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Thermal Shift Calculations (I): The Theory for Thermal Shift of Crystal Field Spectra of Rare Earth or Transition Metal Ions

The thermal shift of crystal field spectra of rare earth or transition metal ions includes four contributions of different characteristics. In this paper we develop a theory of calculating all those contributions in detail. The contributions to thermal shift consist of that of thermal expansion and those of electron-phonon interaction. The thermal shift caused by thermal expansion is interpreted and calculated by making use of theory of pressure-induced spectral shift. The contribution of phonons of optical branches is given by using single frequency model. The contributions of phonons of acoustic branches include two terms, which are derived by taking into account contributions of all the in electron-phonon interaction. The theoretical formulas for parameters in the most important term are given.