Fission valleys of double-magic superheavy nuclei

An alternative Z = 120 proton shell closure is analysed for the superheavy region. The proton magic numbers 114 and 120 are obtained for two different sets of the spin-orbit and l2 strength parameters, κ and μ. The possible double-magic superheavy nuclei 304 120 and 298 114 are compared within a four-dimensional space of deformation which includes mass-asymmetry and three geometrical degrees of freedom. The potential energy is calculated with the macroscopic-microscopic method. A well suited single-particle model for such a study is the two-center shell model. This model is used to obtain the energy levels. The shell corrections are computed using the Strutinsky method and are added to the Yukawa-plus-exponential macroscopic energy. One considers axially symmetric shapes. Spherical ground states are assumed for the initial and final fragments. Different pairs of fragments are obtained by changing the mass asymmetry parameter η. Two energy valleys play a major role in this static study: one leading to the double magic light fragment 132 Sn corresponding to almost symmetric splitting, the other belonging to the double magic heavy fragment 208 Pb at larger mass asymmetry.The lead valley explains the cluster radioactivity for the lighter nuclei. Fission-like barriers are obtained by two intersected spheres with zero neck radius in-between. The fission barriers have been calculated by minimization of the energy within the three dimensional deformation space. At least one magic number and another one close to magic is needed within the fragment pair to shape a valley on the potential energy surfaces. The static barriers are more likely to favour the two fission modes leading to the above mentioned double-magic fragments due to the combined effect of two shell closures on the total energy value. (authors)