New neutron-based isotopic analytical methods; An explorative study of resonance capture and incoherent scattering

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New neutron-based isotopic analytical methods

An explorative study of applications of

resonance capture and incoherent scattering

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New neutron-based isotopic analytical methods

An explorative study of applications of

resonance capture and incoherent scattering

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema, voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op maandag 29 november 2004 te 13.00 uur door

Raffaella Christine PEREGO

Dottore in Chimica, Università di Torino, (Italië) geboren te Torino (Italië)

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Dit proefschrift is goedgekeurd door de promotoren: Prof. dr. G.J. Kearley

Prof. dr. ir. C.W.E. van Eijk

Samenstelling Promotiecommissie

Rector Magnificus, voorzitter

Prof. dr. G.J. Kearley, Technische Universiteit Delft, promotor Prof. dr. ir. C.W.E. van Eijk, Technische Universiteit Delft, promotor Prof. dr. H. Postma, Technische Universiteit Delft

Prof. dr. ir. J.J.M. de Goeij, Technische Universiteit Delft Prof. dr. ir. W. Mondelaers, Universiteit van Gent

Dr. P. Schillebeeckx, JRC-IRMM, Geel

Dr. F.M. Mulder, Technische Universiteit Delft Dr. M. Blaauw heeft als begeleider in belangrijke mate aan de totstandkoming van het proefschrift bijgedragen

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…lasciate ogne speranza, voi ch’intrate. Dante Alighieri, La Divina Commedia, Inferno, Canto III J.J.M. De Goeij, September 2000

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List of symbols

a isotope abundance

A mass number (number of protons and neutrons in nucleus)

A_γ integrated resonance capture cross section [barn eV]

B background content

Win Tot

B

B ratio of background content considering total γ-spectrum and for γ-energy

window

CM central neutron monitor counts

E energy [eV, keV, MeV]

g =

(

2J+1 /

) (

⎡_⎣ 2s+1 2

)(

I+1

)

⎤_⎦; statistical weight factor. For neutrons s=1/2, so

that g=

(

2J+1 / 2 2

)

⎡_⎣

(

I+1

)

⎤_⎦

G gross peak content

( )

G _Tot

B gross peak to background ratio considering total γ-spectrum

( )

Win

G

B gross peak to background ratio for γ-energy window

h Planck’s constant = 6.6262 x 10-34 [J s]

h =h 2Π [J s]

l orbital moment of the incoming neutron

D

L limit of detection [g/g, mol/mol]

Q

L limit of quantification [g/g, mol/mol]

M atomic mass [amu]

eff

M effective mass [amu]

Av

N Avogadro’s number [mol-1]

p probability of γ-ray detection

P number of detected events integrated over a resonance, i.e. peak area

( )

i

P t muon spin depolarisation function along Cartesian direction i

PN normalised peak area

M Tot

P C

⎛ ⎞

⎜ ⎟

⎝ ⎠ net peak content per neutron considering total γ-spectrum

M Win

P C

⎛ ⎞

⎜ ⎟

⎝ ⎠ net peak content per neutron for γ-energy window

Win Tot

P

P ratio of peak content considering total γ-spectrum and for γ-energy window

Q resonance quality factor

r nuclear radius [Å = 10-8 _m]

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s standard deviation

( )

s_{r Tot} normalised relative standard deviation considering total γ-spectrum

( )

s_{r Win} normalised relative standard deviation for γ-energy window

( ) ( )

r Win r Tot

s

s ratio of relative standard deviation considering total spectrum and for γ-energy window

t time of flight [ns]

S(E) Doppler broadening function [eV]

TD Debye temperature [K]

Teff effective temperature [K]

U self shielding factor

v neutron velocity [m/s]

i

w weighting factor of γ-transition i

Z atomic number (number of protons in nucleus)

D

∆ Doppler width parameter [eV]

γ

ε γ-detection efficiency

( )

E

Φ energy dependent neutron flux [cm-2_s-1_eV-1_]

( )

0 E

Φ neutron flux produced by the LINAC [cm-2_s-1_eV-1_]

Γ resonance width [eV]

γ

Γ capture resonance width [eV]

n

Γ neutron resonance width [eV]

γ

ε γ-ray detection efficiency

N

µ

µ nuclear magnetic moment (µ = nuclear magnetron) N

2θ scattering angle

ρ element density [kg/m3_]

bound

σ scattering cross section of the atom rigidly bound to an infinite mass [barn] 0

σ scattering cross section of the free atom [barn]

(

Meff

σ

)

scattering cross section of an atom with effective mass Meff [barn]

H

σ apparent scattering cross section for hydrogen [barn]

Ti

σ apparent scattering cross section for titanium alloy [barn]

tot

σ total cross section [barn]

γ

σ radiative capture cross section [barn]

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List of abbreviations

ADC Analog to Digital Converter

BGO Bismuth germanate

BMC Bone Mineral Content

BMD Bone Mineral Density

BFS Blast Furnace Slag

BUDA “free-gas NIS” simulation program CFD Constant Fraction Discriminator CM1 Central Monitor 1 (for neutron flux)

CNDP Cold Neutron Depth Profiling

CNPGAA Cold Neutron Prompt Gamma Activation Analysis CSH Calcium Silicate Hydrates

