Halo phenomenon in finite many-fermion systems: Atom-positron complexes and large-scale study of atomic nuclei

The analysis method proposed in V. Rotival and T. Duguet [Phys. Rev. C 79, 054308 (2009)] 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 ultraviolet 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, and (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 be found only at the very limit of neutron stability and for a limited number of elements.