research topics on neutron activation analysis

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Home > Books > Imaging and Radioanalytical Techniques in Interdisciplinary Research - Fundamentals and Cutting Edge Applications

Concepts, Instrumentation and Techniques of Neutron Activation Analysis

Submitted: 31 August 2012 Published: 13 March 2013

DOI: 10.5772/53686

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Imaging and Radioanalytical Techniques in Interdisciplinary Research - Fundamentals and Cutting Edge Applications

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Author Information

Lylia hamidatou.

• Department of Neutron Activation Analysis, Nuclear Research Centre of Birine, Algeria

Hocine Slamene

Tarik akhal, boussaad zouranen.

*Address all correspondence to:

1. Introduction

Analytical science to develop the methodology for the investigation of properties and structure of matter at level of single nucleus, atom and molecule, and scientific analysis to determine either chemical composition or elemental contents in a sample are indispensable in basic research and development, as well as in industrial applications.

Following the discovery of neutron by J. Chadwick in 1932 (Nobel prize, 1935) and the results of F. Joliot and I. Curie in 1934, neutron activation analysis was first developed by G. Hevesy and H. Levi in 1936. They used a neutron source (226Ra + Be) and a radiation detector (ionization chamber) and promptly recognized that the element Dy (dysprosium) in the sample became highly radioactive after exposure to the neutron source. They showed that the nuclear reaction may be used to determine the elements present in unknown samples by measuring the induced radioactivity.

Thereafter, the development of the nuclear reactors in the 1940s, the application of radiochemical techniques using low resolution scintillation detectors like NaI (Tl) in the 1950s, the development of semiconductor detectors (Ge, Si, etc.) and multichannel analyzer in the 1960s, and the advent of computers and relevant software in the 1970s, the nuclear technique has advanced to become an important analytical tool for determination of many elements at trace level. In spite of the developments in other chemical techniques, the simplicity and selectivity, the speed of operation, the sensitivity and accuracy of NAA have become and maintained its role as a powerful analytical technique. In 2011, Peter Bode describes in his paper “Neutron activation analysis: A primary method of measurements”, the history of the development of NAA overall the world [ 1 ].

Nowadays, there are many elemental analysis methods that use chemical, physical and nuclear characteristics. However, a particular method may be favoured for a specific task, depending on the purpose. Neutron activation analysis (NAA) is very useful as sensitive analytical technique for performing both qualitative and quantitative multielemental analysis of major, minor and traces components in variety of terrestrial samples and extra-terrestrial materials. In addition, because of its accuracy and reliability, NAA is generally recognized as the "referee method" of choice when new procedures are being developed or when other methods yield results that do not agree. It is usually used as an important reference for other analysis methods. Worldwide application of NAA is so widespread it is estimated that approximately 100,000 samples undergo analysis each year.

The method is based on conversion of stable atomic nuclei into radioactive nuclei by irradiation with neutrons and subsequent detection of the radiation emitted by the radioactive nuclei and its identification. The basic essentials required to carry out an analysis of samples by NAA are a source of neutrons, instrumentation suitable for detecting gamma rays, and a detailed knowledge of the reactions that occur when neutrons interact with target nuclei. Brief descriptions of the NAA method, reactor neutron sources, and gamma-ray detection are given below.

This chapter describes in the first part the basic essentials of the neutron activation analysis such as the principles of the NAA method with reference to neutron induced reactions, neutron capture cross-sections, production and decay of radioactive isotopes, and nuclear decay and the detection of radiation. In the second part we illustrated the equipment requirements neutron sources followed by a brief description of Es-Salam research reactor, gamma-ray detectors, and multi-channel analysers. In addition, the preparation of samples for neutron irradiation, the instrumental neutron activation analysis techniques, calculations, and systematic errors are given below. Some schemes of irradiation facilities, equipment and materials are given as examples in this section.

Finally, a great attention will be directed towards the most recent applications of the INAA and k0-NAA techniques applied in our laboratory. Examples of such samples, within a selected group of disciplines are milk, milk formulae and salt (nutrition), human hair and medicinal seeds (biomedicine), cigarette tobacco (environmental and health related fields) and iron ores (exploration and mining).

All steps of work were performed using NAA facilities while starting with the preparation of samples in the laboratory. The activation of samples depends of neutron fluence rate in irradiation channels of the Algerian Es-Salam research reactor. The radioactivity induced is measured by gamma spectrometers consist of germanium based semiconductor detectors connected to a computer used as a multichannel analyser for spectra evaluation and calculation. Sustainable developments of advanced equipment, facilities and manpower have been implemented to establish a state of the art measurement capability, to implement several applications, etc.

2. Neutron activation analysis

Neutron activation analysis (NAA) is a nuclear process used for determining the concentrations of elements in a vast amount of materials. NAA relies on excitation by neutrons so that the treated sample emits gamma-rays. It allows the precise identification and quantification of the elements, above all of the trace elements in the sample. NAA has applications in chemistry but also in other research fields, such as geology, archaeology, medicine, environmental monitoring and even in the forensic science.

2.1. Basis principles

The sequence of events occurring during the most common type of nuclear reaction used for NAA, namely the neutron capture or (n, gamma) reaction, is illustrated in Figure 1 . Creation of a compound nucleus forms in an excited state when a neutron interacts with the target nucleus via a non-elastic collision. The excitation energy of the compound nucleus is due to the binding energy of the neutron with the nucleus. The compound nucleus will almost instantaneously de-excite into a more stable configuration through emission of one or more characteristic prompt gamma rays. In many cases, this new configuration yields a radioactive nucleus which also de-excites (or decays) by emission of one or more characteristic delayed gamma rays, but at a much lower rate according to the unique half-life of the radioactive nucleus. Depending upon the particular radioactive species, half-lives can range from fractions of a second to several years.

In principle, therefore, with respect to the time of measurement, NAA falls into two categories: (1) prompt gamma-ray neutron activation analysis (PGNAA), where measurements take place during irradiation, or (2) delayed gamma-ray neutron activation analysis (DGNAA), where the measurements follow radioactive decay. The latter operational mode is more common; thus, when one mentions NAA it is generally assumed that measurement of the delayed gamma rays is intended. About 70% of the elements have properties suitable for measurement by NAA.

Diagram illustrating the process of neutron capture by a target nucleus followed by the emission of gamma rays.

The PGAA technique is generally performed by using a beam of neutrons extracted through a reactor beam port. Fluxes on samples irradiated in beams are in the order of one million times lower than on samples inside a reactor but detectors can be placed very close to the sample compensating for much of the loss in sensitivity due to flux. The PGAA technique is most applicable to elements with extremely high neutron capture cross-sections (B, Cd, Sm, and Gd); elements which decay too rapidly to be measured by DGAA; elements that produce only stable isotopes (e.g. light elements); or elements with weak decay gamma-ray intensities. 2D, 3D-analysis of (main) elements distribution in the samples can be performed by PGAA.

DGNAA (sometimes called conventional NAA) is useful for the vast majority of elements that produce radioactive nuclides. The technique is flexible with respect to time such that the sensitivity for a long-lived radionuclide that suffers from interference by a shorter-lived radionuclide can be improved by waiting for the short-lived radionuclide to decay or quite the contrary, the sensitivity for short-lived isotopes can be improved by reducing the time irradiation to minimize the interference of long-lived isotopes. This selectivity is a key advantage of DGNAA over other analytical methods.

In most cases, the radioactive isotopes decay and emit beta particles accompanied by gamma quanta of characteristic energies, and the radiation can be used both to identify and accurately quantify the elements of the sample. Subsequent to irradiation, the samples can be measured instrumentally by a high resolution semiconductor detector, or for better sensitivity, chemical separations can also be applied to reduce interferences. The qualitative characteristics are: the energy of the emitted gamma quanta (Eγ) and the half life of the nuclide (T ½ ). The quantitative characteristic is: the Iγ intensity, which is the number of gamma quanta of energy Eγ measured per unit time.

The n-gamma reaction is the fundamental reaction for neutron activation analysis. For example, consider the following reaction:

58 Fe is a stable isotope of iron while 59 Fe is a radioactive isotope. The gamma rays emitted during the decay of the 59 Fe nucleus have energies of 142.4, 1099.2, and 1291.6 KeV, and these gamma ray energies are characteristic for this nuclide (see figure 2) [ 2 ]. The probability of a neutron interacting with a nucleus is a function of the neutron energy. This probability is referred to as the capture cross-section, and each nuclide has its own neutron energy-capture cross-section relationship. For many nuclides, the capture cross-section is greatest for low energy neutrons (referred to as thermal neutrons). Some nuclides have greater capture cross-sections for higher energy neutrons (epithermal neutrons). For routine neutron activation analysis we are generally looking at nuclides that are activated by thermal neutrons.

The most common reaction occurring in NAA is the (n,γ) reaction, but also reactions such as (n,p), (n,α), (n,n′) and (n,2n) are important. The neutron cross section, σ, is a measure for the probability that a reaction will take place, and can be strongly different for different reaction types, elements and energy distributions of the bombarding neutrons. Some nuclei, like 235U are fissionable by neutron capture and the reaction is denoted as (n,f), yielding fission products and fast (highly energetic) neutrons [ 1 ].

Decay scheme of 59 Fe.

Neutrons are produced via

Isotopic neutron sources, like 226 Ra(Be), 124 Sb(Be), 241 Am(Be), 252 Cf. The neutrons have different energy distributions with a maximum in the order of 3–4 MeV; the total output is typically 10 5 –10 7 s -1 GBq -1 or, for 252 Cf, 2.2 10 12 s -1 g -1 .

Particle accelerators or neutron generators. The most common types are based on the acceleration of deuterium ions towards a target containing either deuterium or tritium, resulting in the reactions 2H(2H,n)3He and 3H(2H,n)4He, respectively. The first reaction, often denoted as (D,D), yields monoenergetic neutrons of 2.5 MeV and typical outputs in the order of 10 8 –10 10 s −1 ; the second reaction (D,T) results in monoenergetic neutrons of 14.7 MeV and outputs of 10 9 –10 11 s −1 .

Nuclear research reactors. The neutron energy distribution depends on design of the reactor and its irradiation facilities. An example of an energy distribution in a light water moderated reactor is given in Fig. 2 .3 from which it can be seen that the major part of the neutrons has a much lower energy distribution that in isotopic sources and neutron generators. The neutron output of research reactors is often quoted as neutron fluence rate in an irradiation facility and varies, depending on reactor design and reactor power, between 10 15 and 10 18 m -2 s -1 .

Owing to the high neutron flux, experimental nuclear reactors operating in the maximum thermal power region of 100 kW -10 MW with a maximum thermal neutron flux of 10 12 -10 14 neutrons cm -2 s -1 are the most efficient neutron sources for high sensitivity activation analysis induced by epithermal and thermal neutrons. The reason for the high sensitivity is that the cross section of neutron activation is high in the thermal region for the majority of the elements. There is a wide distribution of neutron energy in a reactor and, therefore, interfering reactions must be considered. In order to take these reactions into account, the neutron spectrum in the channels of irradiation should be known exactly. E.g. if thermal neutron irradiations are required, the most thermalized channels should be chosen.

Although there are several types of neutron sources (reactors, accelerators, and radioisotopic neutron emitters) one can use for NAA, nuclear reactors with their high fluxes of neutrons from uranium fission offer the highest available sensitivities for most elements. Different types of reactors and different positions within a reactor can vary considerably with regard to their neutron energy distributions and fluxes due to the materials used to moderate (or reduce the energies of) the primary fission neutrons. This is further elaborated in the title “Derivation of the measurement equation”. In our case, the NAA method is based on the use of neutron flux in several irradiation channels of Es-Salam Research reactor. In 2011, Hamidatou L et Al., reported “Experimental and MCNP calculations of neutron flux parameters in irradiation channel at Es-Salam reactor” the core modelling to calculate neutron spectra using experimental and MCNP approaches. The Es-Salam reactor was designed for a thermal power output of 15 Mw, with 72 cylindrical cluster fuel elements; each fuel element consists of 12 cylindrical rods of low enriched UO2. In addition the both of fuel throttle tube of the cluster and fuel element tube encloses heavy water as moderator and coolant. The fuel elements are arranged on a heavy water square lattice. The core of the reactor is constituted by a grid containing 72 fuel elements, 12 rods for reactivity control and two experimental channels.

