Effect of the finite range of the nuclear force on the dynamics of fission and heavy-ion collisions

We study the effect on dynamical calculations of fission and heavy-ion collisions of replacing the surface energy of the liquid-drop model with a modification that takes into account the lowering of the nuclear macroscopic energy due to the finite range of the nuclear force. This energy is caculated by performing a two-dimensional volume integral over the nuclear density of a two-body attractive Yukawa potential, in analogy with the calculation of the electrostatic energy of a charge distribution. The kinetic energy of the nuclear liquid drop is calculated for incompressible, nearly irrotational hydrodynamical flow by use of the Werner-Wheeler method. The dissipation of collective energy into internal, single-particle excitation energy is neglected. In the case of fission, the liquid-drop model and finite-range model give similar results, although the liquid-drop model predicts a somewhat larger fission-fragment excitation energy. In the case of heavy-ion collisions, the surface energy of the liquid-drop model causes a large coupling of energy from relative center-of-mass motion into higher-degree collective motion. This increases the energy over the onedimensional interaction barrier that is needed to cause compound-nucleus formation in head-on collisions for symmetric systems. For an $A=250\mathrm{}$ compound system, the predicted energy over the barrier is about 170 MeV in the liquid-drop model, as compared to about 40 MeV in the finite-range model. We conclude that the effect of the finite range of the nuclear force is small in calculations of fission, but that it must be included in calculations of heavy-ion collisions.