Orientation dependent behavior of the Coulomb barrier parameters for deformed–deformed nuclei

The Coulomb barrier parameters (radius, image, and height, image) 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 image and image for the reactions image, image, image, and image 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 image (image) and the nuclear radii of the deformed nuclei dose not give the values of image and image. 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.