Judd–Ofelt theory

Judd–Ofelt theory is a theory in physical chemistry describing the intensity of electron transitions within the 4f shell of rare-earth ions in solids and solutions. It provides a mathematical framework for predicting and analyzing the spectra of rare-earth ions in solids and solutions, in particular branching ratios, radiative lifetimes, and oscillator strengths.

Theory

Judd-Ofelt theory may be used to predict and analyze the intensities of intra 4f electronic dipole transitions. Such transitions are disallowed by Electronic Dipole Transition Selection rules in free space, as the initial and final states have the same parity. However, intra 4f transitions have been observed. The transition strengths and the transition changing the orbital angular momentum quantum number are not consistent with them being Magnetic Dipole Transitions.

This apparent discrepancy is reconciled by treating the crystal field an ion in a solid experiences as a perturbation to the free space Hamiltonian. This perturbation mixes free space electronic states of opposite parity (namely the rare earth ion's ground 4fn electronic configuration with the opposite parity 4fn-15d). Thus Electronic Dipole transitions between these crystal field perturbed electronic states do not violate this parity change selection rule.

The theory quantitatively describes this mixing using three phenomenological parameters particular to the host crystal, denoted as

Ω

λ

{\displaystyle \Omega _{\lambda }}

(where

λ

=

2

,

4

,

6

{\displaystyle \lambda =2,4,6}

).