Theoretical study of evaporation-residue cross sections of superheavy nuclei
Abstract
Based on the empirical coupled-channel model for calculating capture cross section and the statistical model for calculating survival probability, we propose an analytical formula for describing the fusion probability. The cold-fusion and hot-fusion reactions leading to superheavy nuclei have been systematically investigated. For both the cold-fusion and hot-fusion reactions, the measured evaporation-residual (ER) cross sections can be reproduced acceptably well by using the formula with the same parameter set. Simultaneously, the ER cross sections for some reactions producing elements $Z=\phantom{\rule{2pt}{0ex}}119$ and 120 are studied. It is found that the projectile-target combinations $^{50}\mathrm{Ti}$ $+$ $^{249}\mathrm{Bk}$ and $^{50}\mathrm{Ti}$ $+$ $^{249,251}\mathrm{Cf}$ are considered as the most promising reactions for the syntheses of the next two superheavy elements beyond Og. The maximal ER cross section for $^{50}\mathrm{Ti}$ $+$ $^{249}\mathrm{Bk}$ is 48.2 fb at the incident energy ${E}_{\mathrm{c}.\mathrm{m}.}$ = 226 MeV. For $^{50}\mathrm{Ti}$ $+$ $^{249,251}\mathrm{Cf}$, the maximal ER cross section is about 10 fb at the incident energies around ${E}_{\mathrm{c}.\mathrm{m}.}=232$ MeV.