FP Flight Path

FTD Fast Time Digitiser

GELINA Geel Electron LINear Accelerator GGBS Ground Granulated Blast-furnace Slag

ICP-MS Inductively Plasma Coupled Mass Spectrometry INAA Instrumental Neutron Activation Analysis

IRMM Institute for Reference Materials and Measurements

LINAC LINear ACcelerator

MCNP Monte Carlo N-Particle (code)

MRI Magnetic Resonance Imaging

NAA Neutron Activation Analysis

NaI(Tl) Thallium doped sodium iodide

NG0 Neutron Guide 0

NG7 Neutron Guide 7

NIS Neutron Incoherent Scattering

NIST National Institute of Standards and Technology NRCA Neutron Resonance Capture Analysis

PGNAA Prompt-Gamma Neutron Activation Analysis

PIXE Proton-Induced X-ray Emission

QENS Quasi Elastic Neutron Scattering

ROI Region Of Interest

SANS Small Angle Neutron Scattering

TOF Time Of Flight

w/c water/cement

XRD X-Ray Diffraction

XRF X-Ray Fluorescence

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1.Prologue

One of the objectives of the Interfaculty Reactor Institute (IRI) is to develop and improve facilities that are specific to the institute, such as the research reactor and the Van der Graaff accelerator, and to offer these methods to the Dutch scientific community. When the research described in this thesis was started, a source of pulsed neutrons at IRI was taken into consideration, as well as the possibility of a cold neutron source. It was a good moment then to explore new techniques that held promise for the future.

Latest financial developments have however drastically changed the picture and, at the time of writing, it is unlikely that any of such projects will be realised at IRI in the immediate future.

In the frame of the considerations above, two neutron-based techniques were explored that are both relatively new and under development: Neutron Resonance Capture Analysis (NRCA, first published in 2001 [1]) and Neutron Incoherent Scattering (NIS, first published in 1998 [2]). NRCA is closely related and complimentary to Instrumental Neutron Activation analysis (INAA), in that, based on the well-known phenomenon of neutron capture, it determines isotopic - and thus usually also elemental - amounts in solids non-destructively. In NIS the large incoherent scattering cross section of hydrogen is employed to determine low hydrogen concentrations.

Both techniques are studied and developed with practical applications in mind. NRCA is pursued in the frame of various applications, such as osteoporosis and bone tumour related studies; determination of chlorine in marble matrixes and determination of lead content in archaeological objects. The physics behind NIS is investigated by analysing samples consisting of hydrogen-loaded titanium chips and samples exhibiting the evolution of hydrating cement pastes in time.

The fields of application and the samples analysed may appear quite heterogeneous and vast: the leading thread through the thesis is the development of novel neutron-based techniques for analytical purposes, NRCA being based on a pulsed neutron source and NIS requiring a cold neutron source.

In the thesis, NRCA is described first. In Chapter One the applications envisaged for NRCA are described, followed by the principles of the technique that are highlighted in

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Chapter Two. In Chapter Three the ameliorations that were made to improve the technique are presented. Finally in Chapter Four the validation of the NRCA technique for the practical applications targeted with some results on the samples analysed is described.

Subsequently, the NIS method and the experiments performed are discussed. In particular, the understanding of the experiments is improved by analysing and interpreting the results employing a more complex model than in 1998. The idea is to render NIS a suitable method for the determination of hydrogen concentration in a variety of materials. In Chapter Five the NIS technique is briefly introduced and the applications treated in the thesis are described. Chapter Six describes the NIS technique in detail, together with the supporting techniques utilised to better understand the results. These were Cold Neutron Prompt Gamma Activation Analysis (CNPGAA), isothermal calorimetry, and µSR (Muon Spin Resonance). In Chapter Seven experiments on hydrogen-in-titanium samples are presented and discussed. Finally in Chapter Eight experiments performed on hydrating cement pastes are treated.

References

[1] H. Postma, M. Blaauw, P. Bode, P. Mutti, F. Corvi, P. Siegler, “Neutron resonance capture analysis of materials”, J. Radioanal. Nucl. Chem., 248, 115-120 (2001)

[2] V.V. Kvardakov, H.H. Chen-Mayer, D.F.R. Mildner, V.A. Somenkov, “Cold neutron incoherent scattering for hydrogen detection in industrial materials”, J.

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1.Chapter One

Neutron Resonance Capture Analysis

(NRCA)

Abstract

After a short introduction, the applications targeted with NRCA are presented. Following, the basic physics necessary to understand the NRCA method are outlined.

1.1 Introduction: NRCA applications

Neutron Resonance Capture Analysis (NRCA) is a novel technique for the elemental analysis of materials and objects [1, 2, 3]. It is based on the well-known phenomenon of neutron capture. A detailed description of its principles is provided in the following sections.

NRCA has been applied to the analysis of historic and artistic artefacts. To this end the resonances at low energy (up to 1000 eV) of several elements were used, primarily Sn, Cu, Sb, As, Ag, Fe and In [1].

The goal of the work described in this thesis was to improve the experimental conditions for NRCA measurements, that is, to improve the detection limits. In particular, the possibility of studying resonances at higher energies, i.e. up to 100 keV, was investigated. This would allow for the analysis of a larger number of elements, since many elements (especially the low-Z ones and some high-Z ones, such as lead) only show resonances in the high energy range. The principal problems encountered in the high-energy region are the high background and the low neutron flux, which combined, result in resonance peaks being less distinguishable from the background. The majority of the efforts has been devoted to quenching the background, especially at high energy, in order to broaden the application field of NRCA.

