Average Oscillator Strength Per State of a one-dimensional disordered Frenkel exciton system in the Coherent Potential Approximation

We report the results of studies of the low energy side of the Average Oscillator Strength Per State $f(E) = F(E)/\rho(E)$, where $F(E)$ is the line shape function and $\rho(E)$ is the density of states function of one dimensional Frenkel excitons in the Coherent Potential Approximation (CPA). A Gaussian distribution of the transition frequencies with rms width $\sigma $ ($0.07\le \sigma \le 0.4)$ is used. Our CPA theory predicts that on the low energy side of the peak the tails are short and independent of the disorder parameter $\sigma $; implying a behavior consistent with the Urbach rule. Our CPA results are in excellent agreement with previous investigations.