Adiabatic fission barriers in superheavy nuclei

Abstract

Using the microscopic-macroscopic model based on the deformed Woods-Saxon single-particle potential and the Yukawa-plus-exponential macroscopic energy we calculated static fission barriers B f for 1305 heavy and superheavy nuclei 98 ≤ Z ≤ 126, including even -even, odd -even, evenodd and odd -odd systems. For odd and odd-odd nuclei, adiabatic potential energy surfaces were calculated by a minimization over configurations with one blocked neutron or/and proton on a level from the 10-th below to the 10-th above the Fermi level. The parameters of the model that have been fixed previously by a fit to masses of even-even heavy nuclei were kept unchanged. A search for saddle points has been performed by the "Imaginary Water Flow" method on a basic five-dimensional deformation grid, including triaxiality. Two auxiliary grids were used for checking the effects of the mass asymmetry and hexadecapole non-axiallity. The ground states were found by energy minimization over configurations and deformations. We find that the non-axiallity significantly changes first and second fission barrier in many nuclei. The effect of the mass -asymmetry, known to lower the second, very deformed barriers in actinides, in the heaviest nuclei appears at the less deformed saddles in more than 100 nuclei. It happens for those saddles in which the triaxiallity does not play any role, what suggests a decoupling between effects of the mass-asymmetry and triaxiality. We studied also the influence of the pairing interaction strength on the staggering of B f for oddand even-particle numbers. Finally, we provide a comparison of our results with other theoretical fission barrier evaluations and with available experimental estimates.

Static fission properties of actinide nuclei

“…To find the first saddles on such a giant gird we used the imaginary water flow method, (see e.g. [4,10]). It is worth mentioning that for all those saddles we carried out an additional test of their stability against massasymmetry.…”

“…Using such an approach based on a deformed Woods-Saxon single -particle potential [2] and the Yukawa-plusexponential macroscopic energy [3] we have recently [4] systematically calculated static fission barrier heights B f for 1305 heavy and SH nuclei beyond berkelium, including even-even, odd-even, even-odd and odd-odd systems. In this paper we report a similar study for actinide nuclei for which experimental fission data are available.…”

Shape isomers in Pt, Hg and Pb isotopes with $${\hbox {N}}\le 126$$

“…Ref. [27]), but turns out to be very slowly converging at large nuclear elongations (as shown in Refs. [11,12,28]).…”

Effect of non-axial octupole shapes in heavy and superheavy nuclei

“…potential, the pairing strength, and the macroscopic energy, are equal to those used previously in the calculations of masses [31] and fission barriers [32][33][34] in actinides and the heaviest nuclei. In particular, we took the "universal set" of potential parameters and the pairing strengths G n = (17.67 − 13.11 · I)/A for neutrons, G p = (13.40 + 44.89 · I)/A for protons (I = (N − Z)/A).…”

“…One has to notice though, that the presented picture involves the minimization over other deformations, while finding the height of the saddle would require another method, like, for example, the imaginary water flow (e.g. [34,35]), applied in the whole deformation hypercube.…”