Nuclear Energy Density Functional

A theoretical framework aiming at the microscopic description of nuclear masses and capable of extrapolating into an unknown territory must fulfill several strict requirements. First, it must be general enough to be confidently applied to a region of the nuclear landscape whose properties are largely unknown. Second, it should be capable of handling symmetry-breaking effects resulting in a large variety of intrinsic nuclear deformations. Thirdly, it should describe finite nuclei and the bulk nuclear matter. Finally, in addition to observables, the method should provide associated error bars.

These requirements are met by the DFT in the formulation of Kohn and Sham [7]. The main ingredient of the non-relativistic nuclear DFT [8] (for relativistic nuclear DFT, see Ref. [9]) is the energy density functional that depends on densities and currents representing distributions of nucleonic matter, spins, momentum, and kinetic energy, as well as their derivatives (gradient terms). Standard Skyrme functionals employed in self-consistent mean-field calculations are parametrized by means of about ten coupling constants that are adjusted to basic properties of nuclear matter (e.g., saturation density, binding energy per nucleon) and to selected data on magic nuclei. The functionals are augmented by the pairing term which describes nuclear superfluidity [10]. When not corrected by additional phenomenological terms, standard functionals reproduce total binding energies with an rms error of the order of 2 to 4 MeV [11,12,13]. However, they have been successfully tested over the whole nuclear chart to a broad range of phenomena, and usually perform quite well when applied to energy differences, radii, and nuclear moments and deformations [8].

Historically, the first nuclear energy density functionals appeared in the context of Hartree-Fock (HF) or HFB methods and zero-range interactions such as the Skyrme force. However, it was realized afterwards that - in the spirit of the DFT - an effective interaction could be secondary to the functional, i.e., it is the density functional that defines the force. This is the strategy that we are going to follow.