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1 will no longer be equally populated and produce an over­ all aspherical 5d-charge cloud surrounding the 4f-charge cloud. Similar arguments were already presented for p electrons in Fig. 1. Since the 5d and 6p valence electrons are located on the same atom as the 4f electrons, this on-site valence-electron asphericity pro­ duces an electrostatic field that may be much larger than that due to the charges of the considerably more remote ligand atoms. It is clear that results obtained by means of the point-charge approximation are not expected to be correct in these cases.

A typical situation, where the atom carrying the unpaired electrons is situated in a uniaxial crystal field, is shown in Fig. 1. If J is the total angular-momentum quantum number of the magnetic atom, the (2J + 1)fold degeneracy of its ground state will be lifted in the presence of a magnetic as well in the presence of a crystal field. This will result in changes in the magnetic properties of the corresponding compound if a crystal field is present. In order to derive the magnetic properties, it is necessary to solve the Hamiltonian of the crystal–field interaction explicitly.

Since we have chosen enough, the ground state is of course large One may easily obtain the ground-state energy by calculating In order to find the ground-state energy for one has to diagonalize the Hamiltonian in Eq. 3). 1). It can be shown that the ground-state wave function is of the type We will not further investigate this wave function except by stating that, owing to the it corresponds to an expectation value which is predominance of almost equal to In fact, almost the full moment is obtained along the x-direction (at zero Kelvin).

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