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1 Analysis of calcium and phosphorus in a bone matrix, in the frame of stable-isotope tracer experiments in osteoporosis related studies. Calcium has six stable isotopes.

2 Analysis of tin in a bone matrix, to study the uptake of tin based

radiopharmaceuticals for the palliative treatment of bone metastases, again with stable-isotope tracer experiments in mind. Tin has ten stable isotopes.

3 Analysis of chlorine in marble. Chloride ions cause deterioration in marble architectural elements and monuments.

4 Analysis of lead in bronze archaeological artefacts. Lead can be present in varying amounts in such artefacts, and the concentration and/or isotope ratios may shed light on the provenance of the artefact.

1.1.1 Calcium and phosphorus in bone in view of the osteoporosis problem

Bone is an extremely specialised sort of connective tissue composed of hard living material that provides structural support to the body of most vertebrates. Like all living tissues, it has a very complex and differentiated structure, but for the scope of this thesis it can be described as a tissue consisting of a hard matrix of calcium salts deposited around protein fibres. The minerals make bone rigid and the proteins (collagen) provide strength and elasticity. Being a living organ, bone is continuously broken down by bone absorbing cells, the osteoclasts, and subsequently rebuilt by osteoblasts, responsible for bone formation. This cycle obviously involves exchange of calcium with the blood. The periosteum, a fibrous membrane, covers the outside of bone. This is rich with capillaries that care for the bone nourishment. The outer, harder layer of bone is called cortical bone. This makes up for 80% of the bone mass. Cancellous or trabecular bone is an inner spongy structure which accounts for 20% of bone mass. Finally the inner bone cavities contain bone marrow where red blood cells are produced [4].

Osteoporosis is a metabolic bone disease characterised by a decrease in bone density of normally mineralised bone, resulting in thinning and increased porosity of the bone and structural deterioration of bone tissue. This leads to bone fragility and increased susceptibility to fractures of the hip, spine, and wrist. It has been reported in all ethnical backgrounds and affects mostly elderly people, especially women.

An inadequate supply of calcium over the lifetime is thought to play a significant role in the development of osteoporosis. As a result, the dairy industry has used osteoporosis as a marketing tool, but milk does not seem to be the answer. In fact, many studies show that dairy products have little effect on osteoporosis [5]. For the vast majority of people, the answer is not boosting calcium intake but, rather, limiting calcium loss. The skeleton acts as the biggest calcium reservoir for the human body and a very crucial factor is the ratio of the amount of calcium taken in from the diet to the amount of calcium continuously lost to the blood to keep the blood values in balance. This process is regulated by hormones and this is one of the reasons for the calcium balance change in women after menopause. Moreover it was recently found that the proteins present in milk

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and meat have a negative effect on the uptake of calcium by the organism [6]. The amino acids (which are the building blocks of proteins) cause the blood to become slightly more acidic. To neutralise this acidic effect, bone material is dissolved, which is believed to lead to the loss of calcium via urine. Another factor playing a role in the calcium balance is the calcium to phosphorus ratio. It is believed that diets in which phosphorus and calcium intake are roughly equal help keep to calcium in the body, while diets in which the two are unbalanced are thought to harm calcium balance. Calcium supplements can help slowing down the process of bone loss.

From the above it may become clear that a good knowledge of the effect of the various constituents of the supplement on the uptake in bone is essential to design better calcium supplements. Recently, a study has been performed to analyse the effect of various calcium supplements with nuclear analytical techniques [7]. In particular, the content of calcium, strontium and zinc has been determined by NAA in bones from a large number of rats treated with different calcium supplements and subsequently executed. NRCA offers possibilities for this kind of research, since it is an isotope-specific technique and thus allows for multi-tracer elemental analysis. Calcium has six stable isotopes. This would allow one to study the uptake of calcium from different diet supplements in the bone directly and with less experimental effort both in vivo and in vitro, as one could study as many supplements simultaneously as there are stable isotopes that can be detected separately.

A further application of NRCA could be in the evaluation of bone condition. This is usually assessed by indirect factors, e.g. blood values, but also by direct methods, e.g. Bone Mineral Density (BMD) evaluation, which can be determined in vivo in various ways. Some of the techniques used are X-rays, CT scanning, magnetic resonance imaging (MRI), bone scintigraphy and ultrasonography [8]. In X-ray or γ-ray single or dual absorptiometry the variation in attenuation coefficient between bone and soft tissue is applied to determine the bone mineral content (BMC) [9, 10, 11]. The accuracy of these measurements is jeopardised by the presence of varying amounts of soft tissue (fat and muscle) in the human body. Moreover, some authors [12, 13] dragged the attention on the fact that the above BMD measurements might not specify the cause of the decrease in bone density: it could be due to a decrease in calcium or phosphorous or to different decreases in both. Furthermore, the Ca/P ratio in bone seems to change with age, suggesting age-related alterations beyond the usual bone loss that accompanies ageing. In other words, the Ca/P ratio might also be of importance in the assessment of bone related diseases [13]. The measurement of these two elements in vivo can be done with neutron activation analysis. However the measurement is not optimised for the simultaneous determination of both (see [13] and references therein). G. Fountos et al. suggested a new method, which is a modification of the dual X-ray absorptiometric method [12, 13]. Subsequently they validated the technique with neutron activation analysis in vitro [14].

