**6. Gamma radiation spectral analysis**

32 Gamma Radiation

signals for both detectors should be very high, without jitter. The width of the coincidence window and the neutron flux are interconnected: the random coincidence rate increases

The API technique was used in such systems as SENNA (Vakhtin et al., 2006), EURITRACK

Pulsed fast neutron transmission spectroscopy (PFTNS) is the only technique in this section, which examines the resulting neutron spectrum, instead of the gamma ray spectrum. In this technique, a broad energy beam of neutrons is directed at an array of neutron detectors. The object under interrogation is passed through the beam and the resulting attenuated neutron spectrum is measured using the neutron detectors. This method is the same method that

The pulsing in PFTNS allows the system to perform neutron TOF measurements. These TOF measurements are used to determine the energy of the neutrons with flight paths of 4 to 10 m. The resulting neutron spectrum is used to estimate the attenuation of neutrons as function of energy. Light elements such as H, C, N, and O have high cross-sections for neutron attenuation at these energies. Thus the relative amounts of H, C, N, and O can be determined, and the "imaging" of elements is possible. The voxel sizes would be similar to

Due to the high neutron fluences and precise timing required for PFTNS, this system needs an accelerator similar to the one utilized by PFNA. The TOF path means that the systems take a large amount of space. These are two of the reasons that these systems were not

with the higher neutron flux thus limiting neutron yield of the generator.

(Perret et al., 2006), and UNCOSS (Eleon et al., 2010).

Fig. 6. Associated particle imaging technique

**5.5 Pulsed fast neutron transmission spectroscopy** 

researchers use to perform neutron cross-section measurements.

those of PFNA due to the limits of the speed of the neutrons.

widely adopted by the security community.

Neutron based material analysis methods generally require a skilled analyst to interpret the gamma ray spectral data collected, and to classify the interrogated object using the elemental parameters extracted from the spectral data. Automatic spectral analysis algorithms and the object's classification algorithms are required for real world applications where access to nuclear spectroscopy expertise is limited, or the autonomous and/or the robotic operation is necessary.

#### **6.1 Analysis of neutron induced gamma ray spectra**

The first step in the data analysis process is to extract the sample's elemental information from the measured gamma ray spectra. The spectrum analysis algorithms that are used for that purpose should simultaneously provide quick, accurate, and objective analysis of gamma ray spectra by evaluating the intensities of the characteristic photon peaks. For spectra measured with high resolution detectors such as HPGe, the approach can be based on the peak finding algorithm using the regions of interest (ROIs). Usually, the "blank" spectrum (measured with no sample present) is subtracted from the "sample" spectrum (measured with the sample) before the spectral analysis. It takes into account the signatures of the same elements that are present in surrounding materials, and in the sample. The "nuclear" ROI parameters such as the net peak area in counts /second units are proportional to the number of isotopes in the sample that emitted the fingerprint gamma rays. The "nuclear" parameters may be converted into other appropriate units, if needed, using the elemental calibration library (for example, "chemical" parameters accepted in the coal or the cement analysis industry, etc.). These libraries are created for the system using calibration measurements using known samples.

The simple ROI-based method may be appropriate for non-complicated spectra with the peaks that are well resolved. For spectra with many closely positioned peaks, or low resolution spectra with overlapping peaks, the peak-shape fitting algorithms are required. The mathematical method of measured spectrum fitting as the linear combination of single element's detector responses, that are measured experimentally, was developed by George Vourvopoulos and Phillip Womble (Vourvopoulos & Womble, 2001). To use this method, one must first measure the response of the low resolution detector to -rays from pure elements. For example, a block of pure graphite is used to determine the detector's elemental response to the carbon -rays. To determine the detector's elemental response to hydrogen, a response is measured from a water sample, and so on. The counts in i-th channel of the spectrum of a sample S can be represented by the equation:

