Physics of even-even superheavy nuclei with $96 < Z < 110$ in the Quark-Meson-Coupling Model

The quark-meson-coupling (QMC) model has been applied to the study of the properties of even-even superheavy nuclei with 96 <= Z <= 110, over a wide range of neutron numbers. The aim is to identify the deformed shell gaps at N = 152 and N = 162, predicted in macroscopic-microscopic (macro-micro) models, in a model based on the mean-field Hartree-Fock+BCS approximation. The predictive power of the model has been tested on proton and neutron spherical shell gaps in light doubly closed (sub) shell nuclei Ca-40, Ca-48, Ni-56, Ni-56, Ni-78, Zr-90, Sn-100, Sn-132, Gd-146, and Pb-208, with results in a full agreement with experiment. In the superheavy region, the ground-state binding energies of 98 <= Z <= 110 and 146 <= N <= 160 differ, in the majority of cases, from the measured values by less than +/- 2.5 MeV, with the deviation decreasing with increasing Z and N. The axial quadrupole deformation parameter, beta(2), calculated over the range of neutron numbers 138 <= N <= 184, revealed a prolate-oblate coexistence and shape transition around N = 168, followed by an oblate-spherical transition towards the expected N = 184 shell closure in Cm, Cf, Fm, and No. The closure is not predicted in Rf, Sg, Hs, and Ds as another shape transition to a highly deformed (beta(2) approximate to 0.4) shape in Sg, Hs, and Ds for N > 178 appears, while (288)Rf (N = 184) remains oblate. The bulk properties predicted by QMC, such as ground-state binding energy, two-neutron separation energy, the empirical shell-gap parameter delta(2n) and Q(alpha) values, are found to have a limited sensitivity to the deformed shell gaps at N = 152 and 162. However, the evolution of the neutron single-particle spectra with 0 <= beta(2) <= 0.55 of Cm-244, Cf-248, Fm-252, No-256, (260)Rf, (264)Sg, (268)Hs, and (272)Ds, as representative examples, gives a (model-dependent) evidence for the location and size of the N = 152 and 162 gaps as a function of Z and N. In addition, the neutron number dependence of neutron pairing energies provides supporting indication for existence of the energy gaps. Based on these results, the mean-field QMC and macro-micro models and their predictions of deformed shell structure of superheavy nuclei are compared. Clearly the QMC model does not give results as close to the experiment as the macro-micro models. However, considering that it has only four global variable parameters (plus two parameters of the pairing potential), with no local adjustments, the results are promising.