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NRCA is used for the determination of elemental ratios and, in this respect, it could be a suitable technique for the determination of the Ca/P ratio in vivo.

However, the goal of some of the research performed in this thesis is restricted to the investigation on the possibilities that NRCA might offer in the frame of stable-isotope experiments to be applied to the osteoporosis problem. Therefore, no experiments on living animal or human material have been performed.

1.1.2 Tin in bone: bone tumour treatment

Aggressive bone tumours occur both among young and old people and are very difficult to treat. Further, bone metastases occur frequently parallel to the most common malignancies (prostate, breast, lung etc.), impairing the quality of the remaining life of the patient with pain and complications, e.g. fractures.

Radionuclides are extensively used for the diagnosis and treatment of bone cancer and metastases. The problem encountered with this kind of treatment is to achieve therapeutic doses in bone tumours while avoiding the risk of marrow depression. The research in this field is very extended and this particular problem is one of the principal issues. An overview of the issues in tumour diagnosis and treatment may be found in references [15, 16, 17, 18]. As bone tumours often occur in the extremities, isolated limb perfusion, has been proposed [19]. Whatever technique is used to get the radionuclides to the bone, the purpose is to establish the conditions that will result in maximum uptake of the radionuclide in bone tumours and minimum uptake in healthy tissue to achieve a therapeutical or palliative effect. To this end, basic knowledge of the binding of the radioactive compounds to hydroxyapatite, the mineral phase of bone, as well as the effect of plasma proteins and other biomolecules must be acquired. Research in this field is usually performed with the use of radioactive labelled compounds of the metals of interest. One of the metals studied is tin, in particular the metastable isotope 117m_Sn,

because of its interesting properties (i.e. both emission of gammas and electrons) [16]. For research purposes, more stable isotopes of the element tin than radioactive ones are available - tin has ten stable isotopes. Since NRCA is an isotope specific analysis technique that, as opposed to radiochemical labelling, can detect stable isotopes, it allows for the study of complex dynamical equilibria between different tin compounds, each labelled with enriched isotopes of tin. Also for this application, no experiments on living organisms were performed, but only the feasibility of NRCA to analyse tin in a bone matrix was tested.

1.1.3 Chloride in marble

Marble, an aggregate of calcite (CaCO3)crystal granules, is a stone used in structural

and non-structural elements both in ancient and modern buildings. It is the most frequently used metamorphic rock*_{for thin wall panels. It is formed by the}

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metamorphosis of limestone (a sedimentary rock composed of calcite) and its composition depends on the type of carbonate present in the original rock and its purity. If it is formed from pure calcite grains, a white marble will result. Impurities will change its colour even if present only in very small amounts. For instance, manganese traces result in pink coloured marbles and magnesium oxide gives a yellow colour. The metamorphic processes change the original limestone from a porous rock with voids to a more crystalline product with medium to coarse grain size, resulting in a mosaic-like structure with maximum density and strength and minimum pore space [20].

Regardless of their very dense structure, weathering can cause serious problems to marble structures. As these processes involve solid-state reactions in a very compact structure, the time scale of the reactions is usually long; however, the presence of moisture may significantly increase the deterioration processes. In case of frost, the volume increase due to ice forming may cause dramatic cracks in stone structures. Thermal cycles due to sun heating during the day and cooling at night are also dangerous as they cause irreversible expansion of calcite, which crystallises with preferentially orientations in marble. In particular, when heated, calcite expands along the long axis and contracts along the short one; as the process is irreversible, residual stresses will remain after cooling, which can cause the marble to disintegrate [21]. Temperature changes also cause the water trapped in narrow capillaries to vary in volume, thus exerting forces on the capillary walls that may damage the structure in the long run. Frost produces volume expansion due to ice formation, which has the same effects [20]. Such adverse conditions favour the ingress of ions such as chlorides or sulphates, transported by wind and especially rain water. This can cause the dissolution of the calcium carbonate on the surface of the structures or, after water evaporation, salt crystallisation. This may cause stone decay due both to the tension generated by crystal growth or by build up of internal pressure on the pore walls due to water adsorbed by anhydrous salts crystallised in the pores [21]. A famous example of damage in marble caused by chlorides is the Willem van Oranje tomb in the Nieuwe Kerk in Delft. The chloride is difficult to remove, and the methods currently employed to preserve the artefacts are disputed because they are irreversible, e.g. impregnation with plastic.

NRCA offers a tool to determine chloride relative amounts in the sample without need of polishing or treating the sample prior to analysis. Compared to INAA, less

- igneous or primary rocks, which crystallise from a hot silicate melt, the magma. An example of such rocks is granite

- sedimentary or layered rocks, which are formed by accumulation of fragmentary rock material by streams, waves and wind or by organic accumulation and chemical precipitates. Their structure and composition is very variable

- metamorphic rocks, which form when igneous or sedimentary rocks are subjected to high pressures and temperatures by burial beneath accumulating sediments or movements of the earth’s crust. In response to these changes, the original rocks crystallise to more stable mineral phases. Such rocks are usually tightly interlocked and show a serrated texture [20]

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activation occurs. As both the neutrons and prompt gammas have high penetrating power, measurements of chloride concentrations deep into the marble are feasible.

