Pairing-induced speedup of nuclear spontaneous fission

Abstract

Background: Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes.Purpose: To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of 264 Fm and 240 Pu using the state-of-the-art self-consistent framework. Methods:We employ the superfluid nuclear density functional theory with the Skyrme energy density functional SkM * and a density-dependent pairing interaction. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates.Results: Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of 264 Fm, where the effect of triaxiality on the fission barrier is large, the geometry of fission pathway in the space of shape degrees of freedom is weakly impacted by pairing. This is not the case for 240 Pu where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory. Conclusions:The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom.PACS numbers: 24.75.+i, 25.85.Ca, 21.60.Jz, 21.30.Fe, 27.90.+b Introduction -Nuclear fission is a fundamental phenomenon that is a splendid example of a large-amplitude collective motion of a system in presence of many-body tunneling. The corresponding equations involve potential, dissipative, and inertial terms [1]. The individualparticle motion gives rise to shell effects that influence the fission barriers and shapes on the way to fission, and also strongly impact the inertia tensor through the crossings of single-particle levels and resulting configuration changes [2][3][4]. The residual interaction between crossing configurations is strongly affected by nucleonic pairing: the larger pairing gap ∆ the more adiabatic is the collective motion [5][6][7][8][9].

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].…”

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

“…As for init , we verified that going from 1.10 −12 to 1.10 −14 impacts the fission yields by a maximum of 2.10 −6 % only. The convergence with respect to the space and time parameters was checked by performing series of calculations in the vicinity of the set (32). For each parameter, we explored a wide range of values while the other one remained unchanged.…”

“…In practice, this can be very effectively achieved by introducing a small set of collective variables such as multipole moments, pairing fields, etc., and precalculating the potential energy surface of the nucleus as a function of these variables. This strategy has proven especially fruitful to compute spontaneous fission halflives through simple multi-dimensional quantum tunneling [2,7,[26][27][28][29][30][31][32]. As we will show in this work, it is also the ideal framework to compute charge and mass distributions.…”