Fission barriers at the end of the chart of the nuclides

Abstract

We present calculated fission-barrier heights for 5239 nuclides, for all nuclei between the proton and neutron drip lines with 171 ≤ A ≤ 330. The barriers are calculated in the macroscopicmicroscopic finite-range liquid-drop model (FRLDM) with a 2002 set of macroscopic-model parameters. The saddle-point energies are determined from potential-energy surfaces based on more than five million different shapes, defined by five deformation parameters in the threequadratic-surface shape parameterization: elongation, neck diameter, left-fragment spheroidal deformation, right-fragment spheroidal deformation, and nascent-fragment mass asymmetry. The energy of the ground state is determined by calculating the lowest-energy configuration in both the Nilsson perturbed-spheroid (ǫ) and in the spherical-harmonic (β) parameterizations, including axially asymmetric deformations. The lower of the two results (correcting for zero-point motion) is defined as the ground-state energy. The effect of axial asymmetry on the inner barrier peak is calculated in the (ǫ, γ) parameterization. We have earlier benchmarked our calculated barrier heights to experimentally extracted barrier parameters and found average agreement to about one MeV for known data across the nuclear chart. Here we do additional benchmarks and investigate the qualitative, and when possible, quantitative agreement and/or consistency with data on β-delayed fission, isotope generation along prompt-neutron-capture chains in nuclear-weapons tests, and superheavy-element stability. These studies all indicate that the model is realistic at considerable distances in Z and N from the region of nuclei where its parameters were determined.

Adiabatic fission barriers in superheavy nuclei

“…Since, as it was discussed previously, the inclusion of traxiality is absolutely necessary in the SH region, we have chosen only models which take this into account. In fact, there is only one systematic calculation, including triaxiality and odd-particle-number nuclei -the Finite Range Liquid Drop Model [13,60,64] The first conclusion from the comparison between our results and those of FRLDM is that a conspicuous barrier staggering between odd-and even-particle number nuclei is obtained in the Woods-Saxon model. As mentioned before, this results from the blocking treatment of pairing.…”

“…23, for Flerovium isotopes the barriers calculated here are in agreement with the experimental (empirical) estimates [61] and with the selfconsistent calculations [62] based on the SKM* interaction. The FRLDM [64] overestimates these quasiempirical barriers [61] significantly. Although only the lower limit for the barrier height has been estimated in [61], which would reproduce the known cross sections on the picobarn level, such a high barrier seems problematic, see discussion in [65,66].…”

Dynamical effects in fission investigated at high excitation energy

“…The timedependent formulation of this model using a Fokker-Planck equation with a dissipative term describing the coupling between the collective and singleparticle degrees of freedom was introduced by Grangé and collaborators [6]. An analogue formulation is the one based on the Langevin equation [2] or as a random walk, in the limit of strong dissipative coupling [7], on a multidimensional macroscopic-microscopic potential energy surface [8].…”

Recent Achievements In Fission Dynamics Investigated At High Energies

“…The time-dependent formulation of this model, using a Fokker-Planck equation with a dissipative term describing the coupling between the collective and single-particle degrees of freedom, was introduced by Grangé and collaborators [4]. Analogue formulations make use of the Langevin equation [5] or the random walk algorithm, in the limit of strong dissipative coupling [6], on a multidimensional macroscopic-microscopic potential energy surface [7].…”