Noninteracting-band model for dielectric screening and local-field corrections in bcc transition metals: Application to paramagnetic chromium

An isotropic-noninteracting-band model is constructed using the energy eigenvalues calculated by Gupta and Sinha along the three principal symmetry directions [100], [110], [111] and along the three off-symmetry directions [310], [311], and [221]. It is found that three $d$ subbands and the $s$ band are partially filled and two $d$ subbands are completely filled. The numbers of electrons per atom are assigned to the partially filled $d$ subbands in the ratio of the volume occupied by them. The contributions to the dielectric matrix $\epsilon (\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{G}}, \overrightarrow{\mathrm{q}}+{\overrightarrow{\mathrm{G}}}^{\prime })$, which arise because of the intraband and interband transitions, are evaluated explicitly using the free-electron approximation for the electrons in the $s$ band, and a simple tight-binding scheme for the electrons in the $d$ subbands. The diagonal part of the dielectric function is compared with the detailed calculations of Gupta and Sinha. The anisotropy of the dielectric function is found to be small. The nondiagonal part of the dielectric function, which gives rise to local-field corrections, is found to be larger than the diagonal part for large values of the wave vector.