Examining the entrance channel effects on the synthesis of the double deformed nucleus Hs270 : A theoretical study using the dynamical cluster-decay model including Skyrme forces

Abstract

The fusion evaporation residue cross sections ${\ensuremath{\sigma}}_{xn}$ for the decay of the compound nucleus (CN) $^{274}\mathrm{Hs}^{*}$ via $3n$- to $5n$-decay channels, synthesized in $^{248}\mathrm{Cm}+^{26}\mathrm{Mg}, ^{238}\mathrm{U}+^{36}\mathrm{S}$, and $^{226}\mathrm{Ra}+^{48}\mathrm{Ca}$ reactions, are studied including deformations ${\ensuremath{\beta}}_{2i}$ for compact hot orientations ${\ensuremath{\theta}}_{i}$ at various excitation energies of ${E}^{*}=40$ to 51 MeV, which support symmetric fission, in agreement with experiments. For the nuclear interaction potentials, we use the Skyrme energy density functional based on the semiclassical extended Thomas-Fermi approach, which means an extension of our earlier study of excitation functions of $^{248}\mathrm{Cm}+^{26}\mathrm{Mg}, ^{238}\mathrm{U}+^{36}\mathrm{S}$, and $^{226}\mathrm{Ra}+^{48}\mathrm{Ca}$ reactions, based on the dynamical cluster-decay model (DCM). In the present work the above reactions have been investigated by using a hot compact configuration. The Skyrme forces used here are the conventional SIII and the newer GSkI and KDE0(v1) given for both normal and isospin-rich nuclei, with densities added in the frozen density approximation. Interestingly, with the inclusion of both conventional and new Skyrme forces, the DCM gives an excellent fit within one parameter fitting of $\mathrm{\ensuremath{\Delta}}R$ to the measured data on the fusion evaporation residue for all three incoming channels at the energy range ${E}^{*}=40$ to 51 MeV, independent of the entrance channel and the Skyrme force used. The possible fusion-fission and quasifission mass-regions of fragments on the DCM are also predicted. The DCM with Skyrme forces is further used to look for all the possible target-projectile combinations forming the ``cold'' CN $^{274}\mathrm{Hs}^{*}$ at the CN excitation energy of ${E}^{*}$ for ``hot compact'' configurations. The role of magic shells is shown in enhancing the evaporation residue cross sections, not only for the entrance channel $^{226}\mathrm{Ra}+^{48}\mathrm{Ca}$ but also for the residue $^{270}\mathrm{Hs}$, compared to its neighboring isotopes ${}^{269\ensuremath{-}271}\mathrm{Hs}$. The fusion evaporation residue cross sections for the proposed new reactions in synthesizing the CN $^{274}\mathrm{Hs}^{*}$ are also estimated for future experiments.