Nuclear Physics A489 (1988) 461-476 North-Holland, Amsterdam COMPARISON BETWEEN THE SYMMETRIC FISSION AND FUSION PATHS J. MIGNEN, G. ROYER and F. SEBILLE Laboratoires de Physique Nucldaire ( UA CNRS n ° 57) et de Physique Thdorique 2, rue de la Houssini~re, 44072 NANTES C~dex 03, France Received 23 June 1988 (Revised 1 August 1988) Abstract" The symmetric fission path leading to smooth extended shapes and the fusion or new fission path going through the two tangent sphere configuration are investigated within the liquid-drop model including the nuclear proximity energy. Analytical formulae are given for the various shape-dependent functions which govern the dynamics. The quadrupole moment, the perpendicular moment of inertia and the Coulomb energy are similar in the two paths. In contrast, the neck radius, the rupture point between the fragments, the parallel and effective moments of inertia, the surface energy and the critical angular momentum against fission are quite different in the two valleys. The introduction of the proximity energy strongly lowers the deformation energy in the fusion valley and for the light, medium and very heavy nuclei the barrier heights are nearly equal in the two paths. This flattening of the potential surface by the proximity forces allows to better understand the sudden transition between the one- and two-body configurations. 1. Introduction The different shapes of a fissioning nucleus were investigated some time ago 1-3) assuming that the fission process is only governed by the balance between the repulsive Coulomb force and the attractive surface tension force and that the nucleus will explore all the shape degrees of freedom in seeking its way across the saddle. The commonly used development of the radius of the system in terms of legendre polynomials leads to smooth elongated one-body configurations which have been able to explain the bulk of the current knowledge on nuclear fission. However, this development does not allow to explore the strongly distorted shapes and the rupture into two compact fragments 4-6). This other region of the multi-dimensional potential surface has been studied within the two overlapping or separated spheroid configur- ation 7). This path is also capable of accounting for most experimental fission data (at least for nuclei lighter than radium). Beside the Coulomb and surface energies, recent nuclear studies 8-9) have clearly pointed out the necessity to take into account the proximity energy resulting from the strong nuclear interaction between the two surfaces of a crevice or between two separated fragments. In the sheet of potential- energy surface corresponding to one-body smooth extended shapes (the so-called fission valley or first valley), this proximity contribution is small since the necks are shallow. In contrast, in the valley rapidly leading to compact separated fragments 0375-9474/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)