Dependence of Phonon Frequencies on the Pseudopotential Form Factor for Aluminum

The phonon frequencies were calculated for aluminum from a theory based on Coulomb interactions among the ions, Born-Mayer repulsion between nearest-neighbor ion cores, and a local pseudopotential interaction between ions and conduction electrons. For both a Harrison modified point-ion potential and a local Heine-Abarenkov potential, the parameters of the theory were determined to give the best over-all fit to the measured phonon dispersion curves. For the two pseudopotentials so determined, the Born-Mayer repulsion was found to be negligible, the screened form factors $w_q$ are the same for $0\le q\le 1.8k_F$ and are in good agreement with Fermi-surface data, and the calculated phonon frequencies are the same. The calculated frequencies depend sensitively on $\left|w_q\right|$ for $0\le q\le 2k_F$, and also depend strongly on some average of $\left|w_q\right|$ for larger $q$.