1.1.4 Analysis of lead in bronze archaeological artefacts

NRCA has already been employed for the analysis of bronze archaeological artefacts [1, 2]. The resonances in the TOF spectra, specific to each isotope, are used to identify the elements present in the sample. In these bronze objects, apart from copper and tin, other elements, such as arsenic, antimony, silver, gold, iron, indium, cobalt and lead, might be present as impurities. The presence and concentration of various impurities is helpful for archaeologists to assess the origin of the tin and the copper employed for the fabrication of the objects. This, in turn, gives information on the period and on the culture in which the object was manufactured. Further, the absence of impurities such as arsenic, antimony and silver might show that an object was made with modern materials, i.e. a falsification, since in the ancient times, the technology to purify and to separate the metals from their ore was less sophisticated than it is today.

NRCA was successful in determining the elements indicated above, all having resonances in the low-energy range. However, in the case of lead, which shows interesting resonances only in the keV range, the sensitivity was not satisfying, due to the high background at this energy. The goal of the research performed in this thesis is the improvement of the experimental conditions for the quantification of lead in bronze artefacts.

1.2 The NRCA principle

Three aspects of neutron interaction with nuclei can be employed for the elemental analysis of a variety of objects and materials. These are [22]:

1) radioactive nuclei produced by neutron capture 2) prompt γ-rays emitted after neutron capture

3) resonances occurring in the cross section as a function of neutron energy.

The method based on the first aspect, which was also the first to be applied, is known as neutron activation analysis (NAA) and identifies radionuclides based on their half-lives, radiation characteristics and chemical behaviour. Later the method was further developed by employing high resolution γ-detectors, which allowed for the identification and quantification of isotopes based both on the energy of the γ-rays emitted as well as on their half-lives. This method is named Instrumental Neutron Activation Analysis (INAA) and is a very valuable analytical tool.

The second aspect involves the determination of the energy of the prompt γ-rays emitted after capture of neutrons. This is the base of a technique known as Prompt Gamma Neutron Activation Analysis (PGNAA), which is employed in a number of

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institutions and has reached a high degree of sophistication at the Budapest Research Reactor in the group of Molnar.

The third aspect, concerning resonances occurring in the neutron cross section as a function of energy, is employed in Neutron Resonance Capture Analysis (NRCA). When a neutron is captured by a nucleus A_{X, a nucleus}A+1_X*_{of the same element in an excited}

state is formed. If the sum of the kinetic energy of the neutron and its binding energy is equal to the energy associated with an excited state of the new nucleus, a resonance effect occurs, which increases the probability of neutron capture. This results in resonance peaks in the nuclear reaction probability as a function of neutron energy, which is expressed as cross section. Since the resonances occur at neutron energies specific to each isotope, this method may be used to identify isotopes and elements. The neutron energy is determined with the time of flight (TOF) technique by detection of the prompt γ-radiation emitted immediately after capture. In order to apply the TOF technique a pulsed neutron source is used.

Because of the high penetrating power of prompt gammas and neutrons, NRCA determines bulk concentrations. This renders it a complementary technique to XRF (X-ray Fluorescence) and PIXE (Proton Induced X-(X-ray Emission) which give information of the composition of a very thin surface layer. Also, NRCA does not require any treatment prior to analysis, while XRF or PIXE require sample surface cleaning, which may not be suitable for unique or very valuable samples, e.g. historical artefacts. For NRCA it is not necessary to take samples from an object and dissolve them, as is usual in chemical analysis, e.g. atomic absorption and optical emission spectroscopy. By employing an open detector system, large objects may be examined. NRCA has been first applied for archaeological objects [1, 2, 23]. Finally, the induced radioactivity can be very low, especially when filters are employed to cut out low-energy neutrons from the neutron beam. These features render NRCA a fully non-destructive technique - even more so than instrumental neutron activation analysis.

Since isotopes of the same element are chemically identical, each can be used to study the behaviour of the element. Radioactive isotopes have often been used to this end. In some cases, it is also possible to use enrichment of stable isotopes to label a compound and trace its fate. This is necessary if no radionuclide with a suitable half-life and/or radiation emission is available, or if the use of radioactivity itself is unwanted. When stable isotopes are used, isotope-specific analysis techniques are required. Inductively coupled plasma mass spectrometry (ICP-MS) is the obvious choice for liquid samples, and INAA for solid samples that might be difficult to dissolve. But INAA can only detect those stable isotopes that yield a suitable radionuclide after neutron capture, whereas NRCA can detect any isotope that exhibits suitable resonance capture cross sections. In practice and depending on neutron energy, some resonances are more convenient than others; however, with the right choice or combination of detectors, many elements can be detected at very low concentrations, as will be shown hereafter.

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NRCA offers essential advantages as compared to various neutron activation analysis techniques. In standard NAA, the produced radionuclide may not decay during the measurement. In PGNAA irradiation and measurement are simultaneous, so that each capture event may be detected. NRCA shares this advantage with PGNAA. In PGNAA, however, the identification is based on γ-ray energy and the required high-resolution detection of rays in the 10 MeV range results in low detection efficiencies. Since the γ-radiation in NRCA only serves to indicate the moment in time when the capture event occurred, the precise knowledge of the γ-ray energy is not necessary. As a consequence, a γ-ray detection system with high energy resolution is not needed; instead, a system with large detection efficiency and good time resolution may be chosen. Keeping in mind that in general capture events are followed by the emission of up to six prompt γ- rays, the detection efficiency is considerable – in the order of 10-1_.