There is also a heavy water in the middle of the core including five experimental channels called inner reflector, In addition, all fuel elements have a reflector at each end called upper and lower reflector. The core is reflected laterally by heavy water maintained in aluminium tank followed by the graphite.

2.2. Neutron activation analysis procedure

In the majority of INAA procedures thermal reactor neutrons are used for the activation: neutrons in thermal equilibrium with their environment. Sometimes activation with epithermal reactor neutrons (neutrons in the process of slowing down after their formation from fission of 235U) is preferred to enhance the activation of elements with a high ratio of resonance neutron cross section over thermal neutron cross section relatively to the activation of elements with a lower such a ratio. In principle materials can be activated in any physical state, viz. solid, liquid or gaseous. There is no fundamental necessity to convert solid material into a solution prior to activation; INAA is essentially considered to be a non-destructive method although under certain conditions some material damage may occur due to thermal heating, radiolysis and radiation tracks by e.g. fission fragments and α-radiation emitting nuclei. It is essential to have more than two or three qualified full-time member of the staff with responsibility for the NAA facilities. They should be able to control the counting equipment and have good knowledge of basic principles of the technique. In addition, the facility users and the operators must establish a good channel of communication. Other support staff will be required to maintain and improve the equipment and facility. It seems, therefore, a multi-disciplinary team could run the NAA system well.

The analytical procedure is based on four steps:

Step 1: sample preparation ( Figure 3) means in most cases only heating or freeze drying, crushing or pulverization, fractionating or pelletizing, evaporation or pre-concentration, put through a sieve, homogenising, weighing, washing, check of impurities (blank test), encapsulation and sealing irradiation vial, as well as the selection of the best analytical process and the preparation of the standards. The laboratory ambiance is also important for preservation and storage of the samples. Standardization is the basis for good accuracy of analytical tools and often depends on particular technology, facility and personnel. For production of accurate data, careful attention to all possible errors in preparing single or multi-element standards is important, and standards must be well chosen depending on the nature of the samples.

Some instruments and materials used for the sample preparation.

Step 2: irradiation of samples can be taken from the various types of neutron sources according to need and availability. For the INAA, one pneumatic transfer system installed in the horizontal channel at Es-Salam research reactor for short irradiation of samples ( Figure 4) . In addition, two vertical channels located in different sites of the heavy water moderator and the graphite reflector have been used for long irradiations. The neutron spectrum parameters at different irradiation channels such as alpha, f, Tn, etc are experimentally determined using cadmium ratio, cadmium cover, bare triple monitor and bi-isotopic methods using HΦgdhal convention and Westcott formalism Table 1 and Table 2 . The calibration of the irradiation positions has been carried out to implement the k 0 -NAA in our laboratory.

The parameters α, f and r ( α ) T n / T 0 obtained by different methods.

Neutron spectrum parameters in the irradiation site at es-Salam research reactor.

Step 3: after the irradiation the measurement is performed after a suitable cooling time (t c ). In NAA, nearly exclusively the (energy of the) gamma radiation is measured because of its higher penetrating power of this type of radiation, and the selectivity that can be obtained from distinct energies of the photons - differently from beta radiation which is a continuous energy distribution. The interaction of gamma- and X-radiation with matter results, among others, in ionization processes and subsequent generation of electrical signals (currents) that can be detected and recorded.

The instrumentation used to measure gamma rays from radioactive samples generally consists of a semiconductor detector, associated electronics, and a computer-based multi-channel analyzer (MCA/computer).

Pneumatic system for short irradiations using a thermal neutron flux at Es-Salam research reactor.

Most NAA labs operate one or more hyper-pure germanium (HPGe) detectors, which operate at liquid nitrogen temperature (77 K). Although HPGe detectors come in many different shapes and sizes, the most common shape is coaxial. These detectors are very useful for measurement of gamma rays with energies in the range from about 60 keV to 3.0 MeV. The two most important characteristics a HPGe detector are its resolution and efficiency. Other characteristics to consider are peak shape, peak-to-Compton ratio, pulse rise time, crystal dimensions or shape, and price. The detector’s resolution is a measure of its ability to separate closely spaced peaks in the spectrum, and, in general, the resolution is specified in terms of the full width at half maximum (FWHM) of the 122 keV photopeak of 57 Co and the 1,332 keV photopeak of 60 Co. For most NAA applications, a detector with 0.5 keV resolution or less at 122 keV and 1.8 keV or less at 1,332 keV is sufficient. Detector efficiency for a given detector depends on gamma-ray energy and the sample and detector geometry, i.e. subtended solid angle. Of course, a larger volume detector will have a higher efficiency.

At Es-Salam NAA Lab, four gamma-ray spectrometers of Canberra for which one of them consists of a HPGe detector 35% relative efficiency connected with Genie 2k Inspector and the three other spectrometers are composed of detectors (30, 35 and 45 % relative efficiency) connected with a three Lynx® Digital Signal Analyser, It is a 32K channel integrated signal analyzer based on advanced digital signal processing (DSP) techniques. All spectrometers operate with Genie™2000 spectroscopy software. A radiation detector therefore consists of an absorbing material in which at least part of the radiation energy is converted into detectable products, and a system for the detection of these products. Figure 5 illustrates Gamma-ray spectroscopy systems. The detectors are kept at liquid nitrogen temperatures (dewers under cave). The boxes in the left and in the right of the computer are the Lynx Digital Spectrometer Processing.

Gamma-ray spectroscopy systems in NAA/CRNB laboratory.

Step 5: Measurement, evaluation and calculation involve taking the gamma spectra and the calculating trace element concentrations of the sample and preparation of the NAA report.

In this part of work, Peter bode describes clearly in his paper [ 1 ] the analysis procedure of gamma-spectrum to the determination of the amount of element in sample. The acquisition of gamma spectrum Fig.6 and Fig.7 via the spectroscopy system Fig. 5 is analyzed to identify the radionuclides produced and their amounts of radioactivity in order to derive the target elements from which they have been produced and their masses in the activated sample. The spectrum analysis starts with the determination of the location of the (centroids of the) peaks. Secondly, the peaks are fitted to obtain their precise positions and net peak areas. The Analytical protocol adopted in our NAA laboratory is presented in Fig.8 .

Gamma-ray spectrum showing several short-lived elements measured in a CRM-DSD-12 standard irradiated at Es-salam research reactor for 30 seconds, decayed for 30.7 minutes, and counted for 5 minutes with an HPGe detector.

The positions – often expressed as channel numbers of the memory of a multi-channel pulse height analyzer – can be converted into the energies of the radiation emitted; this is the basis for the identification of the radioactive nuclei. On basis of knowledge of possible nuclear reactions upon neutron activation, the (stable) element composition is derived. The values of the net peak areas can be used to calculate the amounts of radioactivity of the radionuclides using the full energy photopeak efficiency of the detector.

The amounts (mass) of the elements may then be determined if the neutron fluence rate and cross sections are known. In the practice, however, the masses of the elements are determined from the net peak areas by comparison with the induced radioactivity of the same neutron activation produced radionuclides from known amounts of the element of interest. The combination of energy of emitted radiation, relative intensities if photons of different energies are emitted and the half life of the radionuclide is unique for each radionuclide, and forms the basis of the qualitative information in NAA. The amount of the radiation is directly proportional to the number of radioactive nuclei produced (and decaying), and thus with the number of nuclei of the stable isotope that underwent the nuclear reaction. It provides the quantitative information in NAA.

Gamma-ray spectrum ( a ) from 0 to 450 keV, ( b ) from 450 to 1000 keV and ( c ) from 1000 to 2000 keV: showing medium- and long-lived elements measured in a sample of CRM-GSD-12 standard irradiated at Es-salam research reactor for 4 hours, decayed for 5 days, and counted for 90 minutes on a HPGe detector.

The measured in NAA – the quantity intended to be measured – is the total mass of a given element in a test portion of a sample of a given matrix in all physico-chemical states. The quantity ‘subject to measurement’ is the number of disintegrating nuclei of a radionuclide. The measurement results in the number of counts in a given period of time, from which the disintegration rate and the number of disintegrating nuclei is calculated; the latter number is directly proportional to the number of nuclei of the stable isotope subject to the nuclear reaction, and thus to the number of nuclei of the element, which finally provides information on the mass and amount of substance of that element (see Eq. 16) . An example of typical ranges of experimental conditions is given in Table 3 [1].

In practice, our laboratory proceeds in the treatment of spectra and calculation of elemental concentrations of analyzed samples according the approach illustrated in figure 8 .

Analytical protocol adopted in NAA/CRNB laboratory [ 13 ].

Example of typical ranges of experimental conditions of an INAA procedure.

2.3. Derivation of the measurement equation

The reaction rate R per nucleus capturing a neutron is given by:

σ (v) is the (n,γ) cross section (in cm 2 ; 1 barn (b) = 10 -24 cm 2 ) at neutron velocity v (in cm s -1 );

σ (E) is the (n,γ) cross section (in cm 2 ) at neutron energy E (in eV);

Φ’(v) is the neutron flux per unit of velocity interval (in cm -3 ) at neutron velocity v;

n’(v) is the neutron density per unit of velocity interval (in cm -4 s) at neutron velocity v;

Φ’(E) is the neutron flux per unit of energy interval (in cm -2 s -1 eV -1 ) at neutron energy E.

In Eq.(1) , σ (v) = σ (E) with E (in erg = 6.2415.10 11 eV) = ½ m n v 2 [m n rest mass of the neutron = 1.6749 10 -24 g]. Furthermore, per definition, φ’(v) dv = φ’(E)dE (both in cm -2 s -1 ).

In Eq.1 , the functions σ(v) [= σ (E)] and φ’(v) [ φ’(E)] are complex and are respectively depending on the (n,γ) reaction and on the irradiation site.

In 1987, F De Corte describes in his Aggregate thesis “Chapter 1: fundamentals [ 3 ] that the introduction of some generally valid characteristics yields the possibility of avoiding the actual integration and describing accurately the reaction rate in a relatively simple way by means of so-called formalisms or conventions. In short, these characteristics are:

In nuclear research reactors – which are intense sources of neutrons – three types of neutrons can be distinguished. The neutron flux distribution can be divided into three components (see Figure 9) :

Fission or fast neutrons released in the fission of 235U. Their energy distribution ranges from 100 keV to 25 MeV with a maximum fraction at 2 MeV. These neutrons are slowed down by interaction with a moderator, e.g. H2O, to enhance the probability of them causing a fission chain reaction in the 235U.

The epithermal neutron component consists of neutrons (energies from 0.5 eV to about 100 keV). A cadmium foil 1 mm thick absorbs all thermal neutrons but will allow epithermal and fast neutrons above 0.5 eV in energy to pass through. Both thermal and epithermal neutrons induce (n,γ) reactions on target nuclei.

The thermal neutron component consists of low-energy neutrons (energies below 0.5 eV) in thermal equilibrium with atoms in the reactor's moderator. At room temperature, the energy spectrum of thermal neutrons is best described by a Maxwell-Boltzmann distribution with a mean energy of 0.025 eV and a most probable velocity of 2200 m/s. In general, a 1 MW reactor has a peak thermal neutron flux of approximately 10 13 n/cm 2 .

