  The fusion probability in "hot" fusion reactions leading to the synthesis of
super-heavy nuclei is investigated systematically. The quasi-fission barrier
influences the formation of the super-heavy nucleus around the "island of
stability" in addition to the shell correction. Based on the quasi-fission
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 50Ti+249Bk are about 10-150fb at energies around the
entrance-channel Coulomb barrier. For the fusion reactions synthesizing element
120 with projectiles 54Cr and 58Fe, the cross sections fall to a few femtobarns
which seems beyond the limit of the available facilities.
