Solid State Luminescence Theory and Oscillator Strengths in KCl: Tl

Abstract

The existing quantitative treatment by Williams of the Seitz model for the KCl: Tl luminescent system has been extended to include a prediction of the oscillator strengths of the 1960 A and 2475 A absorption lines. These $f$ values are simply related to those of the associated free-ion transitions. In the course of the computations it is found that the best available ${\mathrm{Tl}}^{+}$ wave functions are inaccurate for the free ion and are therefore not of great value for the KCl: Tl center. Free-ion oscillator strengths are (a) computed with these functions and are (b) estimated by analysis of experimental spectra; the results of both methods, when modified for KCl: Tl, are in poor agreement with experimental $f$ values in the solid. A review and critique are given for the present Williams dynamical treatment of the Seitz-Williams model, and it is concluded that a sensitive test for the model would be its successful prediction of the ratio of these (1960 A and 2475 A) oscillator strengths in KCl: Tl; the observed values are from three to five times as large as the predicted value. We conclude that the KCl: Tl problem is not as well understood as it has been believed, since the existing quantitative theory (a) is subject to considerable arbitrariness in the construction of excited-state configurational coordinate curves, (b) appears to be in fortuitous agreement with experiment insofar as its quantitative predictions depend on thallous ion wave functions, and (c) does not, in our simple extension, predict the observed ratio of oscillator strength corresponding to the electronic transitions assumed responsible for the behavior of the center.