Local minimum in effective pairpotentials: Pseudopotential theory revisited

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.