An important avenue is to enrich the density dependence of the isoscalar and isovector coupling constants, both in the p-h [45,46] and p-p channels [47,48,49]. In particular, as the energy functional is supposed to describe those nuclear features that are related to collective dynamics, it seems important to enrich the density dependence of the effective mass in order to differentiate between its value in the bulk and at the Fermi surface [50,20].

One of the crucial challenges in microscopic theory of nuclear masses is to better understand salient features of the nuclear symmetry energy. The symmetry energy can be extracted directly from the calculated binding energy of finite nuclei, after subtracting shell effects [51]. The goal is to understand connections between the symmetry energy and isoscalar and isovector mean fields, and in particular the influence of effective mass and pair correlations on symmetry energy versus the isospin. Such understanding will allow us to better determine isospin corrections to nuclear mean fields and energy density functionals.

Recently, important indications on how to construct the nuclear energy functional have been obtained within the effective field theory (see, e.g., Refs.[52,53,54]). Even if one still has to readjust and fine-tune the parameters for a precise description of nuclear data, one can gain important insights into the structure of the functional, especially the dependence of the coupling constants on nuclear densities. In addition, the systematic, controlled momentum expansion on which the effective field theory is based offers a way to estimate theoretical errors (see Sec. 4.4).