Material Analysis Using Characteristic Gamma Rays Induced by Neutrons 35

Clouds have circular structure, and create specific patterns for classes of different materials. Fig. 7 shows a two-dimensional slice of the elemental space. It represents two isotopes: oxygen and nitrogen. Four materials that contain different amounts of oxygen and nitrogen were used as samples for measurements in various environmental conditions. The (nitrogen,

The classification decision is made using the boundaries calculated to separate these classes. For the well separated clouds, the boundaries can be found easily, and simple decision making logic "trees" can be constructed. But in many cases, the patterns for threats and innocuous materials are overlapped in the multidimensional space of parameters making

The decision-tree algorithm for the identification of the particular threat material ("ANFO") amongst four classes of materials is shown in Fig.8. It can be described as the following: if detected oxygen signal lies between lower and higher thresholds, then nitrogen signal is checked. If nitrogen signal lies between lower and higher thresholds, then substance can be identified as "ANFO". The thresholds in the decision tree (Nlow, Nhigh, Ohigh) can be varied in order to achieve better results. Each threshold value can be represented as a horizontal (oxygen threshold) or vertical (nitrogen threshold) line. In order to pick best low and high thresholds, parameters of the decision making tree were varied and Receiver Operating Characteristics (ROC) curves were plotted. In signal detection theory, a ROC curve is a graphical plot of true positive rate (or sensitivity) versus false positive rate for a binary classifier system as its discrimination threshold is varied. The ROC-analysis provides tools to select possibly optimal decision boundaries. The ROC curve methodologies are discussed

oxygen) points from many measurements shape the 2D clouds on the figure.

the differentiation task challenging for classical decision-tree algorithms.

Fig. 7. Data points for four different substances

elsewhere (Fawcett, 2006).

$$S\_i = K \cdot BL\_i + \sum\_{j=1}^{m} A\_j \cdot RF\_{i,j} \tag{4}$$

Here: BLi is the blank spectrum at the i-th channel and K is its coefficient; RFi,j is the detector's elemental response of the j-th element at the i-th channel and Aj is its coefficient, and *m* is the total number of elements used for this spectrum decomposition procedure. The coefficients K and Aj are found by the least squares algorithm minimizing the 2 to find the "best fit". As the result of this decomposition procedure, the intensities of peaks of j elements used in this fitting are found in counts /second.

Another spectral decomposition technique developed by Robin Gardner and colleagues (Shyu et al., 1993) utilizes the detector's elemental responses that are calculated using Monte Carlo methods. The experimental method of detector's elemental response generation provides detailed realistic spectral features (i.e. electronics noise, peak broadening, neutron activation effects, etc.), but it is time intensive, and the set of pure element samples may be limited. The computational method allows generation of responses for the larger set of elements, but it may be problematic to represent detailed spectral features because not all processes in a Monte Carlo code may be taken into account.

Bruce Kessler applied the original mathematical method based on multi-wavelets to analyze the neutron induced photon spectra (Kessler, 2010). In this approach, the set of special scaling vector components was developed for spectrum fitting. Wavelet decompositions ignore signal components up to the approximation space of the basis, so the wavelet analysis is used to look for patterns over the top of spectral "noise". The measured sample spectrum wavelets are decomposed using a variable linear combination of the wavelets from the decompositions of detector's elemental responses providing the intensities of characteristic gamma ray peaks. The algorithm was shown to be effective for both high resolution and low resolution spectra.

#### **6.2 Classification algorithms**

The object's classification algorithms are responsible for material identification using the characteristic gamma ray peak data that are produced by the spectral analysis algorithms. The classification uses the fact that the amount of particular isotopes varies for different materials (i.e. based on their chemical formula, taking the reaction cross sections into account).

The suitable approach is to represent the measurement result as a "point" in the space of several parameters (elemental intensities). Different materials containing the same isotopes but in different ratios are represented by points that are segregated in such "elemental" space. The dimension of this space is determined by the number of isotopes.

