The energy density functional has the form
The actual form of the nuclear energy functional is unknown. The
strategy adopted by many practitioners is to build a functional around
that generated by the Skyrme interaction. The most general form of the
energy density functional that is quadratic in local densities and
preserves the basic symmetries of the strong interaction, such as
time-reversal symmetry, charge invariance, and proton-neutron symmetry,
has been proposed in Ref. .
In practical applications, however, simplified forms of this functional
have been used. For instance, one particular representation
of the energy functional for the ground states of
even-even nuclei can be written
The p-p energy functional (5) corresponds to a density-dependent delta interaction. Usually, , =0.16 fm, and =0, 1, or 1/2 for volume-, surface-, or mixed-type pairing. In Eq. (4), stands for the Coulomb energy density with the exchange term treated in the Slater approximation.
As seen from Eqs. (4) and (5), typical Skyrme density functionals include about 14 unknown parameters. Some of them are usually adjusted to reproduce the basic properties of the infinite nuclear matter while the remaining coupling constants are fitted to known nuclear masses, radii, and other measured properties.