Microscopic Determinations of Fission Barriers (Mean-Field and Beyond)

Abstract

With a help of the selfconsistent Hartree-Fock-Bogoliubov (HFB) approach with the D1S effective Gogny interaction and the Generator Coordinate Method (GCM) we incorporate the transverse collective vibrations to the one-dimensional model of the fission-barrier penetrability based on the traditional WKB method. The average fission barrier corresponding to the least-energy path in the two-dimensional potential energy landscape as function of quadrupole and octupole degrees of freedom is modified by the influence of the transverse collective vibrations along the nuclear path to fission. The set of transverse vibrational states built in the fission valley corresponding to a successively increasing nuclear elongation produces the new energy barrier which is compared with the least-energy barrier. These collective states are given as the eigensolutions of the GCM purely vibrational Hamiltonian. In addition, the influence of the collective inertia on the fission properties is displayed, and it turns out to be the decisive condition for the possible transitions between different fission valleys.

Finite Element Method for Solving the Collective Nuclear Model with Tetrahedral Symmetry

“…The mass tensor B ij (x 1 , x 2 ) has been calculated [9] in the terms of the average nuclear deformations x = (x 1 , x 2 ) = (q 20 , q 32 ) determine in [15], and shown in Fig. 1a-d.…”

Microscopic structure inputs for reaction models of fission

“…As discussed in [2] the least action approach to fission path is well-suited to study the problem of transitions between various energy valleys separated from each other by a relatively low energy barrier and corresponding to different fission modes.…”

“…We present here some recent results obtained for fission barriers [2] and shape isomers partial γ-back decay and fission lifetimes [3]. Calculations have been performed using the D1S Gogny force and the Generator Coordinate Method Approach with the Gaussian Overlap Approximation based on Constrained-Hartree-Fock-Bogoliubov states.…”