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I have a question about one of the values presented in a paper, which is crucial in calculating energy transfer probability between two Yb^{3+}ions.

This is the paper:

T. Kushida, "Energy Transfer and Cooperative Optical Transitions in Rare-Earth Doped Inorganic Materials. I. Transition Probability Calculation",J. Phys. Soc. Jpn.1973,34, 1318-1326. DOI: http://dx.doi.org/10.1143/JPSJ.34.1318

The summary of this paper is that it uses similar approach to Judd-Ofelt theory (spherical harmonics with Coulomb interaction operator and extensive use of reduced matrix elements) to derive equations for dipole-dipole, dipole-quadrupole, quadrupole-quadrupole interactions. For the calculation of the actual values of these rates, one needs reduced matrix elements of the electronic transition.

In line 27 and 36-37 of page 1323, the author presents the reduced matrix element values for^{2}F_{5/2}→^{2}F_{7/2}transition of Yb^{3+}ions, namely <f^{13}^{2}F_{5/2}||U^{(2)}||f^{13}^{2}F_{7/2}> = 6/49, <f^{13}^{2}F_{5/2}||U^{(4)}||f^{13}^{2}F_{7/2}> = 20/49, and <f^{13}^{2}F_{5/2}||U^{(6)}||f^{13}^{2}F_{7/2}> = 6/7. However, there is no reference to where these values came from. If it is a theoretical value, it still wouldn't make sense because Judd-Ofelt calculations for Yb^{3+}is impossible considering that it only has one excited state level (Judd-Ofelt analysis requires several to make sense).

How do you get these parameters?

Actually, there is another paper by O.L. Malta:

O. L. Malta, "Mechanisms of non-radiative energy transfer involving lanthanide ions revisited",J. non-Cryst. Solids2008,354, 4770-4776. DOI: http://dx.doi.org/10.1016/j.jnoncrysol.2008.04.023

In page 4775, there is a calculation of energy transfer rate, but also provides no values they used for the calculation. They provide ΣΩ_{k}<f^{13}^{2}F_{5/2}||U^{(k)}||f^{13}^{2}F_{7/2}>, but that is only enough to calculate dipole-dipole, and every other multipole calculation requires reduced matrix element of each tensor rank.

Am I missing something in the theoretical or experimental aspect?

Thank you,

HAYAO

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# A Question about energy transfer between Rare-Earth ions

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