  A new analysis method to investigate halos in finite many-fermion systems is
designed, as existing characterization methods are proven to be
incomplete/inaccurate. A decomposition of the internal wave-function of the
{$N$-body} system in terms of overlap functions allows a model-independent
analysis of medium-range and asymptotic properties of the internal one-body
density. The existence of a spatially decorrelated region in the density
profile is related to the existence of three typical energy scales in the
excitation spectrum of the {$(N-1)$-body} system. A series of model-independent
measures, taking the internal density as the only input, are introduced. The
new measures allow a quantification of the potential halo in terms of the
average number of fermions participating to it and of its impact on the system
extension. Those new "halo factors" are validated through simulations and
applied to results obtained through energy density functional calculations of
medium-mass nuclei. Performing spherical Hartree-Fock-Bogoliubov calculations
with state-of-the-art Skyrme plus pairing functionals, a collective halo is
predicted in drip-line Cr isotopes, whereas no such effect is seen in Sn
isotopes.
