Polaron Model of Electron-Excess Color Centers

Abstract

A polaron model of electron-excess color centers in ionic crystals is formulated from the many-particle point of view. This is done by adopting the concepts of the electronic polaron and lattice polaron. We have used our theoretical results and some recent experimental results to give a critical analysis of the semicontinuum model and the dielectric-continuum-effective-mass model of electron-excess centers. The theory also provides a criterion for choosing the so-called dielectric constant appearing in these models.

Theoretical Studies on Z1‐Bands in Alkali Halide Crystals

“…We expect from previous work [12,14] that the possible error resulting from replacing m by m, is a ) negligible to the groundstate energy because the present ground state is a small orbit state and b) rather large to the excited state of interest because the size of the electronic orbit of the present excited state is rather large. Accordingly, if the effective mass correction is taken into consideration, then the transition energy may be increased by a small amount (probably the order of 0.2eV for NaCl or KCl).…”

“…The method t o determine the parameter C (thc present C accounts for the same thing as does that in 1131 and has the identical value) and the form of the chosen wavefunction were discussed in [ 131. The values for the other constants used in this calculation are the same as those of [12].…”

“…As was seen in the polaron model [12] On making use of an operator B,,, which was first defined in [12] by t,he The last term in (13) is a constant resulting from the canonical transformation and can be omitted in t,he present calculation. The last term in (14) can be…”

“…(19)), we have used the treatment described in [12] and chosen R = 0 for the exciton part (i.e. the eighth term of (28)) and R = 0.85 d for the phonon part (i.e.…”

“…I n the perturbation method outlined in [12] only the exciton part (FIH,,IF) is treated by second-order perturbation theory and the phonon part (@lII,,,,l@) is assumed to be the same as that for the ground state. The second-order perturbat,ion thcory yields, as shown in [12], This is known as the self-energy of the trapped elechron, i.e. theinteraction of the electron with its own field -the exciton field.…”