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Abstract
It is evident that the Coulomb interaction between two nuclei is an important contribution of the nucleus-nucleus interaction. It is a fundamental quantity in many problems of nuclear physics. It enters in calculating most of the physical quantities like fusion and fission cross-sections. Moreover it is needed to describe the formation and decay of new elements and is very important in the field of super-heavy nuclei. For these reasons, the present thesis concerns with testing the validity of approximate expressions of the Coulomb interaction for spherical-deformed and deformed-deformed pairs of interacting nuclei. These expressions which are simple and free from complicated integrals are used frequently in recent works.
In the first chapter, we derive in details a very simple formula; containing a small number of terms and free from complicated integrals, for the Coulomb potential between two deformed nuclei. It corresponds to the uniformly charged bodies with sharp edges in the limit where the separation distance of the center of mass of the two nuclei is larger than the sum of the two nuclear radii. This formula was first introduced by C. Y. Wong, about 37 years ago. We develop this formula to include hexadecupole deformation parameter. Also another formula for calculating the HI Coulomb potential is introduced that is derived on the basis of multipole expansion for the density of the deformed nucleus.