Calculation of the light pulse distributions induced by fast neutrons in organic scintillation detectors

We develop a fully analytic and self-contained description of the amplitude distribution of light pulses in an organic scintillation detector due to a monoenergetic source of fast neutrons. To this end, two classes of problems have to be handled. One is a formula for the light pulse amplitude distribution for the complete life history of neutrons slowing down in a mixture of hydrogen and carbon as a statistical average over all collision sequences that can occur, accounting also for neutron leakage. A complete solution is given in terms of a non-recursive convolution integral expansion with respect to the various possible collision histories. These latter are dependent on the collision probabilities of neutrons of a given energy. The second is the calculation of this collision probability from analytical expressions for the geometry of the detector, in the present case a right cylinder. This quantity was taken from Monte Carlo simulations in previous work. Recursive formulae are derived for the probabilities of arbitrary collision sequences, and quantitative results are given for up to five consecutive collisions of all combinations. These probabilities can be used to determine how to truncate the non-recursive expansion of the full light amplitude distribution in quantitative work. The calculational method serves to lend insight and understanding into the structure of the pulse height spectra, as well as it provides a computationally cheap method of generating a large number of such spectra for various detector compositions, sizes and neutron energies, for the development and test of new spectrum unfolding techniques.