depends on the value and sign of hexadecapole deformation and it is more than 2.2 times compared to the light deformed target nucleus N17. The presence of hexadecapole deformation does not affect the value of σR averaged over all orientation of the target nucleus. A geometrical model was proposed to account for the orientation dependence of σR. We found that the error in this model is less than 10%.

The fusion cross section and the barrier distribution for deformed spherical pair are calculated by the WKB approximation, and it is compared with the results of Wong's formula. We found that the latter is a very good approximation to the more complicated WKB one, starting from energy less by 5% than the lowest fusion barrier height occurring at orientation angle of the deformed target nucleus B=0.