Model Pseudopotential and the Kohn Effect in Lead

A model local pseudopotential for lead is proposed and two parameters adjusted so that the pseudo-potential leads to the correct vibration frequency for two selected modes. Two potentials are found to satisfy these conditions and one is selected which resembles the pseudopotential suggested from other experiments. Kohn anomalies in the spectrum are found which are of the same general magnitude of those observed. The model does not, however, lead to the correct stable structure, nor does it appear to describe well the effective interaction between ions at small distances. Similar adjustment of the model to fit the vibration spectrum of aluminum gives a pseudopotential similar to that computed from first principles and leads to the correct stable structure, but again does not give correctly the effective interaction potential at short distances.