Intensity and bandwidth of multiphonon vibronic transitions of rare-earth ions in crystals

The theory of multiphonon vibronic coupling to electronic transitions is applied in analysing fluorescence spectra of Eu2+ in BaFCl, which consist of the 4f(7) (P-6(7/2)) --> 4f(7) (S-8(7/2)) and 4f(6)5d --> 4f(7) transitions, and the 4f(7)-4f(6) d excitation spectrum of Ce3+ in YPO4. The 4f electrons are weakly coupled to lattice vibration modes so that only weak one- and two-phonon sidebands are observable in the 4f-4f optical transitions, whereas the electron-phonon coupling is significantly stronger for a 5d electron. Accordingly, intensive multi-phonon vibronic transitions overwhelmingly dominate the 4f(6)5d --> 4f(7) spectrum. It is shown that the extended Judd-Ofelt theory for weak vibronic coupling in the framework of the M-process is equivalent to the Huang-Rhys theory for the Delta-process. In the analysis of experimental data, contributions from local ligand modes and lattice acoustic modes are separated, and the coupling strength is evaluated, in terms of the Huang-Rhys parameter S, for the 4f-4f and 5d-4f vibronic transitions.