Spontaneous fission lifetimes from the minimization of self-consistent collective action

Abstract

The spontaneous fission lifetime of 264 Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the non-perturbative mass parameters, the dynamic fission pathway becomes strongly triaxial and it approaches the static fission valley. On the other hand, when the standard perturbative cranking inertia tensor is used, axial symmetry is restored along the path to fission; an effect that is an artifact of the approximation used. Introduction.-The spontaneous fission (SF) of a nucleus plays important role in many areas of science and applications [1][2][3]. In particular, it determines the stability of the heaviest and superheavy elements [4,5] and it impacts the formation of heavy elements at the final stages of the r-process through the recycling mechanism [6][7][8]. Therefore, a capability of theory to predict SF lifetimes in a reliable way is essential.The main ingredients for a theoretical determination of SF lifetimes are the collective potential and inertia tensor. For heavy systems, these quantities can be calculated by using the self-consistent mean field theory based on the energy density functional [9]. The potential energy surface (PES) is obtained by solving constrained HartreeFock-Bogoliubov equations (HFB) in a multidimensional space of collective coordinates. The collective inertia (or mass) tensor is obtained from the self-consistent densities by employing the adiabatic time-dependent HFB approximation (ATDHFB) [10][11][12]. Since SF is a quantummechanical tunneling process and the fission barriers are usually both high and wide, the SF lifetime is obtained semi-classically by minimizing the fission action integral in the collective space.The main objective of this work is to study SF by combining the microscopic density functional input with the sophisticated action minimization techniques. We demonstrate that the predicted SF pathway strongly depends on the choice of the collective inertia. In particular, in the commonly used perturbative cranking approximation, the variations of mass parameters due to level crossings (configuration changes) are underestimated; this re-

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

“…As it was shown years ago [88,89] and also in recent publications [29,30,68,90] the minimisation of the reduced action integral instead of the potential energy leads to larger fission probabilities or equivalently to shorter fission HLs. The latter are generally reduced by one to two orders of magnitude in comparison to statically calculated HLs.…”

“…The dynamic treatment of some internal degrees of freedom like e.g., pairing gap (see [91] and the very recent paper [70]) or particle number fluctuation parameter λ 2 in Lipkin-Nogami pairing model [68,29,30] seems to be more significant than a similar treatment of space-type deformation coordinates described above. While the latter is already well known to be similar for all instances the former depends on the considered nucleus.…”

“…Since then substantial progress has been made in the development of models and methods especially by Lublin-Madrid collaboration [23,24], LublinOak Ridge-Warsaw group [25,26,27,28,29,30], and Erlangen-Darmstadt team [31] -energy density functional (EDF) HFB approaches -and in the MM model by the Warsaw [32,33,34], Los Alamos school [35] and the relativistic mean-field (RMF) [36].…”

Pairing-induced speedup of nuclear spontaneous fission

“…The important milestone was a recent paper [19], which demonstrated that predicted SF pathways strongly depend on the choice of the collective inertia and approximations involved in treating level crossings. The main objective of the present work is to elucidate the role of nucleonic pairing on SF by studying the dynamic fission trajectories of 264 Fm and 240 Pu in a four-dimensional collective space.…”

“…[19]. In the semi-classical approximation, the SF half-life can be written as [23,24] T 1/2 = ln 2/(nP ), where n is the number of assaults on the fission barrier per unit time (here we adopt the standard value of n = 10 20.38 s −1 ) and P = 1/(1 + e 2S ) is the penetration probability expressed in terms of the fission action integral,…”