Synthesis of the doubly magic deformed nucleus108270Hs162in the decay of274Hs*formed via hot fusion reactions: Entrance-channel effects and role of magicity of48Ca and270Hs

Abstract

Quantum mechanical fragmentation theory (QMFT) is used to look for all possible target-projectile (t,p) combinations forming the ``cold'' compound nucleus (CN) ${}^{274}$Hs${}^{*}$ at the CN excitation energy ${E}^{*}$ of ``hot, compact'' configuration. The predicted reactions, referring to potential energy minima, include all the three reactions ${}^{248}$Cm + ${}^{26}$Mg, ${}^{238}$U + ${}^{36}$S, and ${}^{226}$Ra + ${}^{48}$Ca already used in experiments, and a few more. The optimum ``cold'' and ``compact'' (t,p) combination, corresponding to lowest interaction barrier and smallest interaction radius, is one with largest mass asymmetry, but because of the doubly magic ${}^{48}$Ca nucleus, the evaporation residue cross sections for the ${}^{226}$Ra + ${}^{48}$Ca reaction are shown to be further enhanced. For the decay of CN ${}^{274}$Hs${}^{*}$, synthesizing ${}^{269--271}$Hs via 3$n$--5$n$ emission, we use the dynamical cluster-decay model (DCM) with effects of quadrupole deformations and ``hot'' compact orientations included in it, which support symmetric fission, in agreement with experiments. The fusion evaporation residue cross sections ${\ensuremath{\sigma}}_{xn}$, for $x=3$, 4, and 5 neutrons emission from the above-mentioned three entrance channels, are calculated within one parameter fitting, namely, the neck length. For best fitted neck-length parameter, the roles of entrance channel and that of magic shells are analyzed. In spite of different entrance channels resulting in different evaporation residue cross sections, the neck-length parameter at a given ${E}^{*}$ is shown to be independent of the entrance channel. The role of magic shells is shown in enhancing evaporation residue cross sections, not only for the entrance channel ${}^{226}$Ra + ${}^{48}$Ca, but also for the residue ${}^{270}$Hs, compared to its neighboring isotopes ${}^{269,271}$Hs. The fusion evaporation residue cross sections for the proposed new reactions, in synthesizing CN ${}^{274}$Hs${}^{*}$, are also estimated for future new experiments.