Energy dependent ratios of level-density parameters in superheavy nuclei

Abstract

The nuclear level densities and level-density parameters in fissioning nuclei at their saddle points of fission barriers, ${a}_{f}$, as well as those for neutron, ${a}_{n}$, proton, ${a}_{p}$, and $\ensuremath{\alpha}$-particle, ${a}_{\ensuremath{\alpha}}$, emission residues at the ground states are calculated for isotopic chains of superheavy nuclei with $Z$ = 112--120. The calculations are performed with the superfluid formalism using the single-particle energies obtained from the diagonalization of the deformed Woods-Saxon potential. Spectra were generated at global minima of the adiabatic potential energy surfaces, found by the multidimensional minimization method, and at the proper saddle points, found by the ``immersion water flow'' technique on multidimensional energy grids, with allowed reflection and axial symmetry breaking. The influence of shell effects on the energy dependence of the ratios of level-density parameters corresponding to residues of the considered decay modes to those of neutron emission is studied. As shown, in contrast to the ${a}_{f}/{a}_{n}$ ratio, the ${a}_{p}/{a}_{n}$ and ${a}_{\ensuremath{\alpha}}/{a}_{n}$ ratios do not show characteristic maxima depending on the excitation energy of the compound nucleus being formed. In the case of $\ensuremath{\alpha}$ decay, we identified the collective enhancement caused by cluster degrees of freedom as playing quite an important role. The energetic course of the variability of the level-density parameters before reaching the asymptotic value, not taken into account so far, is of great importance for the estimation of the probabilities of de-excitation cascades via light particles emission in competition with fission and, thus, for the determination of the survival probabilities and finally for the total production cross sections of superheavy nuclei.