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Capability of the Free-Ion Eigenstates for Crystal-Field Splitting

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Any electronic eigenstate of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities for and 6 related to the second moments of the relevant crystal-field splittings by , where . The A

_{k}as the reduced matrix elements can serve as a reliable measure of the state capability for the splitting produced by the k-rank component of the crystal-field Hamiltonian. These multipolar characteristics allow one to verify any fitted crystal-field parameter set by comparing the calculated second moments and the experimental ones of the relevant crystal-field splittings. We present the multipole characteristics A_{k}for the extensive set of eigenstates from the lower parts of energy spectra of the tripositive 4 f^{N}ions applying in the calculations the improved eigenfunctions of the free lanthanide ions obtained based on the M. Reid f-shell programs. Such amended asphericities are compared with those achieved for the simplified Russell-Saunders states. Next, they are classified with respect to the absolute or relative weight of A_{k}in the multipole structure of the considered states. For the majority of the analyzed states (about 80%) the A_{k}variation is of order of only a few percent. Some essential changes are found primarily for several states of Tm^{3+}, Er^{3+}, Nd^{3+}, and Pr^{3+}ions. The detailed mechanisms of such A_{k}changes are unveiled. Particularly, certain noteworthy cancelations as well as enhancements of their magnitudes are explained.KEYWORDS

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J. Mulak and M. Mulak, "Capability of the Free-Ion Eigenstates for Crystal-Field Splitting,"

*Journal of Modern Physics*, Vol. 2 No. 11, 2011, pp. 1373-1389. doi: 10.4236/jmp.2011.211170.

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