Prediction of accidental cancellation of different deformation components and optimum fusion orientations

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, image and image, in addition to the lower order ones. This correlation has been reported in our previous work (Ismail and Seif, 2010) in presence of the lower order (image, image and image) 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 image. 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 image and image.