Clustering phenomenon in nuclei is studied within the relativistic as well as non-relativistic mean field approaches, and also as a collective clusterization process in the decaying hot compound nucleus.

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The dynamical cluster-decay model (DCM), with deformations and orientation degrees of freedom of the incoming nuclei and of outging fragments included, is used to study the excitation functions of the "equatorial" compact hot fusion reaction 244 Pu +48 Ca →292114* (compact orientation angle θc=90° for 244 Pu ). Considering the higher multipole deformations up to hexadecapole deformation β4 and configurations with "compact" orientation θc, the model is shown to give a good description of the measured individual light-particle decay channels σxn, here x=3, 4 and 5, and other decay channels, the fusion-fission σff and quasi-fission σqf (equivalently, capture σ cap ) with in one parameter fitting, the neck length ΔR. The quasi-fission is also considered as a cold process with an elongated "polar" configuration. The xn-channel cross-sections for collisions between nuclei with static deformations at their respective compact orientations are shown to be much more than for the case of the nuclei taken to be spherical, signifying the increase in fusion threshold for an intermediate hot fusion reaction to be associated with the static deformation of the target nucleus and its orientation at the point of collision in its path toward the (spherical) compound nucleus. The shell effects in both the potential and kinetic energy (the mass parameters) terms of the Hamiltonian are shown to be important. The free parameter ΔR of the model is shown to depend strongly on limiting angular momentum, which in turn depends on the use of sticking or non-sticking moment of inertia for angular momentum effects. For the sticking moment of inertia, the evaporation residue (neutron emission) is shown to occur almost promptly (largest ΔR), followed by the competing (hot/cold) quasi-fission and ending finally with fusion-fission of hot compound nucleus. Different ΔR's (equivalently, relative separations) for the three processes means to predict that the processes ER, ff and qf happen in different time-scales, in agreement with the indications of experiments.

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.