Formation of superheavy elements 119 and 120 in the ${}^{50}$Ti+${}^{249}$Bk and ${}^{50}$Ti+${}^{249}$Cf reactions: dinuclear system dynamics, survival probability, and decay chains of the evaporation residues

Abstract

The ${}^{50}$Ti+${}^{249}$Bk and ${}^{50}$Ti+${}^{249}$Cf reactions leading to the compound nuclei ${}^{299}$119 and ${}^{299}$120 are studied in the framework of the dinuclear system (DNS) model. The capture cross section has been calculated by solving the dynamical equations of motion for all orientation angles of the deformed target nucleus and for the zero-point vibrations of the projectile. The charge distribution of the DNS fragments has been obtained from the transport master equation with transition rates obeying detailed balance, and the compound nucleus formation probability has been calculated as the branching ratio of the level densities over the intrinsic fusion, quasifission, and symmetry barriers. The survival probability has been calculated in the Hauser-Feshbach formalism for every excitation energy and angular momentum of the compound nucleus, with the fission barriers of the macroscopic-microscopic model with triaxial saddle points. The normalization of the saddle-point level density has been fixed by the measured evaporation residue (ER) cross sections of the ${}^{48}$Ca+${}^{244}$Pu reaction. The largest ER cross sections are obtained in the 3n channel, 18 fb at $E_{\mathrm{CN}}^{\ast }=32$ MeV for ${}^{50}$Ti+${}^{249}$Cf and 27 fb at 33 MeV for ${}^{50}$Ti+${}^{249}$Bk. At the energy of the GSI experiments, the calculated sums of the 3n and 4n cross sections, 4 and 6 fb, respectively, are well below the upper limits of 200 and 65 fb obtained there. With the normalization refitted, the alternative mass tables and fission barriers considered here give the maximum 3n cross sections smaller by up to a factor of 25. The $\alpha$-decay chains of the residues have been predicted; the isotopes of element 120 are expected to have half-lives of 1-12 $\mu$s and those of element 119 of 16-230 $\mu$s.

arXiv comment22 pages, 8 figures, 8 tables