| The analysis method proposed in Ref.~\\cite{rotival07a} is applied to characterize halo properties in finite many-fermion systems. First, the versatility of the method is highlighted by applying it to light and
medium-mass nuclei as well as to atom-positron and ion-positronium complexes. Second, the dependence of nuclear halo properties on the
characteristics of the energy density functional used in self-consistent
Hartree-Fock-Bogoliubov calculations is studied. We focus in particular on the influence of (i) the scheme used to regularize/renormalize the ultra-violet divergence of the local
pairing functional, (ii) the angular-momentum cutoff in the single-particle basis, as well as (iii) the isoscalar effective
mass, (iv) saturation density and (v) tensor terms characterizing the particle-hole part of the energy
functional. It is found that (a) the low-density behavior of the pairing functional and the
regularization/renormalization scheme must be chosen coherently and with care to provide meaningful predictions, (b) the impact of
pairing correlations on halo properties is significant and is the result of two competing effects, (c)
the detailed characteristics of the pairing functional has however only little importance, (d) halo properties
depend significantly on any ingredient of the energy density functional that influences the location of
single-particle levels; i.e. the effective mass, the tensor terms and the saturation density of nuclear matter. The latter dependencies give
insights to how experimental data on medium-mass drip-line nuclei can be used in the distant future to
constrain some characteristics of the nuclear energy density functional. Last but not least, large scale
predictions of halos among all spherical even-even nuclei are performed using specific sets of particle-hole and
particle-particle energy functionals. It is shown that halos in the ground state of medium-mass nuclei will only
be found at the very limit of neutron stability and for a limited number of elements. |
