Effective density functionals beyond mean field

Abstract

I present a review on non relativistic effective energy-density functionals (EDFs). An introductory part is dedicated to traditional phenomenological functionals employed for mean-field-type applications and to several extensions and implementations that have been suggested over the years to generalize such functionals, up to the most recent ideas. The heart of this review is then focused on density functionals designed for beyond-mean-field models. Examples of these studies are discussed. Starting from these investigations, some illustrations of ab-initio-based or ab-initio-inspired functionals are provided. Constructing functionals by building bridges with ab-initio models represents an extremely challenging and timely objective. This will eventually reduce/eliminate the empirical character of EDFs and link them with the underlying theory of QCD. Conclusions are presented in the last part of the review.

Neutron shell closure at N = 32 and N = 40 in Ar and Ca isotopes

“…The variation of the energy functional given by eq (14) with respect to Dirac spinor ψ(r) leads to RHB (Relativistic Hartree-Bogoliubov) energy density functional as:…”

Turning the nuclear energy density functional method into a proper effective field theory: reflections

“…See refs. [68,69] for a review of these ideas. At this stage these are all worthwhile avenues to pursue; none of them is conclusive as yet.…”

Topology change and nuclear symmetry energy in compact-star matter

“…(3) 0 − af 2 π Tr (ω i ω i ) , (A10) whereâ (3) 0 is the SU (2) part ofâ 0 . After choosing the specific direction of the angular velocity as, for example x-direction, the basic quantities in (A10) an be written as…”

“…The nuclear symmetry energy E sym (n, α) at baryonic density n that appears quadratically in α = (N − P )/(N + P ) in the energy per nucleon E(n, α) where P (N ) is the number of protons (neutrons) in many nucleon systems given by E(n, α) = E(n, α = 0) + E sym (n)α 2 + O(α 4 ) + · · · , (1) plays the most important role in the equation of state (EoS)) for compact-stars [1,2]. In standard nuclear physics approaches (SNPAs) anchored on the effective density functional (EDF) such as the Skyrme potential, relativistic mean field (RMF) and varieties thereof ( [3] for a recent review) and on standard chiral perturbation (SχPT) expansion up to manageable chiral order (e.g., [4]), equipped with a certain number of parameters fit to available empirical data, the E(n, α) can be more or less reliably determined in the vicinity of the nuclear matter equilibrium density n 0 ∼ 0.16 fm −3 . It has also been extended, with a rather broad range of uncertainty, up to slightly above n 0 from heavy-ion collision experiments.…”