The (n,γ) cross section function, σ(v) versus v can be interpreted as a σ(v) ~ 1/v dependence, or σ (E) ~ 1/E 1/2 dependence [log σ (E) versus log E is linear with slope -1/2], on which (above some eV) several resonances are superposed see Figure 10 taken from http://thorea.wikia.com/wiki/Thermal,_Epithermal_and_Fast_Neutron_Spectra web page.

A typical reactor neutron energy spectrum showing the various components used to describe the neutron energy regions.

Relation between neutron cross section and neutron energy for major actinides (n, capture).

An NAA technique that employs only epithermal neutrons to induce (n,γ) reactions by irradiating the samples being analyzed inside either cadmium or boron a shield is called epithermal neutron activation analysis (ENAA).

The production of radioactive nuclei is described by:

In which N 0 number of target nuclei, N is the number of radioactive nuclei, λ is the decay constant in s −1 . The disintegration rate of the produced radionuclide at the end of the irradiation time ti follows from:

D is the disintegration rate in Bq of the produced radionuclide, assuming that N=0 at t=0 and N0=constant.

The dependence of the activation cross section and neutron fluence rate to the neutron energy can be taken into account in Eq. (1) by dividing the neutron spectrum into a thermal and an epithermal region; the division is made at En=0.55 eV (the so-called cadmium cut-off energy). This approach is commonly known as the Høgdahl convention [ 4 ].

The integral in Eq. (1) can then be rewritten as:

The first term can be integrated straightforward:

is called the thermal neutron density, with Φ th =nv 0 ,

Φ th is the conventional thermal neutron fluence rate, m −2 s −1 , for energies up to the Cd cut-off energy of 0.55 eV;

σ 0 is the thermal neutron activation cross section, m 2 , at 0.025 eV;

v 0 is the most probable neutron velocity at 20 °C: 2200 m s −1 .

The second term is re-formulated in terms of neutron energy rather than neutron velocity and the infinite dilution resonance integral I 0 – which effectively is also a cross section (m 2 ) – is introduced:

Here, Φ epi the conventional epithermal neutron fluence rate per unit energy interval, at 1 eV.

From this definition of I 0 it can be seen that it assumes that the energy dependency of the epithermal neutron fluence rate is proportional to 1/En. This requirement is fulfilled to a good approximation by most of the (n,γ) reactions.

In the practice of nuclear reactor facilities the epithermal neutron fluence rate Φepi is not precisely following the inverse proportionality to the neutron energy; the small deviation can be accounted for by introducing an epithermal fluence rate distribution parameter α:

The expression for the reaction rate can thus be re-written as:

Expressing the ratio of the thermal neutron fluence rate and the epithermal neutron fluence rate as f=Φ th /Φ epi and the ratio of the resonance integral and the thermal activation cross section as Q 0 (α)= I 0 (α)/σ 0 , an effective cross section can be defined:

It simplifies the Eq. (10) for the reaction rate to:

This reaction rate applies to infinite thin objects. In objects of defined dimensions, the inside part will experience a lower neutron fluence rate than the outside part because neutrons are removed by absorption.

The nuclear transformations are established by measurement of the number of nuclear decays. The number of activated nuclei N(t i ,t d ) present at the start of the measurement is given by:

and the number of nuclei ΔN disintegrating during the measurement is given by:

in which t d is the decay or waiting time, i.e. the time between the end of the irradiation and the start of the measurement t m is the duration of the measurement. Additional correction resulting from high counting rates may be necessary depending upon the gamma-ray spectrometer hardware used as illustrated in chapter 2 [1]. Replacing the number of target nuclei N 0 by (N Av m)/M and using the Eq. (12) for the reaction rate, the resulting net counts C in a peak in the spectrum corresponding with a given photon energy is approximated by the activation formula:

N p is the net counts in the γ-ray peak of E γ ;

N Av is the Avogadro's number in mol −1 ;

θ is isotopic abundance of the target isotope;

m x is the mass of the irradiated element in g;

M a is the atomic mass in g mol −1 ;

I is the gamma-ray abundance, i.e. the probability of the disintegrating nucleus emitting a photon of E γ (photons disintegration −1 );

ε is the full energy photopeak efficiency of the detector, i.e. the probability that an emitted photon of given energy will be detected and contribute to the photopeak at energy E γ in the spectrum.

Although the photons emitted have energies ranging from tens of keVs to MeVs and have high penetrating powers, they still can be absorbed or scattered in the sample itself depending on the sample size, composition and photon energy. This effect is called gamma-ray self-attenuation. Also, two or more photons may be detected simultaneously within the time resolution of the detector; this effect is called summation.

Eq. (15) can be simply rewritten towards the measurement equation of NAA, which shows how the mass of an element measured can be derived from the net peak area C:

2.4. Standardization

Standardization is based on the determination of the proportionality factors F that relate the net peak areas in the gamma-ray spectrum to the amounts of the elements present in the sample under given experimental conditions:

Both absolute and relative methods of calibration exist.

2.4.1.Absolute calibration

The values of the physical parameters determining the proportionality factor θ, N Av , M, σ eff I, λ, are taken from literature. The parameters σ eff respectively I, λ are not precisely known for many (n,γ) reactions and radionuclides, and in some cases θ is also not accurately known. Since the various parameters were often achieved via independent methods, their individual uncertainties will add up in the combined uncertainty of measurement of the elemental amounts, leading to a relatively large combined standard uncertainty. Moreover, the metrological traceability of the values of the physical constants is not known for all radionuclides. The other parameters N p , m x , Φ, ε, t i , t d , t m are determined, calculated or measured for the given circumstances and uncertainties can be established.

2.4.2. Relative calibration

Direct comparator method

The unknown sample is irradiated together with a calibrator containing a known amount of the element(s) of interest. The calibrator is measured under the same conditions as the sample (sample-to-detector distance, equivalent sample size and if possible equivalent in composition). From comparison of the net peak areas in the two measured spectra the mass of the element of interest can be calculated:

in which m x (unk), m x (cal) mass of the element of interest, in the unknown sample and the calibrator, respectively in g.

In this procedure many of the experimental parameters - such as neutron fluence rate, cross section and photopeak efficiency cancel out at the calculation of the mass and the remaining parameters are all known. This calibration procedure is used if the highest degree of accuracy is required.

The relative calibration on basis of element calibrators is not immediately suitable for laboratories aiming at the full multi-element powers of INAA. It takes considerable effort to prepare multi-element calibrators for all 70 elements measurable via NAA with adequate degree of accuracy in a volume closely matching the size and the shape of the samples. Single comparator method Multi-element INAA on basis of the relative calibration method is feasible when performed according to the principles of the single comparator method. Assuming stability in time of all relevant experimental conditions, calibrators for all elements are co-irradiated each in turn with the chosen single comparator element. Once the sensitivity for all elements relative to the comparator element has been determined (expressed as the so-called k-factor, see below), only the comparator element has to be used in routine measurements instead of individual calibrators for each element. The single comparator method for multi-element INAA was based on the ratio of proportionality factors of the element of interest and of the comparator element after correction for saturation, decay, counting and sample weights defined the k-factor for each element i as:

Masses for each element i then can be calculated from these k i factors; for an element determined via a directly produced radionuclide the mass m x (unk) follows from:

where: m x (comp) is the mass of element x in comparator in g.

These experimentally determined k-factors are often more accurate than when calculated on basis of literature data as in the absolute calibration method. However, the k-factors are only valid for a specific detector, a specific counting geometry and irradiation facility, and remain valid only as long as the neutron fluence rate parameters of the irradiation facility remain stable. The single comparator method requires laborious calibrations in advance, and finally yield relatively (compared to the direct comparator method) higher uncertainties of the measured values. Moreover, it requires experimental determination of the photopeak efficiencies of the detector. Metrological traceability of the measured values to the S.I. may be demonstrated.

The k 0 -comparator method

The k 0 -based neutron activation analysis ( k 0 -NAA) technique, developed in 1970s, is being increasingly used for multielement analysis in a variety of matrices using reactor neutrons [ 4 - 10 ]. In our research reactor, the k 0 -method was successfully developed using the Høgdahl formalism [ 11 ]. In the k 0-based neutron activation analysis the evaluation of the analytical result is based on the so-called k 0 - factors that are associated with each gamma-line in the gamma-spectrum of the activated sample. These factors replace nuclear constants, such as cross sections and gamma-emission probabilities, and are determined in specialized NAA laboratories. This technique has been reported to be flexible with respect to changes in irradiation and measuring conditions, to be simpler than the relative comparator technique in terms of experiments but involves more complex formulae and calculations, and to eliminate the need for using multielement standards. The k 0 -NAA technique, in general, uses input parameters such as (1) the epithermal neutron flux shape factor (α), (2) subcadmium-to-epithermal neutron flux ratio ( f ), (3) modified spectral index r ( α ) T n / T 0 , (4) Westcott’s g ( T n )-factor, (5) the full energy peak detection efficiency ( ε p ), and (6) nuclear data on Q 0 (ratio of resonance integral ( I 0 ) to thermal neutron cross section (σ 0 ) and k 0 . The parameters from (1) to (4) are dependent on each irradiation facility and the parameter (5) is dependent on each counting facility. The neutron field in a nuclear reactor contains an epithermal component that contributes to the sample neutron activation [ 12 ]. Furthermore, for nuclides with the Westcott’s g ( T n )-factor different from unity, the Høgdahl convention should not be applied and the neutron temperature should be introduced for application of a more sophisticated formalism [ 14 ], the Westcott formalism. These two formalisms should be taken into account in order to preserve the accuracy of k 0 -method.

The k 0 -NAA method is at present capable of tackling a large variety of analytical problems when it comes to the multi-element determination in many practical samples. In this part, we have published a paper [ 15 ] for which the determination of the Westcott and Høgdahl parameters have been carried out to assess the applicability of the k 0 -NAA method using the experimental system and irradiation channels at Es-Salam research reactor.

During the three last decades Frans de Corte and his co-workers focused their investigations to develop a method based on co-irradiation of a sample and a neutron flux monitor, such as gold and the use of a composite nuclear constant called k 0 -factor [ 3 , 16 ]. In addition, this method allows to analyze the sample without use the reference standard like INAA method. The k-factors have been defined as independent of neutron fluence rate parameters as well as of spectrometer characteristics. In this approach, the irradiation parameter (1+Q 0 (α)/f) ( Eq. (11) ) and the detection efficiency ε are separated in the expression (19) of the k-factor, which resulted at the definition of the k 0 -factor.

The applicability of HØGDAHL convention is restricted to (n,γ) reactions for which WESTCOTT’s g-factor is equal to unity (independent of neutron temperature), the cases for which WESTCOTT’s g = 1 [ 3 , 4 , 17 ], such as the reactions 151 Eu(n, γ) and 176 Lu(n, γ) are excluded from being dealt with. Compared with relative method k 0 -NAA is experimentally simpler (it eliminates the need for multi-element standards [ 3 , 18 ], but requires more complicated calculations [ 19 ]. In our research reactor, the k 0 -method was successfully developed using the HØGDAHL convention and WESTCOTT formalism [ 11 , 15 ]. The k 0 -method requires tedious characterizations of the irradiation and measurement conditions and results, like the single comparator method, in relatively high uncertainties of the measured values of the masses. Moreover, metrological traceability of the currently existing k 0 values and associated parameters to the S.I. is not yet transparent and most probably not possible. Summarizing, relative calibration by the direct comparator method renders the lowest uncertainties of the measured values whereas metrological traceability of these values to the S.I. can easily be demonstrated. As such, this approach is often preferred from a metrological viewpoint. The concentration of an element can be determined as:

Where: the indices x and Au refer to the sample and the monitor, respectively; W Au and W x represent the mass of the gold monitor and the sample (in g); N p is the measured peak area, corrected for dead time and true coincidence; S, D, C are the saturation, decay and counting factors, respectively; tm is the measuring time; G th and G e are the correction factors for thermal and epithermal neutron self shielding, respectively.

