Description of induced nuclear fission with Skyrme energy functionals: Static potential energy surfaces and fission fragment properties

Abstract

Eighty years after its experimental discovery, a description of induced nuclear fission based solely on the interactions between neutrons and protons and quantum many-body methods still poses formidable challenges. The goal of this paper is to contribute to the development of a predictive microscopic framework for the accurate calculation of static properties of fission fragments for hot fission and thermal or slow neutrons. To this end, we focus on the 239 Pu(n,f) reaction and employ nuclear density functional theory with Skyrme energy densities. Potential energy surfaces are computed at the Hartree-Fock-Bogoliubov approximation with up to five collective variables. We find that the triaxial degree of freedom plays an important role, both near the fission barrier and at scission. The impact of the parameterization of the Skyrme energy density and the role of pairing correlations on deformation properties from the ground-state up to scission are also quantified. We introduce a general template for the quantitative description of fission fragment properties. It is based on the careful analysis of scission configurations, using both advanced topological methods and recently proposed quantum many-body techniques. We conclude that an accurate prediction of fission fragment properties at low incident neutron energies, although technologically demanding, should be within the reach of current nuclear density functional theory.

Fission fragment charge and mass distributions inPu239(n,f)in the adiabatic nuclear energy density functional theory

“…At scission, the fragments are still strongly entangled. This point was first mentioned in [53], where a technique to disentangle the fragments based on a unitary transformation of the quasi-particles was introduced; see also [42] for details. If this operation is not performed, we can expect exchanges of nucleons between the two pre-fragments and therefore a broadening of the raw fission yields.…”

“…It is well-known that triaxiality plays a major role in the low deformation region of the PES and especially on the inner barrier height [26,28,42,[63][64][65][66][67]. To estimate its effect on the dynamics, we compare the wave packet propagation for the SkM* EDF based on two PES computed with and without breaking axial symmetry.…”

“…In the case of the Skyrme EDF calculations, the pairing channel is modeled by a density-dependent surface-volume potential characterized by two pairing strengths, one for neutrons and one for protons. These pairing strengths are adjusted on the local three-point odd-even mass difference indicator in 240 Pu; details are given in [42]. As customary for calculations with the Gogny EDF, the same parametrization of the Gogny force is used in both particle-hole and particle-particle channels.…”

“…In practice, the fragment mass number at any point of the frontier is calculated as the integral of the nuclear density on one side of the neck [42]. This procedure produces non integer values.…”

“…We recall that in HFODD basis states are characterized by the Cartesian frequencies ω x , ω y and ω z ; the equivalent spherical frequency ω 0 = (ω x ω y ω z ) 1/3 and the (here, axial) basis deformation ω z /ω x are parametrized as a function of the quadrupole moment according to the formulas given in [42]. In the pairing channel, the usual cut-off in the quasi-particle space is set at E cut = 60 MeV for calculations with surface-volume pairing.…”