The localized electronic state is different from the free atomic state in condensed matter. The strong or weak interaction between localized electronic state and the crystal lattice results in a big or small shift of the atomic balance site in solid states. This phenomenon was called crystal lattice relaxation. Rare earth ions may have a partially filled 4

f

n

(1≤n≤13) electron shell both in free and in bound states. The peculiarities of the physical properties of rare earth compounds are determined by the presence of this partially filled shell. Internal 4

f

electrons remain localized near their own nucleus and interact relatively weakly with the ligands. In this work

a serial of glasses with different ratios of H

3

BO

3

and PbF

2

in molar and with same density of purity was prepared

using the solid melt method. The excitation spectra of Eu

3+

in these glasses were measured with the HITACHI F-4500 fluorescence spectroscopy

and the phonon sideband spectra were obtained from the excitation spectra. A detail script of the theory of electron phonon interaction in the condition of weakly coupling system

such as trivalent rare earth ions in the condensed matter

was confirmed. The experimental technique for obtaining phonon sideband spectra was concluded. Based on the theory

we proposed a method to obtain the Huang-Rhys factor from the phonon sideband spectra of Eu

3+

in these serial glasses with different components. The Huang-Rhys factors for different glasses were calculated. The relationship between Huang-Rhys factor and sample components was obtained and discussed. Then we investigated the dependence of the constant α on the energy gap

between two levels

for different glasses with various Huang-Rhys factors. The available area of energy gap law

A

nr

=

Ce

-αΔ

E

was discussed. Lastly for instance

we ticked off some values of α and

C

in different crystals

obtained by researchers. A detail analysis of effect of α and

C

on the nonradiative transitions was confirmed.