As a consequence of this, very low or no activation needs to occur during irradiation, making it possible to let a sample undergo different treatments and repeated analysis runs.

1.3 Reaction theory

1.3.1 Reaction types [24]

Whenever the nuclei of a given species are bombarded with neutrons, nuclear reactions can be observed with probabilities expressed as cross sections in units of barn (1 b = 10-24_cm2_{). In the range of neutron reactions from thermal to MeV energies, four}

distinct processes can be distinguished: the compound nucleus reactions, the direct reactions, the semi-direct reactions and the potential scattering. These are listed in Figure 1.1.

Potential scattering

σ

p Direct reaction Semi-direct reaction

Compound nucleus reaction Total

reaction (n,tot)

σ

_t

Figure 1.1. Main neutron reactions below 20 MeV [24].

When neutrons collide with a nucleus they may form compound states of very high complexity, decaying usually via particle decay, γ-decay or fission. In some events, the incident neutron may be directly absorbed without intermediate state. The direct reaction such as the direct capture is a one-step reaction in which the nucleons that do not participate to the reaction are left undisturbed. In the semi-direct reaction there are a limited number of nucleon rearrangement steps before the final state is reached. The

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non-resonant “potential” or external scattering reaction is characterised by cross section

( )

2

4Π R' , in which R' is the effective radius of the nucleus in the scattering channel. The

total reaction cross section σ is the sum of the reaction cross sections for the partial t

reactions that occur. These can be: elastic scattering [(n, n), σ ], inelastic scattering [(n, n’), s

'

s

σ ], radiative capture, [(n, γ), σγ], fission [(n, f), σf] and other reactions such as (n, xn), (n, p) and (n, α).

The total and the capture cross section of the 40_{Ca isotope are shown in Figure 1.2.}

The cross sections are characterised by resonance structures. At relatively low energies the resonances are well separated and the distance between them is relatively large compared to their natural line width and the instrumental resolution. With increasing energy the average level distance D decreases and the average total natural line width

Γ increases. Although at intermediate energies the resonance structure still exists, the resonance structure can no longer be resolved. Thus, two resonance regions can be distinguished, that of the resolved resonances (RRR), and that of the unresolved resonances (URR) with overlapping resonances, that is when Γ >> D .

10-3 10-2 10-1 100 101 102 103 104 105 106 107 1E-5 1E-4 1E-3 0.01 0.1 1 10 100 40 Ca(n, γ) 40 Ca(n, tot)

Cross section [barn]

Energy (eV)

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1.3.2 Compound reaction: resonances [24]

In the framework of the Bohr compound nucleus [24], a neutron induced reaction is considered a two-step process:

{ 1 * ' A A Z Z EXIT ENTRANCE _CHANNEL CHANNEL _C C X + →n + X → Y+ 123 i (1.1) 1 A Z

X

+ A Z

X

1 A Z

X

+ A Z

X

Figure 1.3. Neutron capture, elastic and inelastic level scheme. The excited resonances decay by γ-ray emission to lower energy states. Inelastic scattering reactions occur when the energy in the centre of mass exceeds the energy of the first excited state in the target nucleus [24].

The process is depicted in Figure 1.3. Since in general it is impossible to describe the complex nucleus we are dealing with and its excited states in terms of wave functions, the Bohr compound nucleus model provides an adequate description of the interactions through the statistical properties of the nuclear system. The complex interactions between the (A + 1) nucleons lead to the independence hypothesis according to which the formation and the decay of the compound nucleus are independent from one another. In this model, the absorption of the neutron is followed by a rapid distribution of the available energy among the other nucleons. The lifetime is about 10-16_{- 10}-18_{s. The total}

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excitation energy (E*) of the nuclear system is determined by the neutron separation energy (Sn) of the compound nucleus plus the kinetic energy of the incident neutron in the centre of mass system ECM:

*

n CM

E =S +E (1.2)

When the energy of the compound system corresponds to that of an excited state, a resonance is observed at the laboratory energy E0. The relationship between ECM and E0 is expressed as follows: 0 1 CM A E E A ⎛ ⎞ = ⎜_⎝ ₊ ⎟_⎠ (1.3)

where A is the nuclear mass number. The difference between ECM and E0 is negligible when A >> 1. In the remaining part of the thesis ECM is replaced by E. The unbound states of the compound nucleus explain the presence of neutron resonances. The lifetime (τ) is correlated to the total width of the resonance (Γ) by the Heisenberg uncertainty principle:

h

Γτ = (1.4)

The total width of the level is the sum of the partial widths corresponding to the decay possibilities of the compound nucleus. In the case of non-fissile nuclei and neglecting p- and α-emission, only elastic and capture reactions occur in the resolved resonance range. The total width is thus defined as:

n γ

Γ Γ= +Γ (1.5)

in which Γn is the neutron width and Γγ is the capture width.

