Electric multipole interaction of pairs in solids: Ce in LaCl3

The electric multipole interaction (EMI) is studied in general for the case of two rare earth (RE) ions interacting in host crystals possessing C_3h symmetry at the ion sites. The particular case of Ce³⁺ substituted for La³⁺ in LaCl₃ is used as an example. The splitting of two degenerate levels of such a system is studied as an application of elementary group theory, and a notation is proposed for the resulting levels. The angular dependence of the splitting due to the first term of the EMI, namely, the electric quadrupole-quadrupole interaction (EQQ), is obtained for one of the levels of the system under consideration. The ground quartet is studied for the nearest neighbor configuration (nn), and all of the multipoles in the expansion for EMI are kept. The shielding effects, which are very important in this problem, are assumed to depend on one parameter. This makes possible the study of the variation of the splittings with respect to such a parameter. The importance of terms beyond the quadrupole is brought out.