Analysis of Counting Distributions with a Complex Exponential Character

The analysis of counting distributions which can be analytically represented by a sum of exponential functions convoluted with a "prompt instrumental resolution function" has attracted much attention in the past. Because of the difficulty of unfolding the prompt resolution function from the experimental data, experimentalists have analyzed that part of the distribution which occurred at times longer than the time at which the peak of the distribution occurred. A model is proposed which permits the prompt resolution function to be unfolded and the entire counting distribution analyzed in cases where the prompt resolution function can be approximated by a double-sided exponential. The model is tested on Monte-Carlo simulated data. An algorithm which combines the best features of the gradient search and the Taylor-series search is used to obtain a least-squares estimation of the nonlinear parameters. Since the correct parameters are known, a realistic estimation of the errors associated with the analysis is ...