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

Abstract

We calculate the macroscopic potential energy of deformation 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 we represent the system 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 we display the calculated energy 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. The maps illustrate how the topography of the potential energy changes as a function of the nuclear system considered. For example, as we move from lighter to heavier nuclear systems the binary saddle point moves from outside the point of first contact in heavy-ion reactions to inside the contact point. Because of this, the formation of a heavy compound nucleus requires additional energy relative to the maximum in a one-dimensional interaction barrier. The maps also illustrate for moderately heavy systems the presence of separate valleys for binary fission and fusion. For still heavier systems the ternary and quaternary saddle points are no longer present. This means that the ternary and quaternary valleys are accessible by paths that decrease monotonically in energy beyond the binary saddle point. Finally, for nuclear systems heavier than about 300120, the binary saddle point itself disappears, which in the absence of single-particle effects precludes altogether the formation of a compound system.