Sensitivity of the nuclear deformability and fission barriers to the equation of state

The model-dependent analysis of the fission data impacts the extracted fission-related quantities, which are not directly observables, such as the super- and hyperdeformed isomeric states and their energies. We investigated the model dependence of the deformability of a nucleus and its fission barriers on the nuclear equation of state. Within the microscopic–macroscopic model based on a large number of Skyrme nucleon–nucleon interactions, the total energy surfaces and the double-humped fission barrier of ²³⁰Th are calculated in a multidimensional deformation space. In addition to the ground-state (GS) and the superdeformed (SD) minima, all the investigated forces yielded a hyperdeformed (HD) minimum. The contour map of the shell-plus-pairing energy clearly displayed the three minima. We found that the GS binding energy and the deformation energy of the different deformation modes along the fission path increase with the incompressibility coefficient $K_0$, while the fission barrier heights and the excitation energies of the SD and HD modes decrease with it. Conversely, the surface-energy coefficient $a_{surf}$, the symmetry-energy, and its density-slope parameter decrease the GS energy and the deformation energies, but increase the fission barrier heights and the excitation energies. The obtained deformation parameters of the different deformation modes exhibit almost independence on $K_0$, and on the symmetry-energy and its density-slope. The principle deformation parameters of the SD and HD isomeric states tend to decrease with $a_{surf}$.