Session LG: Nuclear Theory 3

SeaLL1: A Minimal Nuclear Energy Density Functional

In this talk I shall describe our recently proposed SeaLL1 nuclear energy density functional (NEDF).  SeaLL1 is systematically constructed to contain the minimal number of phenomenological parameters (7), each related to a specific nuclear property.  Despite this minimal nature, it provides remarkable global mass and radius fits, comparable or better than with current state-of-the-art NEDFs that contain often many more parameters.  Despite only being fit to static phenomena, SeaLL1 displays very reasonable dynamical properties such as fission barriers, suggesting a new paradigm for improving nuclear DFT calculations.   

Coulomb Energy Density Functionals for Nuclear Systems

The Coulomb exchange and correlation contributions to the energy density functionals were tested in the context of atomic nuclei \footnote{T. Naito, R. Akashi, and H. Liang. PRC~97,~044319~(2018).}. Both the local density approximation (LDA) and generalized gradient approximation (GGA) functionals were investigated. We employed the experimental nuclear charge density as input. The GGA exchange functionals of electron systems can be applied with practical accuracy to atomic nuclei. In contrast, the correlation functionals of electron systems are not applicable for atomic nuclei. Self-consistent calculation of the GGA exchange functional was also tested \footnote{T. Naito, X. Roca-Maza, G. Col\`{o}, and H. Liang. In Progress.}. In most cases, the GGA exchange functional represents the exact-Fock Coulomb energy while one of the GGA-functional coefficients is changed. This fact is remarkable since the numerical cost of GGA is $O(N^3)$, whereas that cost of exact Hartree-Fock approximation is $O(N^4)$ for the self-consistent calculations.   

Dynamical properties of the SeaLL1 Nuclear Energy Density Functional

Time dependent density functional theory (TDDFT) is currently the preferred method for tackling calculations of dynamic nuclear properties, given a properly formulated energy functional. However, exact calculations in this framework are computationally expensive. In this talk I consider the less expensive orbital free formulation of the recently proposed SeaLL1 nuclear energy density functional (NEDF), a minimal parameter functional. The dynamical properties of this functional will be discussed, such as the giant dipole resonance (GDR); particular attention will be paid to the effects of the entrainment term.   

A Quantum Mechanical Treatment of Nuclear Collective Motion

 In this work, we deal with a quantum mechanical  treatment of  nuclear collective motion. To carry out this study, we invoke the nuclear Born--Oppenheirmer (NBO) method. We focus in particular on a quantum mechanical approach to nuclear rotations. As an illustration, we deal with non-spherical, permanently deformed nuclei; in particular, we study nuclei that are axially-symmetric and even, but with non-closed shells.  Moreover, we look at a quantum mechanical derivation of formal expressions for the energy and for the moment of inertia. Using a mean-field approximation to describe the intrinsic structure, we show that the NBO formalism yields the Thouless-Valantin formula for the moment of inertia. We then show that this moment of inertia increases with angular momentum, in agreement with experimental data. We show that the NBO formalism is well equipped to describe low-lying as well as high-lying rotational states. Finally, we establish a connection between the NBO method and the self-consistent Cranking (SCC) model, which is known to successfully reproduce vast amounts of experimental data ranging from low-lying rotational states to high angular momentum states.   

Superfluid phase transition and effects of pairing fluctuations in neutron star matter at subnuclear densities

We investigate the s-wave superfluidity in asymmetric nuclear matter in the inner crust and the outer core of the neutron stars. Within the framework of diagrammatic strong coupling theory, which can successfully describe the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover realized in ultracold Fermi atomic gases, we clarify effects of strong pairing fluctuations on the critical temperature of the superfluid phase transition under the presence of the effective-range correction and the short-range repulsion for the neutron-neutron interaction. Furthermore, considering a finite proton fraction, we show the effects of the strong neutron-proton interaction on the spin-triplet deuteron condensation, as well as on the spin-singlet dineutron and diproton condensations.  Our microscopic study on the superfluidity in neutron star matter is important for understanding the astrophysical observations of the thermal properties of neutron stars.   

Spin Polarized Phases in Quark Matter: Interplay between Axial-vector and Tensor Mean Fields

The spontaneous spin polarization of strongly interacting matter due to axial-vector and tensor
type interactions is studied at zero temperature and high baryon-number densities. We start with the
mean- field Lagrangian for the axial-vector and tensor interaction channels, and find in the chiral
limit that the spin polarization due to the tensor mean field  takes place first as the density
increases for sufficiently strong coupling constants, and then that due to the axial-vector mean field
emerges in the region of nite tensor mean field.   

Hohenberg-Kohn-theorem-inspired functional renormalization-group analysis of ground and excited states of a one-dimensional nuclear matter

We present the first successful functional renormalization group(FRG)-aided density-functional (DFT) calculation of the equation of state (EOS) and the density-density spectral function of an infinite nuclear matter (NM) in (1+1) dimensions composed of spinless nucleons. The resultant EOS of the NM coincides with that obtained by the Monte-Carlo method within a few percent for the available range of density. We also reproduce a notable feature of the density density spectral function of the non-linear Tomonaga-Luttinger liquid: The spectral function has singularities at the edge of its support at the lower-energy side. Our result demonstrates that the FRG-aided DFT can be as powerful as any other methods in quantum many-body theory.