Physics – Chemical Physics
Scientific paper
2007-12-27
Physics
Chemical Physics
LaTex2e, 13 pages (2 tables) paper submitted to physica status solidi (b)
Scientific paper
The second moment of the sublevels within the initial state | \alpha SLJ > which constitutes a natural and adequate measure of the crystal-field (CF) effect can be redefined as sigma^{2}=1/(2J+1)\sum_{k} S_{k}^{2} A_{k}^{2}, where S_{k}=[1/(2k+1)\sum_{q}|B_{kq}|^2]^{1/2} is the so-called 2^{k}-pole CF strength, whereas A_{k}= < \alpha SLJ||C^{(k)}||\alpha SLJ > the reduced matrix element of the k-rank spherical tensor operator. Therefore, the CF effect depends on the sum of products of the two factors representing the identical multipole components of two different charge distributions. The term A_{k} expresses the asphericity of the central ion open-shell, whereas the term S_{k} the asphericity of its surroundings. When these two distributions do not fit each other the observed CF splitting can be unexpectedly weak even for considerable values of the total S=(\sum_{k}S_{k}^{2})^{1/2} and A=(\sum_{k}A_{k}^{2})^{1/2}. The tabulated quantities of the A_{k}(|\alpha SLJ >), as the 2^{k}-pole type asphericities, are the intrinsic characteristics of the electron states revealing their multipolar structure and hence their potential susceptibility to CF splitting separately for each effective multipole.
Mulak Jacek
Mulak Maciej
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