In general, the "nuclear" data obtained with neutron based systems differ from elemental composition evaluations based on chemical formula due to several reasons such as statistical nature of nuclear reactions, short measurement times, presence of radiation shielding, and other environmental conditions. Thus, the chemical compound measured in various conditions is represented not by the single "point" in the elemental space, but rather by a cloud-like set of points, where each point corresponds to one measurement.

1

Here: BLi is the blank spectrum at the i-th channel and K is its coefficient; RFi,j is the detector's elemental response of the j-th element at the i-th channel and Aj is its coefficient, and *m* is the total number of elements used for this spectrum decomposition procedure. The coefficients K and Aj are found by the least squares algorithm minimizing the 2 to find the "best fit". As the result of this decomposition procedure, the intensities of peaks of j

Another spectral decomposition technique developed by Robin Gardner and colleagues (Shyu et al., 1993) utilizes the detector's elemental responses that are calculated using Monte Carlo methods. The experimental method of detector's elemental response generation provides detailed realistic spectral features (i.e. electronics noise, peak broadening, neutron activation effects, etc.), but it is time intensive, and the set of pure element samples may be limited. The computational method allows generation of responses for the larger set of elements, but it may be problematic to represent detailed spectral features because not all

Bruce Kessler applied the original mathematical method based on multi-wavelets to analyze the neutron induced photon spectra (Kessler, 2010). In this approach, the set of special scaling vector components was developed for spectrum fitting. Wavelet decompositions ignore signal components up to the approximation space of the basis, so the wavelet analysis is used to look for patterns over the top of spectral "noise". The measured sample spectrum wavelets are decomposed using a variable linear combination of the wavelets from the decompositions of detector's elemental responses providing the intensities of characteristic gamma ray peaks. The algorithm was shown to be effective for both high

The object's classification algorithms are responsible for material identification using the characteristic gamma ray peak data that are produced by the spectral analysis algorithms. The classification uses the fact that the amount of particular isotopes varies for different materials (i.e. based on their chemical formula, taking the reaction cross sections into

The suitable approach is to represent the measurement result as a "point" in the space of several parameters (elemental intensities). Different materials containing the same isotopes but in different ratios are represented by points that are segregated in such "elemental"

In general, the "nuclear" data obtained with neutron based systems differ from elemental composition evaluations based on chemical formula due to several reasons such as statistical nature of nuclear reactions, short measurement times, presence of radiation shielding, and other environmental conditions. Thus, the chemical compound measured in various conditions is represented not by the single "point" in the elemental space, but rather by a

space. The dimension of this space is determined by the number of isotopes.

cloud-like set of points, where each point corresponds to one measurement.

elements used in this fitting are found in counts /second.

processes in a Monte Carlo code may be taken into account.

resolution and low resolution spectra.

**6.2 Classification algorithms** 

account).

(4)

*m i i j i,j j S K BL A RF* 

Clouds have circular structure, and create specific patterns for classes of different materials. Fig. 7 shows a two-dimensional slice of the elemental space. It represents two isotopes: oxygen and nitrogen. Four materials that contain different amounts of oxygen and nitrogen were used as samples for measurements in various environmental conditions. The (nitrogen, oxygen) points from many measurements shape the 2D clouds on the figure.

The classification decision is made using the boundaries calculated to separate these classes. For the well separated clouds, the boundaries can be found easily, and simple decision making logic "trees" can be constructed. But in many cases, the patterns for threats and innocuous materials are overlapped in the multidimensional space of parameters making the differentiation task challenging for classical decision-tree algorithms.

