Localization and clustering in the nuclear Fermi liquid

Using the framework of nuclear energy density functionals we examine the conditions for single-nucleon localization and formation of cluster structures in finite nuclei. We propose to characterize localization by the ratio of the dispersion of single-nucleon wave functions to the average internucleon distance. This parameter generally increases with mass and describes the gradual transition from a hybrid phase in light nuclei, characterized by the spatial localization of individual nucleon states that leads to the formation of cluster structures, toward the Fermi liquid phase in heavier nuclei. Values of the localization parameter that correspond to a crystal phase cannot occur in finite nuclei. Typical length and energy scales in nuclei allow the formation of liquid drops, clusters, and halo structures.

Figure 1

The localization parameter $\alpha$ [Eq. (8)] as a function of the number of nucleons (solid line). The average values of $\alpha$ for ${}^{16}$O ${}^{20}$Ne, ${}^{24}$Mg, ${}^{40}$Ca, and ${}^{90}$Zr, calculated for the microscopic self-consistent solutions obtained using the functional DD-ME2, are denoted by squares.

Figure 2

Self-consistent ground-state densities of ${}^{20}$Ne, calculated with the EDFs SLy4 (top) and DD-ME2 (bottom). The densities (in units of fm${}^{-3}$) are plotted in the the intrinsic frame of reference that coincides with the principal axes of the nucleus.

Figure 3

Same as described in the caption to Fig. 2 but for the nucleus ${}^{28}$Si.