2.5. Sources errors

Many publications reported in literature [ 20 - 25 ] treat the concept of evaluation of uncertainties in large range of analytical techniques.

We can give in this part of chapter, the evaluation of uncertainties for neutron activation analysis measurements. Among the techniques of standardization the comparator method for which the individual uncertainty components associated with measurements made with neutron activation analysis (NAA) using the comparator method of standardization (calibration), as well as methods to evaluate each one of these uncertainty components [ 1 ].

This description assumes basic knowledge of the NAA method, and that experimental parameters including sample and standard masses, as well as activation, decay, and counting times have been optimized for each measurement. It also assumes that the neutron irradiation facilities and gamma-ray spectrometry systems have been characterized and optimized appropriately, and that the choice of irradiation facility and detection system is appropriate for the measurement performed. Careful and thoughtful experimental design is often the best means of reducing uncertainties. The comparator method involves irradiating and counting a known amount of each element under investigation using the same or very similar conditions as used for the unknown samples. Summarizing, relative calibration by the direct comparator method renders the lowest uncertainties of the measured values whereas metrological traceability of these values to the S.I. can easily be demonstrated. As such, this approach is often preferred from a metrological viewpoint. The measurement equation can be further simplified, by substituting:

Where: R θ is the ratio of isotopic abundances for unknown sample and calibrator, R ϕ is the ratio of neutron fluence rates (including fluence gradient, neutron self shielding, and scattering) for unknown sample and calibrator, R σ is the ratio of effective cross sections if neutron spectrum shape differs from unknown sample to calibrator, R ε is the ratio of counting efficiencies (differences due to geometry and γ-ray self shielding) for unknown sample and calibrator, blank is the mass of element x in the blank, f P is the correction for pulse pileup (correction method depends upon the actual hardware used) and f ltc is the correction for inadequacy of live time extension (correction method depends upon the actual hardware used)

Note that the R values are normally very close to unity, and all units are either SI-based or dimensionless ratios. Thus an uncertainty budget can be developed using only SI units and dimensionless ratios for an NAA measurement by evaluating the uncertainties for each of the terms in Eqs. (23) and (24) , and for any additional corrections required (e.g., interferences, dry mass conversion factors, etc.).

Uncertainties for some of the terms in Eq. (24) have multiple components. If we sub-divide the uncertainty for each term in the above equations into individual components, add terms for potential corrections, and separate into the four stages of the measurement process, including: pre-irradiation (sample preparation); irradiation; post-irradiation (gamma-ray spectrometry), and radiochemistry, we arrive at the complete list of individual uncertainty components for NAA listed below in Table 4 . Only uncertainties from the first three stages should be considered for instrumental neutron activation analysis (INAA) measurements, while all four stages should be considered for radiochemical neutron activation analysis (RNAA) measurements. More details are given in chapter 2 of reference [ 1 ] for each subsection of uncertainty component.

Complete list of individual uncertainty components for NAA measurements using the comparator method of standardization; line numbers in this table represent subsections.

2.6. Detection limits of NAA

The detection limit represents the ability of a given NAA procedure to determine the minimum amounts of an element reliably. The detection limit depends on the irradiation, the decay and the counting conditions. It also depends on the interference situation including such things as the ambient background, the Compton continuum from higher energy-rays, as well as any-ray spectrum interferences from such factors as the blank from pre-irradiation treatment and from packing materials. The detection limit is often calculated using Currie's formula:

where: DL is the detection limit and B is the background under a gamma-ray peak. This relation is valid only when the gamma-ray background (counting statistical error) is the major interference.

However, practically, the INAA detection limits depend on:

The amount of material to be irradiated and to be counted. This is often set by availability, sample encapsulation aspects and safety limits both related to irradiation (irradiation containers) and counting (e.g. with Ge well-type detectors), and possibly because of neutron self-shielding and gamma-ray self-absorption effects. For these reasons practically the sample mass is often limited to approximately 250 mg.

The neutron fluxes. These are clearly set by the available irradiation facilities.

The duration of the irradiation time. This is set by practical aspects, such as the limitations in total irradiation dose of the plastic containers because of radiation damage. The maximum irradiation time for polyethylene capsules is usually limited to several hours, for instance 5 hours at 5 × 10 17 m -2 s -1 .

The total induced radioactivity that can be measured is set by the state-of-the-art of counting and signal processing equipment, with additional radiation dose and shielding considerations. As an example, the maximum activity at the moment of counting may have to be limited to approximately 250 kBq.

The duration of the counting time. A very long counting time may set limits to the number of samples processed simultaneously in case the radioactivity decays considerably during this counting time. Moreover, it reduces sample throughput.

The total turn-around time. Although sometimes better detection limits may be obtained at long decay times, the demands regarding the turn-around time often imply that a compromise has to be found between the longest permissible decay time and customer satisfaction.

The detector size, counting geometry and background shielding. The detector's characteristics may be set in advance by availability but several options exist.

It all illustrates that the detection limit for a given element by INAA may be different for each individual type of material, and analysis conditions. In Table 5 are given, as an indication, typical detection limits as derived from the analysis of a plant and a soil material. Peter Bode in his PhD thesis, Instrumental and organizational aspects of a neutron activation analysis laboratory, the typical detection limits as derived from the analysis of a plant and a soil material given in table 5 [ 26 ].

Detection limits of elements in mg.kg -1 as observed in NAA procedure of plant material and a soil material.

3. Applications

It is hardly possible to provide a complete survey of current NAA applications; however, some trends can be identified [ 27 ]. At specialized institutions, NAA is widely used for analysis of samples within environmental specimen banking programmes [ 28 ]. The extensive use of NAA in environmental control and monitoring can be demonstrated by the large number of papers presented at two symposia organized by the IAEA in these fields: "Applications of Isotopes and Radiation in Conservation of the Environment" in 1992 [ 29 ] and "Harmonization of Health-Related Environmental Measurements Using Nuclear and Isotopic Techniques" in 1996 [ 30 ]. Similar trends can also be identified from the topics discussed at the regular conference on “Modern Trends in Activation Analysis (MTAA)” and at the symposia on "Nuclear Analytical Methods in the Life Sciences" [ 31 - 33 ]. Additional sources of recent information on utilizing NAA in selected fields, such as air pollution and environmental analysis, food, forensic science, geological and inorganic materials as well as water analysis can be found in the bi-annual reviews in Analytical Chemistry, for instance cf. Refs [ 34 - 42 ]. It follows from these reviews that NAA has been applied for determining many elements, usually trace elements, in the following fields and sample types:

Archaeology: samples and objects such as amber, bone, ceramics, coins, glasses, jewellery, metal artefacts and sculptures, mortars, paintings, pigments, pottery, raw materials, soils and clays, stone artefacts and sculptures can be easily analyzed by NAA.

Biomedicine: the samples and objects that can be analysed include: animal and human tissues activable tracers, bile, blood and blood components, bone, brain cell components and other tissues, breast tissue, cancerous tissues, colon, dialysis fluids, drugs and medicines, eye, faeces, foetus, gallstones, hair, implant corrosion, kidney and kidney stones, liver, lung, medical plants and herbs, milk, mineral availability, muscle, nails, placenta, snake venom, rat tissues (normal and diseased), teeth, dental enamel and dental fillings, thyroid, urine and urinary stones.

• nd : not detected.

Elemental concentrations in the medicinal seed samples (Black seeds, Fenugreek, Caraway).

Concentration of the major and minor (a) and trace (b) elements in the medicinal seed samples.

Environmental: in this domain, related fields concerned by NAA are: aerosols, atmospheric particulates (size fractionated), dust, fossil fuels and their ashes, flue gas, animals, birds, insects, fish, aquatic and marine biota, seaweed, algae, lichens, mosses, plants, trees (leaves, needles, tree bark), household and municipal waste, rain and horizontal precipitations (fog, icing, hoarfrost), soils, sediments and their leachates, sewage sludges, tobacco and tobacco smoke, surface and ground waters, volcanic gases.

Recently, our laboratory is strongly involved in various areas of application of k 0 -NAA. The present work focuses on the application of the k 0 -NAA method in Nutritional and Health-Related Environmental field [ 44 ]. Tobacco holds a leading position among different commodities of human consumption. The adverse health effects of toxic and trace elements in tobacco smoke on smokers and non-smokers are a special concern. In the present study, the concentration of 24 trace elements in cigarette tobacco of five different brands of Algerian and American cigarettes have been determined by k 0 -based INAA method. The results were compared with those obtained for samples from Iranian, Turkish, Brazilian and Mexican cigarettes tobacco. To evaluate the accurate of the results the SRM IAEA-140/TM was executed.

A multi-element analysis procedure based on the k 0 -NAA method was developed at Es-Salam research reactor allowing to simultaneously determine concentrations for 24 elements (As, Ba, Br, Ca, Ce, Co, Cr, Cs, Eu, Fe, Hf, K, La, Na, Rb, Sb, Sc, Se, Sm, Sr, Ta, Tb, Th, Zn). The determination of toxic and trace elements in cigarette tobacco is important both from the point of view of health studies connected with smoking and more general aspects of the uptake of trace elements by plants ( table 7) . Because of its great sensitivity, k 0 -NAA method is very suitable for determination of heavy metals such as As, Sb, Se and Zn. The accuracy of the results was checked by the analysis of standard reference material and good agreement was obtained with certified or literature values. The results of Algerian tobacco ( table 8) were compared with analyses of Turkey [ 45 ], Iran [ 46 ], Mexican [ 47 ] and Brazilian tobacco [ 48 ].

Concentration values (mg kg-1) of five brands of tobacco by k 0 -NAA method.

Comparison between our results (Algerian cigarettes tobacco) and those reported in the literature.

Forensics: bomb debris, bullet lead, explosives detection, glass fragments, paint, hair, gunshot residue swabs, shotgun pellets.

Geology and geochemistry: asbestos, bore hole samples, bulk coals and coal products, coal and oil shale components, crude oils, kerosene, petroleum, cosmo-chemical samples, cosmic dust, lunar samples, coral, diamonds, exploration and geochemistry, meteorites, ocean nodules, rocks, sediments, soils, glacial till, ores and separated minerals.

Industrial products: alloys, catalysts, ceramics and refractory materials, coatings, electronic materials, fertilizers, fissile material detection and other safeguard materials, graphite, high purity and high-tech materials, integrated circuit packing materials, online, flow analysis, oil products and solvents, pharmaceutical products, plastics, process control applications, semiconductors, pure silicon and silicon processing, silicon dioxide, NAA irradiation vials, textile dyes, thin metal layers on various substrates.

Nutrition: composite diets, foods, food colours, grains, honey, seeds, spices, vegetables, milk and milk formulae, yeast. In this chapter, we focus on the application of the k 0 method of instrumental neutron activation analysis in Nutritional and Health-Related Environmental field [ 49 ]. Three kinds of milk were purchased in the powder form from local supermarket. The samples of milk powder were analyzed using k 0 -NAA method. Concentrations of six elements Br, Ca, K, Na, Rb and Zn have been determined by long irradiation time with a thermal and epithermal flux of 4.7.10 12 n.cm –2 .s –1 and 2.29.10 11 n.cm –2 .s –1 , respectively (see table 9) . The reactor neutron spectrum and detection efficiency calibration parameters such as α, f and εp have been used for the calculation of elemental concentrations. The analytical results for three kinds of milk using k 0 -NAA are compared with the certified values of SRMs. In this work, we have determined six elements in three kinds of milk and two reference materials, IAEA-153 and IAEA-155. The elements Br, Ca, K, Na, Rb and Zn were determined in each kind of the three samples of milk.

Concentration values of Milk: M1, M2 and M3; units are in mg/kg, NB: (value) is the concentration value of indicated by producer.

