Unfolding Techniques for Activation Detector Analysis

Abstract

Activation detectors are widely used in measurements of radiation fields. In particular, the energy dependent radiation spectrum or integral quantities, such as the total flux, dose rate or reaction rates, are of interest in these measurements.Activation detectors do not directly yield the quantities of interest. Solving the radiation spectrum from measured activities requires unfolding or deconvolution. No unique solutions typically exist and prior knowledge is also applied to obtain physically meaningful solutions.Prior knowledge available depends on the application. In reactor neutron spectroscopy theoretical estimates for the shape of the spectrum are available and the unfolding problem may even be reduced to modifying a trial spectrum to match the measured activities. For accelerators or cosmic radiation spectra good trial spectra are often not available, and more general unfolding methods must be used.Dose rate and reaction rates can be calculated from unfolded spectra or, in some cases, directly from measurements. is the unknown distribution, K(E' ,E) is the known kernel or resolution function,is the measured response, and E (E') is the uncertainty.With discrete activation detectors eq. ( 1 ) reduces to A. is the saturation activity of detector 1 E.is the uncertainty of activity A. , 1 1 m is the number of detectors.i,For numerical solution the continuous energy variable is made discrete. Numerical quadrature transforms eq. ( 2 ) to a group ofor in matrix form,where n 1S the number of discrete energy points,is the cross section of reaction i at 1J J 1 J energy point E. multiplied by quadrature weight w .. J J UNFOLDING TECHNIQUES FOR ACTIVATION DETECTOR ANALYSIS 391Nonuniqueness of the Solution Even without uncertainties, E(E'), eq. ( 1 ) would have a unique solution only if the kernel K(E' ,E) had no zero eigenvalues.The experimental errors make the problem of nonuniqueness even worse.Suppose that ¢(E) were a unique solution of eq. ( 1 ) with E(E') = O.There might then exist a number of functions ~(E) for whichand each of functions ¢(E) + ~(E) satisfies eq. ( 1 ) Especially when n > m,the unfolding problem is ill-conditioned in the sense that small changes in the measured responses may cause large relative errors in the solution. Hence, special methods have been developed for unfolding activation measurements. Generally they make use of prior knowledge of the spectrum, such as a trial spectrum to which the solution is tied in some way, or smoothness and nonnegativity conditions. Different KernelsThe choice of the best unfolding method depends on the detector kernel. Problems can be classified as few channel and many channel unfolding problems according to the number of measured responses.Activation detectors typically lead to few channel problems with up to about 10-30 measured responses and 20-100 energy points. In some ... Some codes are oriented to specific apFlications while others can be flexibly used for various problems. Functional RepresentationsIn some cases analytical formulae with a few unknow...