Density functional theory with spatial-symmetry breaking and configuration mixing

Abstract

This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object. The latter can in turn be factorized as the product of the square of a collective wave function and a normalized collective-coordinate-dependent density. Energy minimization translates into a set of coupled equations, i.e. a local Schrödinger equation for the collective wave function and a set of Kohn-Sham equations for optimizing the normalized density at each point in the collective space. These equations reformulate the many-body problem exactly provided one is able to determine density-and collective-wave-function-dependent terms of the collective mass and potential which play a similar role to the exchange-correlation term in electronic Kohn-Sham density functional theory.PACS numbers: 21.60. De, 21.60.Jz for integer m. The wave function minimizing the energy for this choice of f has Ψ cm ( R) = f ( R). Note that J µ , Eq. (57) is, in this case, the average momentum of the system. This quantity is zero for this state, thus J µ ( R) = 0.(75)

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

“…In this example, the localization decreases by about an order of magnitude the tails of the densities, which will have a sizable impact on the interaction energy. Note that, as expected, the total density is invariant under the unitary transformation (23). Figure 16 shows the nuclear interaction energy betwen the fragments for the three functionals considered in this work as a function of the number of particles in the neck.…”

“…On paper, nuclear density functional theory (DFT) represents an excellent compromise between microscopic content and actual feasibility. In particular, DFT lends itself particularly well to separating nuclear excitations into fast intrinsic and slow collective excitations [23,24]. This distinction is especially useful in the context of low-energy nuclear fission, which has timescales of the order of 10 −19 − 10 −20 seconds, i.e.…”

Uncertainty quantification and propagation in nuclear density functional theory

“…The main difficulty of this strict Kohn-Sham scheme, which is more in line with the spirit of DFT as encountered in electronic structure theory, is to incorporate beyond meanfield correlations accounting, for example, for large amplitude collective motion, or symmetry restoration. Recent work suggests that this could be achieved by introducing new densities representing collective degrees of freedom such as two-body or "collective" densities [46,47,48,49] (which may lead to a generalization of the Kohn-Sham equations) or by adding specific terms to the functional designed to cancel symmetry-breaking [50,51].…”

Fluctuations of collective coordinates and convexity theorems for energy surfaces

“…(12), reads, Tr {[H, X] D}, and vanishes ∀X, because of Eq. (9). Then the first order in dλ gives, again ∀X,…”

“…Ideally, to define mathematically a function e(b) of the collective coordinate, one should first diagonalize B within the space provided by the many-body states available for calculations [9]. The resulting spectrum of B should be continuous, or at least have a high density for that chosen trial space.…”