Towards an ab initio covariant density functional theory for nuclear structure

Abstract

Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided. Summary and Perspectives 521. Introduction Brief introduction on nuclear theoryThe discoveries of radioactivity by Becquerel [1] and the Curies [2, 3] and the existence of a compact nucleus at the center of an atom by Rutherford et al. [4] opened the door of nuclear physics. During the hundred years of development in nuclear physics, there emerged several significant milestones, including the discovery of the neutron by Chadwick [5] which verified the composition of the nucleus as protons and neutrons, the meson-exchange theory for the strong interaction between nucleons by Yukawa [6], the independent-particle shell model of the nucleus by Goeppert-Mayer [7], Haxel, Jensen, and Suess [8], and the collective Hamiltonian for nuclear rotation and vibration by Rainwater [9], Bohr and Mottelson [10,11], etc.With the understanding of the composition of a nucleus as protons and neutrons [5] and the meson-exchange theory for the strong interaction between the nucleons [6], nuclear physicists hoped to describe the nucleus, a quantum many-body system, from the underlying nucleon-nucleon interaction. Euler, a student of Heisenberg, assumed the nuclear force as a two-body (2N) interaction with a Gaussian shape and calculated the infinite nuclear system, i.e., homogeneous nuclear matter, using second-order perturbation theory [12]. However, the strong repulsive core of the realistic nuclear force [13] prevents the application of perturbation theory.On the other hand, the nuclear structure model with a phenomenological mean field achieved great success. Goeppert-Mayer [7], Haxel, Jensen, and Suess [8] introduced a strong spin-orbit potential and proposed the nuclear independentparticle shell model that successfully explained the conventional magic numbers in nuclei. Rainwater [9], Bohr and Mottelson [10, 11] explored the nuclear deformation and proposed the nuclear collective mode...

Relativistic density functional theory in nuclear physics

“…Taken from Ref. [6] and RBHF, it reveals that the self-consistency is important to improve the description. Certain rearrangement effects brought by adopting renormalized occupation probabilities in RBHF may further improve the description for finite nuclei, especially for the radii.…”

“…This is clearly seen in the non-relativistic reduction of CDFT via a similarity renormalization method, which provides a possible means to bridge the relativistic and non-relativistic DFTs [5]. As a result, the relativistic framework can provide a good description of nuclear matter and finite nuclei using the Brueckner techniques with only the two-nucleon bare interactions [6]. In the non-relativistic framework, however, three-nucleon interactions, which are still very uncertain, have to be introduced for a reasonable description of nuclear matter and/or finite nuclei.…”

Relativistic Brueckner-Hartree-Fock Theory in Infinite Nuclear Matter

“…(6), which occurs also in the non-relativistic case (see for instance Refs. [6,45]), there are eigenstates of the Dirac operator in Eq. (5) with positive energies (PES) and those with negative energies (NES) and it is evident that one needs for the solution of the relativistic Hartree-Fock problem in Eqs.…”

“…In recent years, microscopic theories of the nuclear manybody problem, starting with the bare nucleon-nucleon forces, showed considerable progress in describing the properties of light and even specific medium-heavy nuclei [1][2][3][4][5][6]. However, the largest part of the nuclear chart is still only accessible in energy density functional (EDF) theories [7] which are based on the mean-field concept.…”

Nuclear density functional theory

“…Chiral NN potentials can at present be tested against the nuclear phenomenology by using many-body methods that, albeit approximate, have control on the nature and the quantitative impact of the approximations, and can in principle be improved up to exact results, as we mentioned at the start of this Section. These methods include Quantum Monte Carlo (QMC) approaches [36,37], the In-Medium Similarity Renormalization Group (IM-SRG) method [38], the Coupled Cluster (CC) approach [39], the Self-Consistent Green's Function Theory (SCGFT) [40], nonrelativistic and covariant Brueckner-Hartree-Fock (BHF) theory [41], and the No-Core Shell Model [42].…”