  Local minimum appearing in the interionic pair interactions, when derived
from local model pseudopotential, for Al (and some other polyvalent metals)
remains as a long standing problem of clear understanding although some
attempts are made by different authors. The origin of this feature of local
minimum is systematically investigated in this article, considering both the
chemical valence, Z, and the core radius, $R_{c}$ as variables. Ashcroft's
empty core model is used to describe the interionic pair-potential, because, it
depends on these two parameters only. Results of this investigation show that
monovalent metals do not exhibit a local minimum at small $r$ but some
polyvalent metals does where, the core radius plays the major role.