Comparison of k 0 -NAA data to certified values for IAEA-153 and IAEA-155.

The accuracy of the measurements was evaluated by analyzing two SRMs Whey powder AIEA-155 and Milk powder AIEA-153. The analysis results illustrated in figure 12 showed that the deviations between experimental and certified values were mostly less than 10%.

As an example, an investigation in the nutrition field was carried out by the radiochemical neutron activation analysis to the proportioning of iodine in food salt [ 50 ].

Quality assurance: this include analysis of reference materials, certification of element contents and homogeneity testing of mainly biological and environmental reference materials of chemical composition and methods inter-comparisons. Additional information about these applications can be found in the Proceedings of the Int. Symposia on Biological and Environmental Reference Materials (BERM). In 2012, Hamidatou L et all reported “k0-NAA quality assessment in an Algerian laboratory by analysis of SMELS and four IAEA reference materials using Es-Salam Research reactor” the internal quality control of the k0-NAA technique [51]. The concept of QC/QA, internal and external validation is considered as an advanced stage in the life cycle of an analytical method.

Our contribution in this domain is considered as periodic activities. Since the Nineties our laboratory participated through AFRA/AIEA projects in different inter-laboratory proficiency tests. Recently, our laboratory was participated in four inter-comparison tests organized by IAEA within the framework of the AFRA project to assess the analytical performance of 18 analytical laboratories participating in the RAF /4/022 project, Enhancement of Research Reactor Utilization and Safety by taking part in analytical proficiency testing IAEA in conjunction with WEPAL, the Wageningen Evaluating Programs for Analytical Laboratories. The Proficiency Testing tests related to the determination of major, minor and trace elements in materials of the International Soil and Plant Analytical Exchange material (Wepal codes ISE, IPE).

Neutron flux characterization: theoretical and experimental study, calibration of irradiation channels, simulations using Monte Carlo Code. In general, the implementation of new techniques based on the neutron beams or flux around the research reactors needs the knowledge of the essential parameters of neutron flux in different sites to obtain a better precision during the development.

In this context, we give a great interest in the neutron study for our irradiation channels by making periodic calibrations using experimental and simulation approaches [ 11 , 15 , 52 ].

4. Conclusions

NAA plays a complementary role in materials analysis in an industrial analytical laboratory. There are applications where it is highly desirable, and may play the dominant role as the method of choice e.g. bulk analysis of Si. The advantages of NAA are still the minimum sample preparation and ultra high sensitivity while turnaround time and lack of spatial resolution is a significant limitation.

The many diverse applications in varied fields show that NAA is extremely useful, even though it is a relatively simple analytical method. Irradiation of samples may be done at nuclear reactors that offer such services. Such centres are easily accessible nowadays. Even if these centres are inaccessible, other neutron sources that emit thermal neutrons may be used. Hence any laboratory that has a gamma counter can perform NAA experiments. Development of research programs based on NAA is accessible to any laboratory that is willing to invest a minimal amount of funds. In this chapter, we have presented the neutron activation analysis in different angles such as: basis principles, derivation of several equations, techniques, procedures, etc. In addition, we have associated in each part of general work, some examples of our technical developments and applications of NAA method in several fields. All analytical works were executed in our centre using irradiation facilities of Es-Salam research reactor and all necessary equipments installed in the NAA department to cover all steps of analytical process.

Acknowledgments

Thanks are due to Dr Derdour Mohamed the responsible of COMENA and Mr Kerris Abdelmoumen General Director of CRNB for financial support. Grateful acknowledgment is made to Mr Salhi Mhamed the director of techniques and nuclear applications division for his highly valuable assistance. Special thanks are due to all colleagues involved for their help during fifteen years.

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© 2013 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1.9: Neutron Activation Analysis (NAA)

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Introduction

Neutron activation analysis (NAA) is a non-destructive analytical method commonly used to determine the identities and concentrations of elements within a variety of materials. Unlike many other analytical techniques, NAA is based on nuclear rather than electronic transitions. In NAA, samples are subjected to neutron radiation (i.e., bombarded with neutrons), which causes the elements in the sample to capture free neutrons and form radioactive isotopes, such as

\[ ^{59}_{27}\ce{Co} + ^1_0 n \rightarrow ^{60}_{27}\ce{Co} \nonumber. \]

The excited isotope undergoes nuclear decay and loses energy by emitting a series of particles that can include neutrons, protons, alpha particles, beta particles, and high-energy gamma ray photons. Each element on the periodic table has a unique emission and decay path that allows the identity and concentration of the element to be determined.

Almost eighty years ago in 1936, George de Hevesy and Hilde Levi published the first paper on the process of neutron activation analysis. They had discovered that rare earth elements such as dysprosium became radioactive after being activated by thermal neutrons from a radon-beryllium ( 266 Ra + Be) source. Using a Geiger counter to count the beta particles emitted, Hevesy and Levi were able to identify the rare earth elements by half-life. This discovery led to the increasingly popular process of inducing radioactivity and observing the resulting nuclear decay in order to identify an element, a process we now know as NAA. In the years immediately following Hevesy and Levi’s discovery, however, the advancement of this technique was restricted by the lack of stable neutron sources and adequate spectrometry equipment. Even with the development of charged-particle accelerators in the 1930s, analyzing multi-element samples remained time-consuming and tedious. The method was improved in the mid-1940s with the availability of the X-10 reactor at the Oak Ridge National Laboratory, the first research-type nuclear reactor. As compared with the earlier neutron sources used, this reactor increased the sensitivity of NAA by a factor of a million. Yet the detection step of NAA still revolved around Geiger or proportional counters; thus, many technological advancements were still to come. As technology has progressed in the recent decades, the NAA method has grown tremendously, and scientists now have a plethora of neutron sources and detectors to choose from when analyzing a sample with NAA.

Sample preparation

In order to analyze a material with NAA, a small sample of at least 50 milligrams must be obtained from the material, usually by drilling. It is suggested that two different samples are obtained from the material using two drill bits of different compositions. This will show any contamination from the drill bits and, thus, minimize error. Prior to irradiation, the small samples are encapsulated in vials of either quartz or high purity linear polyethylene.

How it Works

Neutron activation analysis works through the processes of neutron activation and radioactive decay. In neutron activation, radioactivity is induced by bombarding a sample with free neutrons from a neuron source. The target atomic nucleus captures a free neutron and, in turn, enters an excited state. This excited and therefore unstable isotope undergoes nuclear decay, a process in which the unstable nucleus emits a series of particles that can include neutrons, protons, alpha, and beta particles in an effort to return to a low-energy, stable state. As suggested by the several different particles of ionizing radiation listed above, there are many different types of nuclear decay possible. These are summarized in the figure below.

An additional type of nuclear decay is that of gamma radiation (denoted as γ), a process in which the excited nucleus emits high-energy gamma ray photons. There is no change in either neutron number N or atomic number Z, yet the nucleus undergoes a nuclear transformation involving the loss of energy. In order to distinguish the higher energy parent nucleus (prior to gamma decay) from the lower energy daughter nucleus (after gamma decay), the mass number of the parent nucleus is labeled with the letter m , which means “metastable.” An example of gamma radiation with the element technetium is shown here.

\[ ^{99m}_{43}\ce{Tc} \rightarrow ^{99}_{43}\ce{Tc} + ^0_0\gamma \nonumber \]

In NAA, the radioactive nuclei in the sample undergo both gamma and particle nuclear decay. The figure below presents a schematic example of nuclear decay. After capturing a free neutron, the excited 60m Co nucleus undergoes an internal transformation by emitting gamma rays. The lower-energy daughter nucleus 60 Co, which is still radioactive, then emits a beta particle. This results in a high-energy 60 Ni nucleus, which once again undergoes an internal transformation by emitting gamma rays. The nucleus then reaches the stable 60 Ni state.

Although alpha and beta particle detectors do exist, most detectors used in NAA are designed to detect the gamma rays that are emitted from the excited nuclei following neutron capture. Each element has a unique radioactive emission and decay path that is scientifically known. Thus, based on the path and the spectrum produced by the instrument, NAA can determine the identity and concentration of the element.

Neutron Sources

As mentioned above, there are many different neutron sources that can be used in modern-day NAA. A chart comparing three common sources is shown in the table below.

Gamma and Particle Detectors

As mentioned earlier, most detectors used in NAA are designed to detect the gamma rays emitted from the decaying nucleus. Two widely used gamma detectors are the scintillation type and the semiconductor type. The former uses a sensitive crystal, often sodium iodide that is doped with thallium (NaI(Tl)), that emits light when gamma rays strike it. Semiconductor detectors, on the other hand, use germanium to form a diode that produces a signal in response to gamma radiation. The signal produced is proportional to the energy of the emitted gamma radiation. Both types of gamma detectors have excellent sensitivity with detection limits ranging from 0.1 to 10 6 nanogram element per gram sample, but semiconductor type detectors usually have superior resolution.

Furthermore, particles detectors designed to detect the alpha and beta particles that are emitted in nuclear decay are also available; however, gamma detectors are favorable. Particle detectors require a high vacuum since atmospheric gases in the air can absorb and affect the emission of these particles. Gamma rays are not affected in this way.

Variations/Parameters

Inaa versus rnaa.

Instrumental neutron activation analysis (INAA) is the simplest and most widely used form of NAA. It involves the direct irradiation of the sample, meaning that the sample does not undergo any chemical separation or treatment prior to detection. INAA can only be used if the activity of the other radioactive isotopes in the sample does not interfere with the measurement of the element(s) of interest. Interference often occurs when the element(s) of interest are present in trace or ultratrace amounts. If interference does occur, the activity of the other radioactive isotopes must be removed or eliminated. Radiochemical separation is one way to do this. NAA that involves sample decomposition and elemental separation is known as radiochemical neutron activation analysis (RNAA). In RNAA, the interfering elements are separated from the element(s) of interest through an appropriate separation method. Such methods include extractions, precipitations, distillations, and ion exchanges. Inactive elements and matrices are often added to ensure appropriate conditions and typical behavior for the element(s) of interest. A schematic comparison of INAA and RNAA is shown below.

ENAA versus FNAA

Another experimental parameter that must be considered is the kinetic energy of the neutrons used for irradiation. In epithermal neutron activation analysis (ENAA), the neutrons – known as epithermal neutrons – are partially moderated in the reactor and have kinetic energies between 0.5 eV to 0.5 MeV. These are lower-energy neutrons as compared to fast neutrons, which are used in fast neutron activation analysis (FNAA). Fast neutrons are high-energy, unmoderated neutrons with kinetic energies above 0.5 MeV.

PGNAA versus DGNAA

The final parameter to be discussed is the time of measurement. The nuclear decay products can be measured either during or after neutron irradiation. If the gamma rays are measured during irradiation, the procedure is known as prompt gamma neutron activation analysis (PGNAA). This is a special type of NAA that requires additional equipment including an adjacent gamma detector and a neutron beam guide. PGNAA is often used for elements with rapid decay rates, elements with weak gamma emission intensities, and elements that cannot easily be determined by delayed gamma neutron activation analysis (DGNAA) such as hydrogen, boron, and carbon. In DGNAA, the emitted gamma rays are measured after irradiation. DGNAA procedures include much longer irradiation and decay periods than PGNAA, often extending into days or weeks. This means that DGNAA is ideal for long-lasting radioactive isotopes. A schematic comparison of PGNAA and DGNAA is shown below.

Characterizing archaeological materials

Throughout recent decades, NAA has often been used to characterize many different types of samples including archaeological materials. In 1961, the Demokritos nuclear reactor, a water moderated and cooled reactor, went critical at low power at the National Center for Scientific Research “Demokritos” (NCSR “Demokritos”) in Athens, Greece. Since then, NCSR “Demokritos” has been a leading center for the analysis of archaeological materials.

