Dynamic Derivative Convolution Algorithm for Prompt Gamma Neutron Activation Spectra
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Marcus J. Neuer , Tomasz Szcz¸ e´sniak , Henryk Zastawny , Elmar Jacobs and Martyna Grodzicka 1 2 3
innoRIID GmbH, Am Eichenbroich 19, 41516 Grevenbroich, Germany National Centre for Nuclear Research, A. Soltana 7, 05-400 Otwock-Swierk, Poland Syskon Control Systems of Industrial Processes, Koscierzynska 7, 51 - 416 Wroclaw, Poland
Dynamic Derivative Convolution (DDC)
Introduction
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Context: We would like to quantify the chemical composition of material samples. To do this, the samples are activated by neutrons and the prompt gamma neutron activation spectra (PGNAA) [1] are analyzed. For activation, a neutron generator is utilized.
Peak widths are energy dependent. Along the considered energy range, this dependency becomes relevant. Novel approach: introducing σˆ (E) as function of E and calculate convolution explicitly via, Z
Problem: Analyze peak areas in the spectrum and determine them quantitatively. Peaks are poorly visible in the spectrum and hard to be evaluated. See Fig. 2. Objective: Develop an algorithm that significantly increases the visibility of peaks and that allows for analytically retrieving quantitative peak properties.
H (2.2 MeV)
∞
ξ[, σˆ (E)] = −∞
Z
∞
df (E1, EH 2(2.2 , σˆMeV) (E1)) µ(E1) dE1 × dE1 −∞ df (E2, , σˆ (E2)) × dE2. Ca (4.42 MeV) dE2
(6)
Ca (6.42 MeV)
Formula (6) provides a way for calculating the convolution integral over all energies, featuring the correct value of σˆ for the quantitative peak area given by (4). The function σˆ (E) is obtained by a series of measurements and applying the optimization technique shown in [4].
Ca (4.42 MeV) Ca (6.42 MeV)
DDC spectrum
Ca quantification peak areas
^ σ(E)
E Figure 1: Selected example of a PGNAA Figure 2: Fitted and interpolated curve for the spectrum, here showing a calcium Ca sample. full-width-at-half-maximum (FWHM). High energy counts are noisy and the peaks are difficult to find. Figure 3: Illustration of the σ(E) dependence, displaying the response shape evolution with E. This is an input for the DDC algorithm.
Quasi-Static Convolution Approach Let µ be a measured spectrum, E the energy, σ the statistical variance of the peak and f the shape function of the peak. As scintillators feature gaussian peaks the derivative of f yields
Figure 4: Applying the DDC algorithm (blue 1 curve) to the problem spectrum shown in Fig. 2 compared with background measurement (black curve).
Tests and Results
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df (E, , σi) E − = f (E, , σi). 2 dE σi
(1)
(2)
[1] J. B. Yang, Y. G. Yang, Y. J. Li, X. G. Tuo, Z. Li, Y. Cheng, Y. F. Mou, and W. Q. Huang, “Prompt gamma neutron activation analysis for multi-element measurement with series samples,” Laser Phys. Lett., vol. 10, p. 056002, 2013.
[3] A. Likar and T. Vidmar, “Optimal functions for peak search methods based on spectrum convolution,” Act. Phys. Slov., vol. 53, no. 2, pp. 165–172, 2003.
(3)
Likar and Vidmar showed in [3] that both, peak area P and peak width σˆ can be calculated analytically by
[4] M. J. Neuer, N. Teofilov, Y. Kong, and E. Jacobs, “Evolutionary ensembles that learn spectroscopic characteristics of scintillation and czt detectors,” in 2014 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC), pp. 1–6, Nov 2014.
This work was supported in part by the Polish Program of Applied Research, grant number: PBS2/B2/11/2014, RaM-scaN.
9ˆ σ P = √ sup ξ(, σi), 6π i
(4)
σˆ = arg sup ξ(, σi).
(5)
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References [2] A. Likar and T. Vidmar, “A peak search method based on spectrum convolution,” IOP J. Phys. D: Appl. Phys., vol. 36, pp. 1903–1909, 2003.
∞
df (E, , σi) ξ(, σi) = ζ(E) dE. dE −∞
Calcium (Ca), Aluminum (Al), Manganese (Mg), Iron (Fe), Silicon (Si) and cement mixtures 1
and applying this derivative again yields de-facto the convolution with the second derivative Z
Geant4 emission spectra with dedicated emission lines
Tests were performed on a selected number of real world samples
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∞
df (E, , σi) ζ(, σi) = µ(E) dE dE −∞
I
Convolution with the first derivative of f leads to Z
In-situ algorithm testing
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