Unbound and bound states have a definite spin and parity Jπ. The possible values depend on 1) the spin I and parity πI of the target nucleus, 2) the spin i and parity πi of the incident particle and 3) the orbital momentum l of the incident particle. Their vectorial combinations lead to the channel spin (S) and to the total angular momentum (J) and parity (π) of the compound state:

( )

1 l _I _i I i S I i l S J l S π π π − ≤ ≤ + − ≤ ≤ + = − × × (1.6)

The so called statistical spin factor g gives the probability of getting the correct angular momentum J from the intrinsic spins of the target nucleus and of the incident particle:

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(

2 21 2

)(

1 1

)

J g i I + = + + (1.7)

An interaction may occur if the J'π' value of the exit channel c'={α', l', s', J'}is equal to the Jπ value of the entrance channel c={α, l, s, J}. The α and α' indexes characterise the nature and the number of nucleons of the entrance and outgoing pair, respectively.

In the simplest representation, the capture cross section of a single resonance is described by the so-called Breit-Wigner formula [1]:

(

)

( )

2 0 0 2 2 0 4 2 n E g E _E _E γ γ Γ Γ λ σ π _Γ = − + (1.8) 0

λ being the neutron wavelength.

The maximum value for the capture cross section occurs at energy E0 and is given by

( )

2 2 6 0 0 2 2 2.608 10 1 n n g g A E eV A γ γ Γ Γ Γ Γ λ σ π Γ Γ × ⎛ + = = _⎜ ⎝ ⎠ γ ⎞ ⎟ [barn] (1.9)

The finite mass has a small influence on the cross section through the factor 2 1 A A + ⎛ ⎜ ⎝ ⎠ ⎞

⎟ . This factor is significant only for light nuclei.

1.3.3 Capture area

A factor of importance for NRCA is the integrated resonance capture cross section, that is the area A_γ over the Breit-Wigner formula for capture (Equation 1.8). If E0 >>Γ , the factor E0 ₁

E ≅ may be neglected and the integrated capture cross section becomes: 2 0 6 0 1 4.0966 10 2 n g A A E A γ γ γ Γ Γ π σ Γ Γ + ⎛ = = × × _×⎜ ⎝ ⎠ ⎞ ⎟ [barn eV] (1.10)

This equation is valid also with Doppler broadening, since this effect does not change the resonance area.

1.3.4 Doppler broadening

The Breit-Wigner expression (Equation 1.8), which describes the resonance cross section, does not take into account the thermal motion of the target nuclei, whose velocities at room temperature are not negligible compared to the neutron velocities. This gives rise to a Doppler effect, with a Doppler width that might be larger than the natural resonance width. Equation 1.1 must thus be modified to take this effect into account.

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Many authors have addressed this problem in the past by employing the free gas model [26, 27, 28]. The Doppler broadening may be represented by the following Gaussian function [29, 30]:

( )

(

2

)

2 1 exp rec D D E E S E ∆ ∆ π ⎧ ₋ ⎫ ⎪ ⎪ = _⎨− ⎪ ⎪ ⎩ ⎭⎬ (1.11)

where Erec =E0

(

A+1

)

is the recoil energy and ∆ is the Doppler parameter: D

(

)

4 0.0186

1

D k T Eeff rec Teff E _A

∆ = π = ₊ [eV] (1.12)

k being the Boltzmann constant. The Doppler width at half maximum is

(

2 ln 2

)

∆ . _D The effective temperature, Teff , in the Debye model is given by:

3 3 coth 8 8 D eff D T T T T ⎛ = _⎜ ⎝ ⎠ ⎞ ⎟[K] (1.13)

where TD is the Debye temperature, which can be found tabulated for metals

(e.g.[31]), but not for compounds. At high temperature, 2 9 1 128 D eff T T T T ⎡ _⎛ _⎞ ⎤ = ⎢ + ⎜_⎝ ⎟_⎠ ⎣ ⎦⎥. At low temperatures 3 8 eff D T ≅ T .

The Lorentz resonance line shape described by the Breit-Wigner formula must be folded with the Gaussian broadening function to obtain the real line shape of the resonance.

The Doppler broadened expression for resonance capture may be written as [29]:

( )

0

(

)

0

(

)

2 2 , 2 2 1 4 , exp 1 2 eff x y dy b b ac x x y a γ γ γ σ σ β σ β β π ∞ −∞ ⎧ ₋ ⎫_{− ±} ₋ ⎪ ⎪ = Ψ = _⎨− _⎬ + _⎪_⎩ _⎪_⎭

∫

(1.14) with _x 2 E

(

E0

)

Γ −

= and β =2∆ Γ_D . The integration can be performed only

numerically.

The maximum of the cross section at x=0 is reduced by the factor

(

)

2

( )

1 ₁ , 0 π exp erfc β _β β β ⎛ ⎞ Ψ = × _⎜ _⎟× ⎝ ⎠ (1.15)

If ∆D <<Γ the shape of the resonance curve remains Lorentzian with effective width

( )

2

4 ln 2

eff D

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If , the resonance curve shape becomes similar to the Gaussian represented by Equation (1.11). Since the resonance area does not change as a consequence of broadening, the maximum height of the capture resonance becomes

D ∆ >>Γ 0 0 , 2 D D γ γ γ πσ Γ σ ∆ = (1.17)

Far away from the resonance energy E0 the Lorentzian shape of the wings is retained.