Ceramics, carbonates, silicates, and steatite are routinely analyzed at NCSR “Demokritos” with NAA. A routine analysis begins by weighing and placing 130 milligrams of the powdered sample into a polyethylene vial. Two batches of ten vials, eight samples and two standards, are then irradiated in the Demokritos nuclear reactor for 45 minutes at a thermal neutron flux of 6 x 10 13 neutrons cm -2 s -1 . The first measurement occurs seven days after irradiation. The gamma ray emissions of both the samples and standards are counted with a germanium gamma detector (semiconductor type) for one hour. This measurement determines the concentrations of the following elements: As, Ca, K, La, Lu, Na, Sb, Sm, U, and Yb. A second measurement is performed three weeks after irradiation in which the samples and standards are counted for two hours. In this measurement, the concentrations of the following elements are determined: Ba, Ce, Co, Cr, Cs, Eu, Fe, Hf, Nd, Ni, Rb, Sc, Ta, Tb, Th, Zn, and Zr.

Using the method described above, NCSR “Demokritos” analyzed 195 samples of black-on-red painted pottery from the late Neolithic age in what is now known as the Black-On-Red Pottery Project. An example of black-on-red painted pottery is shown here.

This project aimed to identify production patterns in this ceramic group and explore the degree of standardization, localization, and scale of production from 14 sites throughout the Strymonas Valley in northern Greece. A map of the area of interest is provided below in figure \(\PageIndex{6}\). NCSR “Demokritos” also sought to analyze the variations in pottery traditions by differentiating so-called ceramic recipes. By using NAA, NCSR “Demokritos” was able to determine the unique chemical make-ups of the many pottery fragments. The chemical patterning revealed through the analyses suggested that the 195 samples of black-on-red Neolithic pottery came from four distinct productions areas with the primary production area located in the valley of the Strymon and Angitis rivers. Although distinct, the pottery from the four different geographical areas all had common technological and stylistic characteristics, which suggests that a level of standardization did exist throughout the area of interest during the late Neolithic age.

Determining elemental concentrations in blood

Additionally, NAA has been used in hematology laboratories to determine specific elemental concentrations in blood and provide information to aid in the diagnosis and treatment of patients. Identifying abnormalities and unusual concentrations of certain elements in the bloodstream can also aid in the prediction of damage to the organ systems of the human body.

In one study, NAA was used to determine the concentrations of sodium and chlorine in blood serum. In order to investigate the accuracy of the technique in this setting, 26 blood samples of healthy male and female donors – aged between 25 and 60 years and weighing between 50 and 85 kilograms – were selected from the Paulista Blood Bank in São Paulo. The samples were initially irradiated for 2 minutes at a neutron flux ranging from approximately 1 x 10 11 to 6 x 10 11 neutrons cm -2 s -1 and counted for 10 minutes using a gold activation detector. The procedure was later repeated using a longer irradiation time of 10 minutes. The determined concentrations of sodium and chlorine were then compared to standard values. The NAA analyses resulted in concentrations that strongly agreed with the adopted reference value. For example, the chlorine concentration was found to be 3.41 - 3.68 µg/µL of blood, which correlates closely to the reference value of 3.44 - 3.76 µg/µL of blood. This illustrates that NAA can accurately measure elemental concentrations in a variety of materials including blood samples.

Limitations

Although NAA is an accurate (~5%) and precise (<0.1%) multi-element analytical technique, it has several limitations that should be addressed. Firstly, samples irradiated in NAA will remain radioactive for a period of time (often years) following the analysis procedures. These radioactive samples require special handling and disposal protocols. Secondly, the number of the available nuclear reactors has declined in recent years. In the United States, only 31 nuclear research and test reactors are currently licensed and operating. A map of these reactors shown here.

As a result of the declining number of reactors and irradiation facilities in the nation, the cost of neutron activation analysis has increased. The popularity of NAA has declined in recent decades due to both the increasing cost and the development of other successful multi-element analytical methods such as inductively coupled plasma atomic emission spectroscopy (ICP-AES).

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The McClellan Nuclear Research Center

Neutron activation analysis.

Neutron activation analysis, discovered in 1936, stands at the forefront of techniques used for quantitative multi-element analysis of major, minor, trace, and rare elements. NAA allows the measurement of ~60 elements in small samples. The lower limit of detection is of the order of parts per million to parts per billion depending on the analyzed element and the activity of the bulk sample matrix.

The principle involved in neutron activation analysis consists of first irradiating a sample with neutrons to produce specific radionuclides. After the irradiation, the characteristic gamma rays emitted by the decaying radionuclides are quantitatively measured using gamma spectroscopy, where the gamma rays detected at a particular energy are indicative of a specific radionuclide's presence. Data analysis then yields the concentrations of various elements in the samples being studied. MNRC provides help with sample preparation, data analysis, and report preparation.

Unlike other analytical techniques, neutron activation analysis is a non-destructive method and often samples can be returned to the customer within days to weeks after their irradiation. Furthermore, the chemical form of the sample does not interfere with the assay of various individual elements.  Solid samples are generally preferred, however, liquid samples can be assayed.

The following table provides a list of elements that may be quantitatively analyzed using neutron activation analysis:

Applications of Neutron Activation Analysis (NAA)

NAA can be used for a large variety of applications; the following represent some examples for scientific uses in different disciplines:

• Sourcing of clays and pottery
• Toxins in Fish and agricultural products
• Trace elements in oil and lipids
• Contaminants in salts, pure crystals, and metals
• Composition and contaminants in metals, thin film deposits plastics
• Analysis of bullets and other crime scene materials (paint, glass, metals)
• Sourcing and composition of igneous rocks, sediments, and basalts
• Toxins and trace elements in hair, skin, and nail samples
• Detection of trace levels of naturally occurring radioactive material such as thorium and uranium
• High fidelity measurements of precious and rare earth metals in geological samples
• Detection of trace levels various toxic metals such as mercury, uranium, and thorium

Neutron activation analysis sensitivities

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Large-sample neutron activation analysis in mass balance and nutritional studies

Albert van de wiel.

1 Delft University of Technology, Faculty of Applied Sciences, Radiation Science and Technology, Clinical Medicine and Isotopes for Health, Mekelweg 15, 2629 JB Delft, the Netherlands

Menno Blaauw

2 Reactor Institute Delft, Mekelweg 15, 2629 JB Delft, the Netherlands

Low concentrations of elements in food can be measured with various techniques, mostly in small samples (mg). These techniques provide only reliable data when the element is distributed homogeneously in the material to be analysed either naturally or after a homogenisation procedure. When this is not the case or homogenisation fails, a technique should be applied that is able to measure in samples up to grams and even kilograms and regardless of the distribution of the element. An adaptation of neutron activation analysis (NAA), called large-sample NAA, has been developed and proven accurate and may be an attractive alternative in food research and mass balance studies. Like standard NAA, large-sample NAA can be used to measure both toxic and trace elements relevant for nutrition.

Introduction

Deficiencies of essential elements such as Fe, Zn and Cu are a major health problem both in developed and underdeveloped countries. They may be caused by insufficiencies in food quality, -pattern or -intake or by disorders affecting resorption and metabolism. Information on the actual bioavailability of such elements in meals and food products can be obtained by mass balance studies. In such studies it is crucial that the concentration of those elements is measured very accurately both at the site of intake and at the sites of excretion, such as in urine and faeces. Usually small samples, e.g. 1 g or less, are obtained from food and excretion products (faeces and urine) and used for analysis. However, reliable data will only be obtained when the element of interest is distributed homogeneously and the subsample is truly representative. If that is not the case or homogenisation procedures fail, usual techniques for the measurement of low concentrations of elements such as advanced forms of MS cannot be applied. Large-sample neutron activation analysis (LS-NAA) offers an appropriate alternative.

Mass balance studies

Mass balance studies are used to obtain information on the actual bioavailability of major and trace elements present in meals and food products. Such studies do not usually focus on one meal or one food product but cover a longer period, e.g. 5–7 d in which 8–10 kg of food and 10–14 litres of drinking solutions are consumed. To quantify the intake of a particular element it is common to use the double-portion method: one portion is consumed by the test person while another identical portion is used for the analysis and measurement of the specific element. The intake of an element is calculated either by adding up the amounts of that element present in each component of the food or by homogenising the entire intake and analysing representative subsamples. The quality of the homogenisation can be checked by analysing more (e.g. fifteen) small test portions. However, there are situations where the distribution of an element is not homogeneous or homogenisation procedures are problematic. For instance, it is not unusual to use freeze-drying as part of the homogenisation process. However, if meat is freeze dried, the resulting product is quite a hard piece that cannot be easily crushed in usable small parts. On the other hand, freeze-dried sweet fruits can be easily crushed, but the material, still containing sugar, gets very sticky once liquid N 2 is poured on it ( , 1 ) . Most techniques to measure low concentrations of elements, such as inductively coupled plasma MS (ICP-MS), only use small samples. In recent years the Radiation, Science and Technology department of the Delft University of Technology (TU Delft) has worked intensively on the adaptation of the NAA facility, making it possible to measure even low concentrations of elements in large samples up to kilograms.

Neutron activation analysis

NAA is a technique for qualitative and quantitative multi-element analysis of major, minor, trace and rare elements in all kinds of materials including those from human origin such as blood, nails, hairs and tissue samples. The method is based on the bombardment of a sample with neutrons followed by capture of a neutron by the nucleus of an element and subsequent conversion to a radioactive isotope. NAA requires a source of neutrons, ideally a nuclear reactor.

Samples are first encapsulated in a vial made of either high-purity linear polyethylene or quartz. Samples and standards are then packaged and irradiated in the reactor at a constant, known neutron flux. The research reactor uses uranium fission providing a high neutron flux. The type of neutrons generated are of relatively low kinetic energy (KE), typically less than 0·5 eV, and are termed thermal neutrons. However, experimental parameters can be varied resulting in neutrons with a moderate (0·5 eV–0·5 MeV) or high (>0·5 MeV) KE. Upon irradiation, a thermal neutron interacts with the target nucleus of an isotope of an element via a non-elastic collision, causing neutron capture. This collision forms a compound nucleus which is in an excited state. This state is unfavourable and the compound nucleus will almost immediately de-excite into a more stable configuration through the emission of a prompt particle and one or more characteristic prompt γ photons. In most cases, this more stable configuration yields a radioactive nucleus. The newly formed radioactive nucleus now decays by the emission of both particles and one or more characteristic delayed γ photons ( Fig. 1 ). This decay process is at a much slower rate than the initial de-excitation and is dependent on the unique half-life of the radioactive nucleus. The radioactive emission characteristics and decay paths of the various elements are well known. They are usually measured with a semiconductor detector utilising the semiconducting element germanium. The intensity of the radioactive emissions is proportional to the number of nuclei of the element and based on the information of the spectra of emissions, concentrations of elements, present in the sample, can be calculated. Until the introduction of particle-induced X-ray emission and ICP atomic emission spectroscopy and ICP-MS, NAA was the standard analytical method for performing multi-element analyses with minimum detection limits in the sub-parts per million range ( , 2 ) . The technique is non-destructive, the chemical structures of the sample stay intact, and there is no need to convert and/or dilute a sample into a suitable solution prior to analysis with inherent risks of contamination and element loss. Apart from this simple preparation, it is a highly accurate technique meeting the requirements of a primary method of measurement ( , 3 ) . Drawbacks, however, are that the irradiated samples may remain radioactive for many years after the initial analysis, requiring handling and disposal protocols and that the number of research reactor facilities has declined over the years. This may explain why its use in clinical medical research has been limited while much progress has been made in MS techniques, which also have easier access.

Basic concept of neutron activation analysis.

