Lifetime Measurement by Using the Laplace Transform in Single-Photon-Decay Spectroscopy

Abstract

In this paper we present a method for processing the time-interval data obtained in a single-photon-decay spectroscopy experiment. This method is based on the measurement of the Laplace transform of Pƒ( t) [the probability distribution function of the time of arrival of the first photon (PDFP) after the excitation pulse] instead of the direct measurement of Pƒ( t) by means of a multichannel analyzer. With the use of this method, a good estimation of the lifetime of the signal can be obtained with a shorter measurement time than that used in the conventional method, in which the recorded time intervals are used to construct Pƒ( t). A theoretical model of the error involved in determining the lifetime is obtained for the Laplace method, and it is compared with that corresponding to the measurement of Pƒ( t) by means of a multichannel analyzer. Finally, a computer simulation of the experiment is performed to corroborate the theoretical predictions.