Macroscopic potential-energy surfaces for symmetric fission and heavy-ion reactions

The macroscopic potential energy of deformation is calculated for symmetric configurations of interest in fission and heavy-ion reactions. The shape of the system is characterized in terms of two moments of the matter distribution. These moments correspond to the distance between the centers of mass of the two halves of the system and to the elongation of each half about its center of mass. The configurations studied include a continuous sequence of shapes from the sphere to two-, three-, and four-fragment scission lines. Beyond the scission lines and prior to the line of first contact in heavy-ion reactions the system is represented in terms of separated oblate and prolate spheroids. The macroscopic energy is calculated as the sum of a Coulomb energy and a nuclear macroscopic energy that takes into account the finite range of the nuclear force. For systems throughout the periodic table the calculated energy is displayed as a function of the two moments in the form of contour maps. Some important features of the contour maps are the binary, ternary, and quaternary saddle points, the fission and fusion (or two-fragment) valleys, and the three- and four-fragment valleys. (Auth.)