Multipole characteristics of the open-shell electron eigenstates

Abstract

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.

LaTex2e, 13 pages (2 tables) paper submitted to physica status solidi (b)

References in corpus (2)

• Low-temperature asymptotics of integrable systems in an external field
• On a complementary scale of crystal-field strength

Cited by in corpus (4)

• Capability of the free-ion eigenstates for crystal-field splitting
• A fundamental requirement for crystal-field parametrization
• The limits of the total crystal-field splittings
• The total energy splitting of ionic eigenstates in the axial crystal fields