Fig. 7. Data points for four different substances

The decision-tree algorithm for the identification of the particular threat material ("ANFO") amongst four classes of materials is shown in Fig.8. It can be described as the following: if detected oxygen signal lies between lower and higher thresholds, then nitrogen signal is checked. If nitrogen signal lies between lower and higher thresholds, then substance can be identified as "ANFO". The thresholds in the decision tree (Nlow, Nhigh, Ohigh) can be varied in order to achieve better results. Each threshold value can be represented as a horizontal (oxygen threshold) or vertical (nitrogen threshold) line. In order to pick best low and high thresholds, parameters of the decision making tree were varied and Receiver Operating Characteristics (ROC) curves were plotted. In signal detection theory, a ROC curve is a graphical plot of true positive rate (or sensitivity) versus false positive rate for a binary classifier system as its discrimination threshold is varied. The ROC-analysis provides tools to select possibly optimal decision boundaries. The ROC curve methodologies are discussed elsewhere (Fawcett, 2006).

Material Analysis Using Characteristic Gamma Rays Induced by Neutrons 37

The use of linear boundaries is significantly improving the material identification capabilities of the neutron based system. The use of polynomial functions is a natural generalization of this approach. Other pattern recognition methods can also be used to construct the decision boundaries of complex shapes and can be applied to analyze the detector signals - for example, methods based on R-functions (Bougaev & Urmanov, 2005).

This chapter provided an overview of several material analysis methods using different nuclear reactions induced by pulse neutrons: PGNAA, PFNA, PFTNA, PFTNS, and API. These methods utilize the characteristic gamma radiation and other radiation signatures, prompt and delayed in time, to measure the elemental content of unknown bulk samples. The pulse neutron based elemental analysis is the non-intrusive, non-destructive technique that has yielded the development of in situ material characterization systems in many areas: process control in industry, medicine, security, geological and environmental studies, and others. These applications require automatic, rapid spectra analysis and sample classification algorithms to be effective for the real world use. The methods of spectral decomposition using the combination of single element's detector responses proved to be effective. The pattern

Aleksandrov, V.D.; Bogolubov, E.P.; Bochkarev, O.V.; Korytko, L.A.; Nazarov, V.I.;

Polkanov, Yu.G.; Ryzhkov, V.I. & Khasaev, T.O. (2005). Application of Neutron

recognition methods shown true positive rates ~95% in the material classification.

Fig. 10. Linear boundaries between four classes

**7. Conclusion** 

**8. References** 

Fig. 8. Example of the decision tree used to analyze data from Fig. 7

Each set of parameters of the decision-making algorithm corresponds to the point on the ROC curve (or ROC surface). Therefore, we define the optimal parameters for the decisionmaking algorithm as a set of parameters, which allow the minimum "decision" vector magnitude from (0,1) point (left-upper corner of the ROC graph) to the corresponding point on the ROC curve (see Fig.9). The best low and high thresholds were selected by variation of parameters of the decision making tree aimed to determine the ROC curve with the minimal decision vector length. The optimal decision boundaries for identifying the ANFO material are shown as black lines in Fig.7.

Fig. 9. ROC curve

It is clear that this algorithm does not satisfactory identify substances when classes are overlapping. For example, True Positive rate of the classification between ANFO and urea is only 75%, which is unacceptable for the field deployable system. To improve performance of the classifier, the linear boundary was used. In the case of general linear boundary, the decision making algorithm can be described as the following: if point with experimentally measured nitrogen and oxygen counts (Nex, Oex) lies below the line that is defined as O = k·N + ℓ, then this point belongs to the class A, if it lies above that line, then it belongs to the class B. The parameters for the linear boundary (the slope and the offset) were varied, and the ROC curves were generated. The optimal pair of parameters corresponds to the minimal decision vector magnitude. This approach tested with the same data set as shown in Fig. 7 produced better results: true positive rates for all classifiers are better than 95%. Optimal linear boundaries are shown in Fig.10 as black lines.

Fig. 10. Linear boundaries between four classes

The use of linear boundaries is significantly improving the material identification capabilities of the neutron based system. The use of polynomial functions is a natural generalization of this approach. Other pattern recognition methods can also be used to construct the decision boundaries of complex shapes and can be applied to analyze the detector signals - for example, methods based on R-functions (Bougaev & Urmanov, 2005).

