开壳层电子本征态的多极特性
Multipole characteristics of the open-shell electron eigenstates
摘要：
The second moment of the sublevels within the initial state | αSLJ > 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} = < αSLJ||C^{(k)}||αSLJ > 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} (|αSLJ >), 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.
英文摘要：
The second moment of the sublevels within the initial state | αSLJ > 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}= < αSLJ||C^{(k)}||αSLJ > 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}(|αSLJ >), 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.
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