1995 Volume 79 Issue 11 Pages 687-695
The crystal field splittings of the Eu2+ ion have been calculated with the eigen functions |f6 α1S1L1, sd1;SLJMJ>. The equation for calculating matrix elements of the crystal field Hamiltonian (Hc) was derived from the application of the tensor operator technique. The calculation was carried out for both O h and D 3h symmetries. Complete equality between calculated results and related predictions with the group theory could justify this derived equation. Further energy splittings with the lowest excited multiplets of a Eu2+ free ion were calculated from the matrix of Hamiltonian H=H c+Hel + H so using eigen functions |f6 α1S1L1, sd1;SLJMJ>. Here, Hel and H so denote electrostatic interactions and spinorbit interactions, respectively. It was shown that the lowest excitation levels in arbitrary symmetries could be easily obtained from a single matrix, even in the d-f coupling scheme.