Abstract
The dependence of fission barriers on the excitation energy of the compound nucleus impacts the survival probability of superheavy nuclei synthesized in heavy-ion fusion reactions. We study the temperature-dependent fission barriers by means of the self-consistent nuclear density functional theory. The equivalence of isothermal and isentropic descriptions is demonstrated. The effect of the particle gas is found to be negligible in the range of temperatures studied. Calculations have been carried out for ^{264}Fm, ^{272}Ds, ^{278}112, ^{292}114, and ^{312}124. For nuclei around ^{278}112 produced in "cold fusion" reactions, we predict a more rapid decrease of fission barriers with temperature as compared to the nuclei around ^{292}114 synthesized in "hot fusion" experiments. This is explained in terms of the difference between the ground-state and fission-barrier temperatures. Our calculations are consistent with the long survival probabilities of the superheavy elements produced in Dubna with the ^{48}Ca beam.