Self-consistent calculations of fission barriers in the Fm region

Abstract

The fission barriers of the nuclei 254 Fm, 256 Fm, 258 Fm, 258 No, and 260 Rf are investigated in a fully microscopic way up to the scission point. The analysis is based on the constrained Hartree-Fock-Bogoliubov theory and Gogny's D1S force. The quadrupole, octupole, and hexadecapole moments as well as the number of nucleons in the neck region are used as constraints. Two fission paths, corresponding to the bimodal fission, are found. The decrease with isotope mass of the half-life times of heavy Fm isotopes is also explained.

Fission barriers and probabilities of spontaneous fission for elements with Z≥ 100

“…While the fission probability P strongly depends on E 0 the results of calculation will be different from those where one assumes a constant E 0 = 0.5 MeV for all nuclei (see 6 e.g. [56,51]) or quantum mechanically exact values [31]. The values of the ground state energies E 0 calculated from the Eq.…”

“…The goal of the present section is to recalculate the results of previous estimates for HLs taking into account two facts: First, as it was mentioned in many places (see e.g., [51,52] where the rotational moment of inertia -a part of inertia tensor -is discussed), the Inglis cranking mass is too small in comparison to the full ATDHFB one. In this paper, we use the cranking mass but scaled with a factor 1.3 to simulate the ATDHFB mass.…”

“…The most thorough investigation using the D1S Gogny interaction in the axial symmetry regime has been published in [24]. Details of the method are described in [51]. Fission characteristics are determined not only by the height of the fission barrier but also by its shape and localisation in the deformation space.…”

“…The reflection symmetric character of the barriers brings about symmetric fragment mass distribution in this region. The barrier height may be reduced by a few MeV in the whole region if non-axial deformations are included in the calculations [51].…”

“…Mass parameters are usually calculated within perturbative cranking approximation (or Inglis inertia) or adiabatic time dependent HF or HFB model where one differentiates the fields of the model numerically instead ( see, e.g., [78,52,51,31,79,80]). …”