A stochastic process approach to multilayer neutron detectors

Abstract

The sparsity of the isotope Helium‐3, ongoing since 2009, has initiated a new generation of neutron detectors. One particularly promising development line for detectors is the multilayer gaseous detector. In this paper, a stochastic process approach is used to determine the neutron energy from the additional data afforded by the multilayer nature of these novel detectors. The data from a multilayer detector consist of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. We study the maximum likelihood estimator for the intensity and absorption probability and show its consistency and asymptotic normality, as the number of incoming neutrons goes to infinity. We combine these results with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show its consistency and asymptotic normality.

Estimating the distribution and thinning parameters of a homogeneous multimode Poisson process

“…By iterating the argument, cf. also [3] for a similar and more detailed reasoning, we obtain the following result.…”

“…We have previously studied this problem in the simpler setting of there being exactly one wavelength in the neutron beam, which was then considered to be unknown, cf. [3]. The goal in [3] was to derive an estimator of the unknown wavelength, which was a maximum likelihood estimator (mle), and to derive properties of the estimator, in particular [3] showed the consistency and asymptotic normality of the mle.…”

“…[3]. The goal in [3] was to derive an estimator of the unknown wavelength, which was a maximum likelihood estimator (mle), and to derive properties of the estimator, in particular [3] showed the consistency and asymptotic normality of the mle. Relations between the properties of the mle and the detectors construction are of importance for the physicists, and then in particular for the number of layers used in the detector.…”

“…This paper can be seen as a generalisation of the study in [3], in the sense that we investigate the same detector type, but are now interested in a set of wavelengths with finite cardinality, say s, and that both the wavelengths sizes/values as well as the distribution of the wavelengths in the neutron beam are unknwon. The goal in this paper is to construct an estimate of these 2s parameters, and if possible to derive properties of the constructed estimator.…”

“…In [3], the neutron beam was assumed to be well described by a time homogeneous Poisson process, and we take a similar approach here. We assume that the neutron beam is a sum of individual wavelength neutron beams, each being described by a Poisson process; the proportions q of the individual wavelength neutrons in the total sum is however unknown, and is in fact a parameter that we want to estimate; the total sum is of course still a Poisson process.…”