#### **7. Conclusion**

36 Gamma Radiation

Each set of parameters of the decision-making algorithm corresponds to the point on the ROC curve (or ROC surface). Therefore, we define the optimal parameters for the decisionmaking algorithm as a set of parameters, which allow the minimum "decision" vector magnitude from (0,1) point (left-upper corner of the ROC graph) to the corresponding point on the ROC curve (see Fig.9). The best low and high thresholds were selected by variation of parameters of the decision making tree aimed to determine the ROC curve with the minimal decision vector length. The optimal decision boundaries for identifying the ANFO material

It is clear that this algorithm does not satisfactory identify substances when classes are overlapping. For example, True Positive rate of the classification between ANFO and urea is only 75%, which is unacceptable for the field deployable system. To improve performance of the classifier, the linear boundary was used. In the case of general linear boundary, the decision making algorithm can be described as the following: if point with experimentally measured nitrogen and oxygen counts (Nex, Oex) lies below the line that is defined as O = k·N + ℓ, then this point belongs to the class A, if it lies above that line, then it belongs to the class B. The parameters for the linear boundary (the slope and the offset) were varied, and the ROC curves were generated. The optimal pair of parameters corresponds to the minimal decision vector magnitude. This approach tested with the same data set as shown in Fig. 7 produced better results: true positive rates for all classifiers are better than 95%. Optimal

Fig. 8. Example of the decision tree used to analyze data from Fig. 7

are shown as black lines in Fig.7.

Fig. 9. ROC curve

linear boundaries are shown in Fig.10 as black lines.

This chapter provided an overview of several material analysis methods using different nuclear reactions induced by pulse neutrons: PGNAA, PFNA, PFTNA, PFTNS, and API. These methods utilize the characteristic gamma radiation and other radiation signatures, prompt and delayed in time, to measure the elemental content of unknown bulk samples. The pulse neutron based elemental analysis is the non-intrusive, non-destructive technique that has yielded the development of in situ material characterization systems in many areas: process control in industry, medicine, security, geological and environmental studies, and others. These applications require automatic, rapid spectra analysis and sample classification algorithms to be effective for the real world use. The methods of spectral decomposition using the combination of single element's detector responses proved to be effective. The pattern recognition methods shown true positive rates ~95% in the material classification.

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**3** 

*USA* 

**Gamma Radiation** 

*St. John's University* 

Richard Stalter and Dianella Howarth

The content of this chapter includes a brief history of gamma radiation, units of radiation measurement, ecological importance, tables including the half life of gamma emitting nuclides, comparative sensitivity of living organisms to gamma radiation, biological magnification of radioactive and nuclear materials, and brief descriptions of case studies of Woodwell (1962), Stalter and Kincaid 2009), and nuclear power plant disasters (Three Mile

Gamma radiation is somewhat similar to x-rays in that both pass through living materials easily. Also referred to as "photons" they travel at the speed of light. Gamma rays have sufficient energy to ionize matter and therefore can damage living cells. The damage produced in the cell or tissue is proportional to the number of ionizing paths produced in the absorbing material. Isotopes of elements that are emitters are radionuclides important in

The injurious affect of gamma rays depends on (1) their number (2) their energy and (3) their distance from the source of radiation. Radiation intensity decreases exponentially with increasing distance. Radiation damage on vascular plant species was demonstrated by Woodwell (1962) who subjected a mature pine oak forest at Brookhaven National

Fig. 1. Radiation dose and damage to a pine-oak forest, Brookhaven National Laboratory, 1961. Zones delineated by vertical lines (Woodwell 1962, Stalter and Kincaid 2009).

fission products from nuclear testing, nuclear power plant disasters or waste.

Laboratory to gamma radiation from a cesium 137 source (Figure 1).

**1. Introduction** 

Island, USA, 1980, Chernobyl 1986, Japan 2011).

Richard Stalter and Dianella Howarth *St. John's University USA* 