Large-sample neutron activation analysis

Conventional NAA of human material usually deals with freeze-dried samples of 50–200 mg. In the case of LS-NAA, samples are positioned inside a graphite cylinder, that can contain kilograms of material. The sample is surrounded by eighty neutron flux monitors (Zn foils) positioned in a fixed grid in the walls of the graphite cylinder. The cylinder is then positioned in the thermal column of the reactor ( Fig. 2 ). Irradiation time is usually longer than in small-sample NAA and also the measurement facility is adapted with a greater distance between sample and detector endcap. Although the accuracy and reliability of this method has been proven in the years after its development, the method has not gained much attention in clinical research ( , 4 , 5 ) . Recently, new interest in the technique has been shown by Yagob et al. ( , 6 ) measuring Fe concentrations in commercially available microwave meals and in porridge fine wheat grain products. Comparing standard small-sample NAA with the LS technique showed equivalent results in the measurement of Fe in the porridge fine wheat grain. Measurement of Fe in merged microwave meals containing all sorts of food was not met with analytical problems such as radiolysis or gas formation during irradiation. In other experiments the same research group has shown that NAA can be applied for Fe measurements in blood, blood cells, faeces and urine ( , 1 ) . This allows the use of one and the same technique to measure even low concentrations of elements in various materials obtained in one experiment.

Set up of the large-sample neutron activation analysis facility.

Conclusions

Low concentrations of trace elements in human material can be measured with various techniques and great progress has been made in MS during recent years. However, elements are not always distributed homogeneously neither in human tissue nor in food. Homogenisation may produce representative subsamples, but sometimes such a homogenisation procedure fails to deliver reliable material or there is considerable doubt whether samples are truly representative. In that case a technique, such as LS-NAA, that uses all material and does not depend on sampling is an attractive alternative. Like standard NAA, LS-NAA can be applied to measure most toxic (As, Cd) and trace elements relevant to nutrition like Fe, Zn, Cu, Mg and Mn.

Acknowledgements

There was no financial support for this study.

There are no conflicts of interest.

Neutron Activation Analysis

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Neutron Activation Analysis is a powerful tool for determining isotopes at trace levels in environmental samples. In some cases, it has been used for environmental radioactivity. The main objective of the chapter is the description of the technique. Thus, the most commonly used neutron reactions are described, and the general equation that allows the determination of the mass of the radionuclide of interest is presented. Usually, radiochemical separation is not necessary, although in some cases neutron activation requires it. Both practical approaches are described along the most important interferences that could affect the measurement. Neutron sources needed for activation are also described. Some specific applications to environmental radioactivity are presented.

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García-León, M. (2022). Neutron Activation Analysis. In: Detecting Environmental Radioactivity. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-031-09970-0_19

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Instrumental Neutron Activation Analysis (INAA)

Analytical capabilities and detection limits for elements by NAA

Instrumental neutron activation analysis (INAA), or sometimes referred to as simply NAA, is a method for determination of many elements at low levels in a wide variety of materials.  Samples are usually encapsulated in polyethylene or some other suitable packaging, packed into an irradiation capsule (usually a polyethylene “rabbit”) and irradiated in the reactor core.  Pneumatic tubes allow irradiation at two different reactor positions, at neutron fluence rates of 1 x 10 14 cm -2 s -1 and 3 x 10 13 cm -2 s -1 .  During irradiation elemental nuclei capture neutrons and produce radioactive nuclei.  Since the neutron flux is highly thermalized, single neutron capture reactions are dominant.  After a suitable decay period following irradiation, the nuclides of interest are determined by gamma ray spectroscopy using a high-resolution germanium detector with appropriate signal analyzer and electronics.  Quantification of elements is accomplished by comparison with standards usually irradiated along with the samples. 

Detection limits may be improved by the use of anticoincidence or coincidence counting techniques to improve signal to noise ratio.  The use of loss free counting methods and high throughput detectors allow quantification at higher counting rates with minimal loss of signal or resolution, further improving detection limits.  Detection limits may be further improved by optimizing irradiation, decay, and counting times to the half-life of the element of interest. 

The analysis is essentially “blank free”, if the sample is repackaged after irradiation, and quantitative measurement of the bulk sample is obtained since the neutron and gamma radiation both penetrate the sample.  Because the technique relies on nuclear, rather than chemical reactions, the results are not dependent upon the chemical form of the element.  Samples may be analyzed without dissolution or decomposition, eliminating measurement errors due to incomplete dissolution or loss of volatile elements.  And because the analysis is nondestructive, samples may be analyzed again by NAA or by other techniques if necessary.  Because NAA shares few sources of uncertainty with purely chemical methods of analysis, it serves as an important complementary technique to these methods.  Typical detection limits are at µg/g levels or better.   

Neutron Activation Analysis For Archaeological Research

Yuchen liu february 20, 2022, submitted as coursework for ph241 , stanford university, winter 2022, introduction.

In archaeological investigations where provenance is an aspect of important concern, it has been long recognized that systems of classification based upon form, decoration, and subtleties of workmanship should be supplemented by laboratory techniques that are able to identify distinctive chemical compositions. [1] Due to the penetrating and therefore non-destructive nature of neutrons, characterization methods based upon their usage stand out amongst the wide variety of techniques to play a fundamental role in the investigation of artifacts. [2] By allowing both surface and bulk properties to be measured, neutron methods provide researchers with the necessary means for the examination, conservation, and restoration of ancient material samples. [2] Since its first employment in the mid-1950s, Neutron Activation Analysis (NAA), in particular, has been used extensively as one of the most important neutron-based characterizing and provenancing analytical techniques; it continues to play an essential role in the field of archaeological research today. [3]

History of NAA in Archaeological Investigations

As a versatile quantitative analytical technique with remarkable sensitivity, accuracy, and precision, neutron activation analysis (NAA) is widely applied across disciplines such as archaeology, geochemistry, health, human nutrition, environmental monitoring, and semiconductor technology. [4]

Discovered by G. Hevesy and H. Levi in 1936, the method was first applied towards the investigation of archaeological research in 1956, where it was used to analyze the sherds of Mediterranean terracotta figurines such as the ones shown in Fig 1. [1,4-6] Recognizing the technique's potential for relating artifacts to source materials in a powerful yet convenient way, R. W. Dodson and E. V. Sayre of Brookhaven National Laboratory undertook this investigation at the invitation of R. Oppenheimer. [4,6] NAA grew increasingly popular amongst archaeologists during the 1970s and 1980s and, by the early 1990s, was considered to be the technique of choice for provenance research. [4]

The NAA Method

As a highly sensitive analytical technique, NAA can be used to perform both qualitative and quantitative analysis of major, minor, or trace elements in samples of almost any type of state (i.e., solid, liquid, or gas). [3] By exposing such a sample to neutrons, nuclear reactions are induced and the result is the emission of detectable gamma rays; by measuring the characteristic energies of these gamma rays, the specific nuclear reaction(s) taking place and, therefore, the elements present in the sample, can be identified. [3]

During the most common type of nuclear reaction used for NAA, the neutron capture reaction, a compound nucleus forms in an excited state when a neutron interacts with a target nucleus via a non-elastic collision. [5] This excited compound nucleus will then immediately de-excite into a more stable configuration by emitting one or more characteristic prompt gamma rays. [5] In many cases, however, this new configuration can also yield a radioactive nucleus which also de-excites by emitting one or more characteristic delayed gamma rays, but at a rate that is much slower. [5] Depending on the time of measurement, therefore, NAA falls into two categories: (1) prompt gamma-ray neutron activation analysis (PGNAA), where measurements are taken during irradiation, or (2) delayed gamma-ray neutron activation analysis (DGNAA), where measurements are taken following radioactive decay. [4,5]

In terms of reactors, the ones based on Uranium-235 fission offer the most intense neutron sources currently available for NAA. [4] Neutrons inside a reactor can be divided into 3 types based on an energy spectrum: the fast neutrons of the high-energy region (2-6 MeV), the epithermal neutrons of the 0.5-1.0 MeV region, and the thermal neutrons of the region below energies of 0.5 eV. [4]

Advantages of using NAA

For archaeologists, the advantages of using NAA over other analytical techniques are numerous. The preparation of samples for NAA analysis is extremely simple, requiring, in many cases, only the weighing and placing of portions into containers. [4] Additionally, because NAA can be applied instrumentally (without the need to digest or dissolve the sample), there is no concern of reagent and laboratory contamination, which also reduces labor costs. [4] And finally, NAA presents a highly precise and accurate way of simultaneously measuring multiple elements in a single sample (nowadays, up to 50-60). [2,4] Since the first application of NAA towards archaeological research in the mid-1950s, the technique has successfully established itself as a powerful, reliable, and convenient tool for provenance determination. [1,4]

© Yuchen Liu. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

[1] I. Perlman, F. Asaro, and H. V. Michel, "Nuclear Applications in Art and Archaeology," Annu. Rev. Nucl. Sci. 22 , 383 (1972).

[2] N. Kardjilov and G. Festa, eds., Neutron Methods for Archaeology and Cultural Heritage (Springer, 2017).

[3] M. D. Glascock, "Neutron Activation Analysis (NAA): Applications in Archaeology," in Encyclopedia of Global Archaeology, 2014th Ed. , ed. by C. Smith (Springer, 2013).

[4] M. D. Glascock and H. Neff, "Neutron Activation Analysis and Provenance Research in Archaeology," Meas. Sci. Technol. 14 , 1516, (2003).

[5] L. Hamidatou et al. , "Concepts, Instrumentation and Techniques of Neutron Activation Analysis," in Imaging and Radioanalytical Techniques in Interdisciplinary Research , ed. by F. Kharfi (IntechOpen, 2013).

[6] E. V. Sayre and R. W. Dodson, "Neutron Activation Study of Mediterranean Potsherds," Am. J. Archaeol. 61 , 35 (1957).

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Al-Mugrabi, M. A. "Optimisation of instrumental neutron activation analysis." Thesis, University of Surrey, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377262.

Bernedo, Alfredo Victor Bellido. "Neutron activation analysis of ancient Egyptian pottery." Thesis, University of Manchester, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329729.

Bellido-Bernedo, Alfredo Victor. "Neutron activation analysis of ancient Egyptian pottery." Online version, 1989. http://ethos.bl.uk/OrderDetails.do?did=1&uin=uk.bl.ethos.329729.

Ryde, S. J. S. "Multi element in vivo analysis by neutron activation." Thesis, Swansea University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638733.

Alamin, Mohamed Bachir. "Bulk material elemental analysis using neutron activation techniques." Thesis, University of Surrey, 1995. http://epubs.surrey.ac.uk/843813/.

Kipler-Koch, Debra Ann. "Provenance determination of Bronze Age pottery using neutron activation analysis /." Online version of thesis, 1989. http://hdl.handle.net/1850/11432.

Zhang, Weihua. "Studies on anticoincidence gamma-ray spectrometry in neutron activation analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq24768.pdf.

Shi, Youqing. "Speciation of arsenic by chemical separations and neutron activation analysis." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ66671.pdf.

Farooqi, Asad Saeed. "Nuclear activation techniques and methods of elemental concentration determination in bioenvironmental studies." Thesis, University of Surrey, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280334.

MOURA, PATRICIA L. da C. "Determinação de elementos essenciais e tóxicos em cogumelos comestíveis por análise por ativação com nêutrons." reponame:Repositório Institucional do IPEN, 2008. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11686.

Inyang, Otu Effiong. "Development of a prompt-gamma, neutron-activation analysis facility at the Texas A&M University Nuclear Science Center." Thesis, [College Station, Tex. : Texas A&M University, 2008. http://hdl.handle.net/1969.1/ETD-TAMU-2980.

Wise, Jatara Rob. "The investigation of spices by use of instrumental neutron activation analysis." Texas A&M University, 2008. http://hdl.handle.net/1969.1/86033.

Mackie, Alison. "Total body nitrogen by prompt neutron activation analysis using californium-252." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/26715.

