A simple analytical approach to deal with unobserved feeding in lifetime measurements using a plunger method

Determination of lifetime of low-lying states using a plunger method could be a subject of systematic uncertainty if, among else, correction of unobserved feeding is not properly taken into account. In this paper, a simple analytical approach is proposed to deduce a lifetime of the state of interest if fed directly by observed and unobserved feedings. Evolution of population of the state of interest for 10 target-degrader distances was simulated, using Monte Carlo approach, assuming a decay scheme of three populated states (a state of interest, one observed and one unobserved state). The simulation was performed using a wide range of initial conditions (lifetimes and detection efficiencies of the three states). A fit on simulated evolution of investigated state using analytical solution of described model (by fixing known parameters from direct, observed feeding: initial population and lifetime) successfully reproduced desired lifetime. In order to successfully apply the method, it is necessary to have experimentally available intensities of unshifted components of peak from at least five target-degrader distances.