Unified calculation of thermal shifts and broadenings of sharp lines and zero-field splitting for ruby

A new theory of spectral thermal shifts (TS) and thermal broadenings (TB) has been developed. For the first time, by taking into account all the Gamma M in the electron-phonon interaction (EPI), all the levels and the admixtures of wavefunctions within d(3) electronic configuration, the microscopic expressions; of all the parameters in three terms of TS from EPI have been derived; their values for the R-1, R-2 and ground levels of ruby have been evaluated; the contributions to TS from thermal expansion have also been calculated; the transition probabilities of direct and Raman processes have microscopically been calculated; and then, the unified calculation of the TS of R-1 and R-2 lines and zero-field-splitting (ZFS) for the ground state and the TB of R, R' and B line-groups has been accomplished. The results are in very good agreement with a lot of experimental data. It is found that the contributions from the second-order term of EPI Hamiltonian are dominant in the optical-branch term of ZFS and Raman terms of R-1 line, R-2 line and ZFS; the optical-branch terms play an important role in TS and increase rapidly with temperature, and the optical-branch terms of R1 and R2 lines have opposite signs due to the effects of neighbor levels; the neighbor-level terms for R1 and R-2 lines are very important and it is the admixtures of wavefunctions caused by Coulomb and/or trigonal-field and/or spin-orbit interactions that make them nonzero; the contributions to TS from thermal expansion are also important (especially for ZFS).