Application of a sine transform method to experiments of single-photon-decay spectroscopy: Single exponential decay signals

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Abstract
In this article we present as an experiment in single-photon-decay spectroscopy an alternative method to that based on the measurement of the probability distribution function, Pf(t), of the time intervals for the time of arrival of the first photon after the excitation pulse. We propose the measurement of the sine transform of Pf(t), which gives a maximum when the fluorescence signal is of the single exponential decay type. The existence of this maximum allows us to determine very accurately the value of the decay constant using a number of measurements which is lower than that required to establish a Pf(t) that is accurate enough to draw the same conclusions. A theoretical model of the error is studied and is compared by means of a computer simulation with the usual method of measuring Pf(t). An experiment is performed using a TMMC crystal to verify the validity of the theoretical predictions and of the simulation results.