Thermal Shifts and Electron—Phonon Interactions of ^4T2 and ^4T1 Broad Bands for Ruby

For the first time,by taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d^3 electronic electron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d^3 electronic configuration,the values of parameters in expressions of Raman and optical-branch terms of thermal shifts (TS) due to EPI for three levels,^4T2 band and ^4T1 band of ruby have been evaluated;the contributions to TS of ^4T2 and ^4T1 broad bands from thermal expansion have also been calculated;and then,the TS of the peak energies of ^4T2 and ^4T1 broad bands have been calculated.The results are in satisfactory agreement with observed data.The values of single-electron reduced matrix elements representing the strengths of EPI of ^4T2 and ^4T1 bands have respectively been determined.For TS of the peak energies of ^4T2 and ^4T1 bands,it is found that the contribution to TS from the second-order term in EPI Hamiltonian is dominant;TS due to EPI of acoustic branches are over two times as much as those of optical branches,and both of them increase rapidly with temperature;the neighbor-level term is insignificant;the contribution to TS from thermal expansion is specially important,and all the three terms of TS of ^4T2 or ^4T1 band are red shifts.

Thermal Shifts and Electron-Phonon Interactions of 4T2 and 4T1 Broad Bands for Ruby

For the first timc, by taking into account all the irreducible representations and their components in theelectron-phonon interaction (EPI) as well as all the levels and the admixtures of wavefunctions within d3 electronicconfiguration, the values of parameters in expressions of Raman and optical-branch terms of thermal shifts (TS) due toEPI for three levels, 4T2 band and 4T1 band of ruby have been evaluated; the contributions to TS of 4T2 and 4T1 broadbands from thermal expansion have also been calculated; and then, the TS of the peak energies of 4T2 and 4T1 broadbands have been calculated. The results are in satisfactory agreement with observed data. The values of single-electronreduced matrix elements representing the strengths of EPI of 4T2 and 4T1 bands have respectively been determined. ForTS of the peak energies of 4T2 and 4T1 bands, it is found that the contribution to TS from the second-order term in EPIHamiltonian is dominant; TS due to EPI of acoustic branches are over two times as much as those of optical branches,and both of them increase rapidly with temperature; the neighbor-level term is insignificant; the contribution to TS fromthermal expansion is specially important, and all the three terms of TS of 4T2 or 4T1 band are red shifts.