Mohd, Zin S. "Neutron beam for partial- and whole-body in vivo activation analysis." Thesis, Swansea University, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638218.

Sandhu, S. H. K. "In vivo determination of copper and iron using neutron activation analysis." Thesis, Swansea University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638764.

Curley, R. K. "Radiochemical neutron activation analysis of copper and molybdenum in human tissues." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233790.

LUCIA, SILVIO R. de. "Desenvolvimento de um software de espectrometria gama para analise por ativacao com neutrons utilizando o conceito de codigo livre." reponame:Repositório Institucional do IPEN, 2008. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11743.

Majawa, Louis John. "Neutron activation analysis of plantinum converter and furnace mattes using a D-T sealed tube neutron generator." Master's thesis, University of Cape Town, 2013. http://hdl.handle.net/11427/6650.

Liddy, D. J. "A study of Roman amphoras from North Africa by neutron activation analysis." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355911.

Sullivan, Daniel D. "Neutron activation analysis and chemical inference for the identification of Buena Vista ceramics." PDXScholar, 1986. https://pdxscholar.library.pdx.edu/open_access_etds/3699.

MOREIRA, EDSON G. "Preparo e caracterizacao de um material de referencia de mexiliao Perna perna (Linnaeus, 1758)." reponame:Repositório Institucional do IPEN, 2010. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9529.

GONCALVES, CRISTINA. "Aplicacao do metodo de ativacao neutronica a determinacao de mercurio total e outros elementos de interesse em amostras de solo e sedimento da Serra do Navio e Bacia do Rio Vila Nova, Amapa." reponame:Repositório Institucional do IPEN, 1997. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10647.

LOUREIRO, ANA L. M. "Analise de elementos-traco presentes em aerossois da peninsula Antartica pelo metodo de ativacao com neutrons." reponame:Repositório Institucional do IPEN, 1989. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10218.

Khan, Mohammad Saeed. "Differences in the uptake of caesium by plants studied by neutron activation analysis." Thesis, University of Salford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357005.

Chick, Michael D. "Feasibility of the Use of Neutron Activation Analysis Techniques in an Underwater Environment." TopSCHOLAR®, 2016. http://digitalcommons.wku.edu/theses/1744.

Choi, In Sup. "Trace elements determination in cancerous and noncancerous human tissues using instrumental neutron activation analysis." Diss., Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/13385.

ZAMPIERI, MARIA C. T. "Estudo sobre os efeitos do cobre e zinco no crescimento da plantula de Aechmea blanchetiana (Baker) L.B. Smith cultivada in vitro. Aplicacao da analise por ativacao com neutrons." reponame:Repositório Institucional do IPEN, 2010. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9616.

MATSUBARA, TASSIANE C. M. "Estudo sobre a determinação de antimônio em amostras ambientais pelo método de análise por ativação com nêutrons. Validação da metodologia e determinação da incerteza da medição." reponame:Repositório Institucional do IPEN, 2011. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10042.

AGUIAR, RODRIGO O. de. "Determinacao de elementos em sangue de hamster dourado usando AAN." reponame:Repositório Institucional do IPEN, 2009. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9354.

Natto, S. S. A. "Monte Carlo modelling of systems for the neutron activation analysis of aluminium in vivo." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.638297.

MATEUS, SANDRA F. "Determinacao de componentes inorganicos em plasticos pelo metodo de analise por ativacao neutronica." reponame:Repositório Institucional do IPEN, 1999. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9282.

NOGUEIRA, CLAUDIO A. "Determinacao de Pt, Pd, Ir e Au em materiais geologicos de referencia por analise por ativacao com neutrons: uma comparacao entre dois metodos." reponame:Repositório Institucional do IPEN, 1994. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10415.

CAVALCANTE, CASSIO Q. "Estudo sobre a determinação de paládio em amostras biológicas pelo método de análise por ativação em nêutrons." reponame:Repositório Institucional do IPEN, 2007. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11544.

PIASENTIN, RICARDO M. "Acompanhamento da variacao mineral de duas cultivares de guandu (Cajanus cajan(L.)Millsp) submetidas a diferentes doses de fertilizantes, pelo metodo de analise por ativacao com neutrons." reponame:Repositório Institucional do IPEN, 2001. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10903.

NUNES, KELLY P. "Estudos arqueometricos do sitio arqueologico Hatahara." reponame:Repositório Institucional do IPEN, 2009. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9369.

Taylor, R. J. "The Application of Neutron Activation Analysis and Multivariate Statistics to the Provenance of Roman Ceramics." Thesis, University of Manchester, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.519503.

Ames, Michael Richard. "Development and application of a methodology for measuring atmospheric mercury by instrumental neutron activation analysis." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/36020.

MELO, ADEILSON P. de. "Caracterização do jade e dos silicatos da familia do jade para aplicação em dosimetria das radiações." reponame:Repositório Institucional do IPEN, 2007. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11550.

REIS, ROGERIO A. de S. "Caracterização de componentes inorgânicos em suplementos nutricionais pelo método de análise por ativação com nêutrons." reponame:Repositório Institucional do IPEN, 2006. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11401.

PELLEGATTI, FABIO. "Determinacao de metais pesados e outros elementos em sedimentos da baia de Sepetiba [RJ] por ativacao neutronica." reponame:Repositório Institucional do IPEN, 2000. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9283.

GUIMARAES, GUILHERME M. "Avaliação da concentração de metais e elementos traço em amostras de sedimento do reservatório Guarapiranga, São Paulo-SP, Brasil." reponame:Repositório Institucional do IPEN, 2011. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10002.

FRAZAO, SELMA V. "Estudo da determinacao de elementos traco em cabelos humanos pelo metodo de analise por ativacao com neutrons." reponame:Repositório Institucional do IPEN, 2008. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9356.

ROGERO, SIZUE O. "Aplicacao do metodo de analise por ativacao a determinacao de elementos tracos em amostras do pulmao." reponame:Repositório Institucional do IPEN, 1992. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10287.

ALCALA, ANTONIO L. "Determinacao de elementos terras raras em rochas por analise por ativacao com neutrons com separacao pre-irradiacao." reponame:Repositório Institucional do IPEN, 1991. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10261.

OLIVEIRA, ROSANGELA M. de. "Estudo da determinacao de fosforo em amostras biologicas." reponame:Repositório Institucional do IPEN, 1994. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10401.

TOYOTA, ROSIMEIRI G. "Caracterizacao quimica da ceramica Marajoara." reponame:Repositório Institucional do IPEN, 2009. http://repositorio.ipen.br:8080/xmlui/handle/123456789/11774.

Beauchesne, France. "Analyse non destructive du cuivre et de ses alliages par activation à l'aide de neutrons rapides de cyclotron : application à la numismatique." Orléans, 1986. http://www.theses.fr/1986ORLE0015.

Chenkovich, Robert Jeremy. "Refinement and Validation of Existing Computer Models of the OSU Research Reactor using Activation Analysis and Spectral Unfolding Codes." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1206022975.

CURCHO, MICHEL R. da S. M. "Avaliacao de micro e macroelementos, elementos toxicos (Cd, Hg e Pb) e acidos graxos, em peixes disponiveis comercialmente para consumo em Cananeia e Cubatao, Estado de Sao Paulo." reponame:Repositório Institucional do IPEN, 2009. http://repositorio.ipen.br:8080/xmlui/handle/123456789/9388.

METAIRON, SABRINA. "Determinação de elementos de relevância clínica em tecidos biológicos de camundongos distróficos Dmdsup(mdx)/J por AAN." reponame:Repositório Institucional do IPEN, 2012. http://repositorio.ipen.br:8080/xmlui/handle/123456789/10090.

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Investigating the porosity of sedimentary rock with neutrons

by Technical University Munich

Whether sedimentary rocks store fossil hydrocarbons or act as impermeable layers to prevent the rise of oil, natural gas or stored carbon dioxide—all depends on their porosity. The size, shape, organization, and connectivity of the pore spaces are decisive.

At the Heinz Maier-Leibnitz Research Neutron Source (FRM II) at the Technical University of Munich (TUM), the networks of micropores were characterized using small and very small angle neutron scattering.

Dense, dark, compact—at first glance, the sedimentary rock samples that Dr. Amirsaman Rezaeyan has on his lab desk are only slightly different. Pores are not visible to the naked eye.

Nevertheless, it is precisely the pores that give the mudrocks their special properties: The pores, ranging from a few micrometers to sub-nanometers in size, are formed during sedimentation and compacted over time, determining the permeability. These pores are the decisive factor for the rock's ability to reside oil and natural gas or form impermeable layers under which the fossil fuels collect.

"Depending on the distribution, size and structure of the pores, the fine-grained sedimentary rocks are also suitable for disposing of radioactive waste or sealing carbon dioxide storage," explains Dr. Amirsaman Rezaeyan, a researcher at the University of Calgary in Canada. "The pore structure of mudrocks and its influence on the permeability for fluid flow have hardly been studied to date but are enormously important if you want to assess the potential of mudrocks as oil reservoirs or impermeable layers."

But how do you measure pores that are not bigger than bacteria? There are actually various methods that can be used to quantify the pore volume, but most of them can only detect larger structures or limited pore sizes.

"Only small and very small angle neutron scattering is suitable for fully quantifying pores between a few nanometers and micrometers," says Rezaeyan, who, together with an international team at the Heinz Maier-Leibnitz Research Neutron Source (FRM II) at TUM, has analyzed the porosity of a dozen sedimentary rocks from Europe and America.

Measuring pores with nanometer precision

There are only a few measuring facilities for Small Angle Neutron Scattering (SANS) and Very Small Angle Neutron Scattering (VSANS) around the world. Two of them, KWS-1 and KWS-3, are operated by Forschungszentrum Jülich at the Heinz Maier-Leibnitz Zentrum (MLZ).

The MLZ is the scientific cooperation between TUM, Forschungszentrum Jülich and Helmholtz-Zentrum Hereon, which makes the neutrons of the FRM II available to guest researchers in the form of scientific instruments.

And so Rezaeyan from the Lyell Center at Heriot-Watt University in Edinburgh, Scotland, where he was working at the time, traveled to Garching with his rock samples—all thinly polished and without gas or liquid inclusions—to detect micropores.

The samples were irradiated with neutrons from the reactor in the small-angle scattering instruments at the FRM II. As neutrons only interact with the nuclei of atoms, the diffraction pattern recorded by the detector can be used to deduce the arrangement of the atoms and thus—indirectly—that of the atom-free pores.

Back in Scotland, the researchers correlated the measurements with the microscopic properties of the rock samples. The result has now been published two articles, one in the journal Energy and the other in Energy & Fuels .

The researchers found that the porosity of the fine-grained mudrocks is dependent on the proportion of clay minerals contained in the sediments: The more clay, the greater the probability of smaller pores, which have a diameter of less than 50 nanometers. Rocks with a high clay content are therefore potentially well suited for sealing a disposal or storage place underground as an impermeable layer.

"However, clay content is only one piece of the puzzle: there are a whole range of factors that need to be taken into account when selecting suitable mudrock layers for production of oil and gas or CO 2 storage," emphasizes Rezaeyan. "We therefore included other factors in the data analysis, such as rock compaction and organic matter. Doing this, we were able to establish correlations of high statistical significance."

With the help of these correlations, it should be possible in the future to estimate the physical properties of fine-grained sedimentary rocks based on the sedimentation conditions and to find out whether they are suitable as impermeable layers for nuclear waste repositories and CO 2 storage sites.

Amirsaman Rezaeyan et al, Evolution of Pore Structure in Organic-Lean and Organic-Rich Mudrocks, Energy & Fuels (2023). DOI: 10.1021/acs.energyfuels.3c02180

Journal information: Energy & Fuels

Provided by Technical University Munich

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