  The nucleonic localization function has been used for a decade to study the
formation of alpha-particles in nuclei, by providing a measure of having
nucleons of a given spin in a single place. However, differences in
interpretation remain, compared to the nucleonic density of the nucleus. In
order to better understand the respective role of the nucleonic localization
function and the densities in the alpha-particle formation in cluster states or
in alpha-decay mechanism, both an analytic approximation and microscopic
calculations, using energy density functionals, are undertaken. The nucleonic
localization function is shown to measure the anti-centrifugal effect, and is
not sensitive to the level of compactness of the alpha-particle itself. It
probes the purity of the spatial overlap of four nucleons in the four possible
(spin, isospin) states. The density provides, in addition, information on the
compactness of an alpha-particle cluster. The respective roles of the nucleonic
localization function and the density are also analyzed in the case of
alpha-particle emission. More generally, criteria to assess the prediction of
alpha-cluster in nuclear states are provided.
