Systematics of fusion probability in “hot” fusion reactions

Abstract

The fusion probability in ``hot'' fusion reactions leading to the synthesis of superheavy nuclei is investigated systematically. The quasifission barrier influences the formation of the superheavy nucleus around the ``island of stability'' in addition to the shell correction. Based on the quasifission barrier height obtained with the Skyrme energy-density functional, we propose an analytical expression for the description of the fusion probability, with which the measured evaporation residual cross sections can be reproduced acceptably well. Simultaneously, some special fusion reactions for synthesizing new elements 119 and 120 are studied. The predicted evaporation residual cross sections for ${}^{50}$Ti + ${}^{249}$Bk are $\ensuremath{\sim}$10--150 fb at energies around the entrance-channel Coulomb barrier. For the fusion reactions synthesizing element 120 with projectiles ${}^{54}$Cr and ${}^{58}$Fe, the cross sections fall to a few femtobarns, which seems beyond the limit of the available facilities.