Abstract
The effective pair potential is written as the sum of s-s, d-d, s-d, f-f and s-f contributions. The free electron part of the pair potential is obtained in second-order perturbation theory using rational dielectric function (RDF) in conjunction with Heine-Abarenkov model pseudopotential (HAMP). The exchange-correlation corrections due to Taylor are inherent to RDF. The overlap between d states and f states on different ions and the effect of sd and hybridization are included in an approximate manner, as has been suggested by Wills and Harrison [Phys. Rev. B 28 (1983) 4363], and Harrison [ibid., 550]. An approximate temperature dependence has been included in the effective potential through an asymptotic factor. The ion-ion interaction so defined is used to calculate the phonon dispersion curves for hcp metals Tb and Ho. The calculated phonon frequencies are found to be real and in reasonably good agreement with the neutron inelastic scattering measurements which establishes the validity of the effective pair potential for rare earths.
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