Abstract
MARSHALL et al.1,2 have demonstrated experimentally that the isotope shift in the crystal-field splittings of the magnetic ions doped in some host lattices, δD, is proportional to the mass difference of the isotopic magnetic ions and decreases with temperature. Based on the result that the phonon-induced crystal-field splitting is approximately proportional to the mean square displacement of the atoms3, I have shown4 that the isotope shift in the crystal-field splittings of two isotopic magnetic ions is approximately proportional to the difference between the mean square displacements of these two isotopes, 〈u02〉1 and 〈u02〉2 
In this communication, I shall try to use this result to explain the temperature dependence of the isotope shifts measured by Marshall et al.1.
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References
Marshall, S. A., Hodges, J. A., and Serway, R. A., Phys. Rev., 136, A1024 (1964).
Marshall, S. A., Phys. Rev., 159, 191 (1967).
Huang, C-Y., Phys. Rev., 159, 683 (1967).
Huang, C-Y., Phys. Rev. (in the press, 1968).
Montgomery, D. J., Prog. Nuclear Energy, Ser. 5, 3, 468 (1961).
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HUANG, CY. Isotope Shift in Crystal-field Splitting. Nature 218, 761–762 (1968). https://doi.org/10.1038/218761b0
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DOI: https://doi.org/10.1038/218761b0
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