Establishing the island of stability for superheavy nuclei via the dynamical cluster-decay model applied to a hot fusion reaction⁴⁸Ca +²³⁸U →²⁸⁶112*

Abstract

Considering different magic shells such as Z = 126, 120 or 114, N = 184 or Z = 120, N = 172 for the superheavy mass region, the dynamical cluster-decay model (DCM), with deformation and orientation degrees of freedom of colliding nuclei or decay fragments included, is used to study the complete excitation functions of a 'non-equatorial' compact hot-fusion reaction 48Ca + 238U → 286112* (orientation angle θc = 72° for 238U; θc = 90° for 'equatorial' compact). For the higher multipole deformations taken up to hexadecapole deformations β4i and configurations with 'compact' orientations θci, the DCM gives a good description of the individual light-particle decay channels σxn (x = 3 and 4 neutrons), and other decay channels, the fusion–fission σff and quasi-fission σqf cross-sections, at various incident energies or compound nucleus excitation energies E*, within a single parameter description, the neck-length parameter ΔR. Within the Strutinsly renormalization procedure, in each case, the shell corrections are obtained from an 'empirical' formula with the corresponding liquid-drop energies adjusted to give the experimental binding energies. This is done for all the mass (and charge) fragmentations of the compound system. Of all the four choices of magic numbers considered, the evaporation residue cross-sections (σER = σ3n + σ4n, the sum of light-particle, neutron-channel cross-sections) remain the largest and nearly the same for Z = 126, N = 184 or Z = 120, N = 184, but the fusion–fission cross-sections σff are always the highest for Z = 120, N = 184. Noting that the quasi-fission process is not affected by the magicity of shells, this study supports Z = 120 and N = 184 as the strongest magic numbers for the center of an island of stability for superheavy elements.