In this paper we briefly review our research progress in the past twenty more years on the theory of rare-earth luminescence and spectroscopy

which can be enumerated as follows:1.On one-photon transition intensities:A.Extending the Judd-Ofelt 3-parameter formula to contain the effect of J-mixing caused by even-parity component of crystal field Hamiltonian.The extended formula still uses 3 parameters while introduces J-mixing coefficients which can be obtained from crystal-field splitting data of a few terms.B.Conforming the relative sign between the "dynamic term" and the "static term" contained in the Judd-Ofelt all-parameter formula is still negative by finding another sign error in the original paper.2.On two-photon processes intensities:Presenting a direct calculation scheme of intensities of this sort of processes by simulating energy-wavefunction structure of the intermediate configuration(4f)

N

-1

5d based on the(4f)

N

-1

energy-wavefunction deta of the left labour

RE

3+

and the 5d deta of Ce

3+

.This scheme was used to Tm

3+

compared to the Judd-Ofelt approximation with some discussion.3.On theory of phonon-assistant process of energy transfer(ET) between

RE

ions in solids:It is found that the coherent cancellations occurring in the HLO theory of one-phonon-assisted ET process only holds for diagonal process in which one phonon emits or absorbs from a definite electronic state of the donor or acceptor.For nondiagonal processes in which one phonon emits or absorbs accompanying the electronic electric-dipole transition at the donor or acceptor site

the coherence is enhanced that the most important is one-phonon but two-phonon assisted process.In addition

instead of Debye model used in HLO theory

the running lattice wave is introduced for the first time into the ET theory to describe the phonon involved in the above diagonal and nondiagonal processes.The formulae calculating transition rates etc of both the above processes based on the lattice wave model are given.And it is noticed that contrary to and out of the HLO theory

the contributions to the one-phonon nondiagonal process from optical phonons with wave-vector

q

=0 and corresponding to flat parts of dispersion curves are important.4.On theory of 4f-5d transition spectra:A simple model to calculate approximate term energies of the configuration(4f)

N

-1

5d and the 4f-5d transition intensities based on 3 energy parameters and the quantum numbers of the initial and the final states was presented and developed in the past few years.Therefore

the 4f-5d transition spectra can be analyzed and assigned by executing at the same time energy and intensity fitting.There has been successful examples of

RE

ions from(4f)

3

to(4f)

13

doped in a few hosts.5.On interaction between

RE

ions:The fine structure of zero phonon lines in the low temperature electronic absorption spectra of the elpasolite crystals(like Cs

2

Na

Ln

Cl

6

etc.where

Ln

=Er

Yb) is interpreted by an effective spin hamiltonian model describing superexchange interaction between

RE

ions.