Minimizing the statistical error of resonance parameters and cross-sections derived from transmission measurements

Abstract

Total neutron cross-sections are usually measured by a transmission experiment. In this experiment the transmission through a sample is measured by taking the ratio of the background corrected counts measured with and without the sample in the beam. This procedure can be optimized to reduce the statistical error in the measured cross-section. The objective is to find the optimal sample thickness and time split between the open beam, sample and background measurements. An optimization procedure for constant cross-section measurement is derived and extended to the area under the total cross-section curve of an isolated resonance. The minimization of the statistical error in the measured area also minimizes the statistical error in the inferred neutron width. Comparison of the analytical expression developed in this paper and resonance parameters obtained from the SAMMY (Updated users's guide for SAMMY: Multilevel R-Matrix fits to neutron data using Bays’ equation, version m2, ORNTL/TM/-9179/R4) code is shown. The comparison was done with both simulated data and data from transmission experiments that were previously done at RPI. It is shown that the analytical expression can be used as a design tool for optimizing transmission experiments. This will consequently result in more accurate measurements of resonance parameters and can shorten the time required to reach a given accuracy.