The EDF methods are presently very intensely studied and developed in nuclear physics. Apart from the subjects covered in the present short review, there is a number of topics that could not be discussed here, such as: formal aspects of the DFT for self-bound systems; symmetry breaking effects; ab initio derivation of the EDF from the chiral perturbation and Brueckner-Hartree-Fock theories; studies of weakly-bound systems and the continuum phase-space effects; functionals non-local in time and the adiabatic connection; new-generation functionals with higher-order derivatives and/or richer density dependencies; self-interactions and self-pairing in the EDF; and ambiguities and inconsistencies when extending the EDF methods to multi-reference applications.
Moreover, there are several aspects related to the methodology that were not covered here, such as: the EDF methods based on natural occupation numbers and/or orbitals; second, extended, and/or self-consistent (Q)RPA methods; proton-neutron interactions and isovector terms in the EDF; extrapolations to exotic nuclei and astrophysical applications; equation of state, symmetry energy, and neutron stars; relations between functionals describing infinite systems and finite nuclei; and adjustments of parameters, confidence intervals, and correlations.
There is also a number of other interesting applications of the nuclear EDF methods, such as: description of tensor effects and the spin-orbit splitting; functionals describing pairing correlations; particle-vibration coupling, single-particle spectra, and widths of giant resonances; fusion barriers and cross sections within static and time-dependent calculations; fermion systems in the unitary regime; neutron skins and pygmy resonances; time-odd terms versus spin and orbital M1 resonances, spin-isospin resonances, and particle-vibration coupling and polarization; incompressibility, effective mass, and monopole resonances; cluster structures and models; chirality in rotational bands; di-neutron correlations and deformation in nuclear halos; and Coulomb frustration effects in the superheavy nuclei and crust of neutron stars.
In general, the EDF methods provide us with universal understanding of global low-energy nuclear properties and feature an impressive array of applications. These methods can be rooted in the effective-theory approach whereupon the low-energy phenomena can be successfully modeled without resolving high-energy properties. Further progress strongly relies upon the use of high-power computing and faces the challenge of working out a consistent scheme of consecutive corrections that would allow for the increased precision and predictive power.
During preparation of this talk, I have received suggestions and
comments from very many of my colleagues; I would
like to thank them very much for their help. In particular, I would
like to thank:
Michael Bender,
Karim Bennaceur,
George Bertsch,
Aurel Bulgac,
Rick Casten,
Willem Dickhoff,
Jerzy Dudek,
Nguyen Van Giai,
Bertrand Giraud,
Elvira Moya de Guerra,
Paul-Henri Heenen,
Morten Hjorth-Jensen,
Pieter Van Isacker,
Jan Kvasil,
Denis Lacroix,
Elena Litvinova,
Jérôme Margueron,
Joachim Maruhn,
Jie Meng,
Witek Nazarewicz,
Thomas Papenbrock,
Michael Pearson,
Jorge Piekarewicz,
Nathalie Pillet,
Marek P
oszajczak,
Paul-Gerhard Reinhard,
Peter Ring,
Wojciech Satua,
Paul Stevenson,
Sait Umar,
James Vary, and
Dario Vretenar.
This work was supported by the Academy of Finland and University of Jyväskylä within the FIDIPRO program, by the Polish Ministry of Science and Higher Education under Contract No. N N 202 328234, and by the U.S. Department of Energy under Contract No. DE-FC02-09ER41583 (UNEDF SciDAC Collaboration).