References

[1] H. Postma, M. Blaauw, P. Bode, P. Mutti, F. Corvi, P. Siegler, “Neutron resonance capture analysis of materials”, J. Radioanal. Nucl. Chem., 248, 115-120 (2001)

[2] H. Postma, M. Blaauw, F. Corvi, “Application of neutron resonance capture in archaeology using time of flight technique”, ISINN-9 Conference Dubna, Russia, 497, 22-26 May 2001

[3] M. Blaauw, H. Postma, P. Mutti, “Quantitative neutron capture resonance analysis verified with instrumental neutron activation analysis”, Nucl. Instrum. Methods Phys.

Res. A, 505, 508-511 (2003)

[4] http://www.spineuniverse.com/displayarticle.php/article1224.html

[5] B.L. Riggs, H.W. Wahner, L.J. Melton 3rd, L.S. Richelson, H.L. Judd, W.M. O'Fallon, “Dietary calcium intake and rate of bone loss in women”, Journal Clinical

Investigation, 80 (4), 979-982 (1987)

[6] T. Buclin, M. Cosma, M. Appenzeller, A.F. Jacquet, L.A. Decosterd, J. Biollaz, P. Burckhardt, “Diet acids and alkalis influence calcium retention in bone”, Osteoporosis

International, 12 (6), 493-499 (2001)

[7] S. Hu, X. Mao, Z. Chai, H. Wang, H. Ouyang, J. Zhang, “Effect of calcium supplements on osteoporosis by using nuclear analytical techniques”, J. Radioanal.

Nucl. Chem., 259 (3), 369-373 (2003)

[8] A. Chevrot, J.L. Drape, D. Godefroy, A.M. Dupont, “Imaging of the chronic painful adult hip”, Journal de Radiologie, 81(3), 392-408 Sp. Iss. (2000)

[9] C. E. Neville, P. J. Robinson, L. J. Murray, J. J. Strain, J. Twisk, A. M. Gallagher, M. McGuinnes, G. W. Cran, S. H. Raston, C. A. G. Boreham, “The effect of nutrient intake on bone mineral status in young adults: the Northern Ireland young hearts project”, Calcif. Tissue Int., 70, 89-98 (2002)

[10] J. R. Cameron, J. A. Sorenson, “Measurement of bone mineral in vivo. An improved method”, Science, 142, 230-236 (1963)

[11] G. W. Reed, “The assessment of bone mineralisation from the relative transmission of 241_{Am and}137_{Cs radiations”, Phys. Med. Biol., 11, 174-180 (1996)}

[12] G. Fountos, S. Yasumura, D. Glaros, “The scheletal calcium/phosphourus ratio: a new in vivo method of determination”, Med. Phys., 24 (8), 1303-1310 (1997)

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[13] G. Fountos, M. Tzaphlidou, E. Kounadi, D. Glaros, “In vivo measurement of radius calcium/phosphorus ratio by x-ray absorptiometry”, Appl. Radiat. Isot., 51 (3), 273-278 (1999)

[14] M. Tzaphlidou, V. Zaichick, “Neutron activation analysis of calcium/phosphorus ratio in rib bone of healthy humans”, Appl. Radiat. Isot., 57, 779-783 (2002)

[15] C.J. Anderson, M. Welch, “Radiometal-labeled agents (non-technetium) for diagnostic imaging”; Chem. Rev., 99, 2219-2234 (1999)

[16] W.A. Volkert, T.J. Hoffman, “Therapeutic radiopharmaceuticals”; Chem. Rev., 99, 2269-2292 (1999)

[17] R.E. Weiner, M.L. Thakur, “Metallic radionuclides: applications in diagnostic and therapeutic nuclear medicine”, Radiochim. Acta, 70/71, 273-287 (1995)

[18] G. Stöcklin, S.M. Qaim, F. Rösch, “The impact of radioactivity on medicine”,

Radiochim.. Acta, 70/71, 249-272 (1995)

[19] R.A. Claessens, G. Rakhorst, Z.I. Kolar, J. Elstrodt, J. ter Veen, D.A. Piers, J.R. Van Horn, “Isolated limb perfusion with Sn-117m-bisphosphonate for treatment of bone tumours: feasibility and safety”, Journal of Nuclear Medicine, 42 (5), 1144 Suppl. S (2001)

[20] E.M. Winkler, “Stone in Architecture; properties, durability”, Springer, 1994

[21] M.R. Smith, eds., “Stone: building stone, rock fill and armourstone in construction”, Geological Society, London, Engineering Geology Special Publication, 16, 1999 [22] H. Postma, P. Schillebeeckx, “Non-destructive analysis of objects using neutron

resonance capture”, J. Radioanal. Nucl. Chem., accepted

[23] H. Postma, M. Blaauw, P. Schillebeeckx, G. Lobo, R.B. Halbertsma, A.J. Nijboer, “Non-desctructive elemental analysis of copper-alloy artefacts with epithermal neutron-resonance capture”, Czech. J. Phys., 53 (Suppl. A), A233-A240 (2003)

[24] B. J. Allen, “Theory of slow neutron – Radiative capture”, in “Neutron Physics and Nuclear Data in Science and Technology. Volume 3: Neutron Radiative Capture”, R. E. Chrien Ed., Pergamon Press, Oxford, 1984

[25] N. Bohr, “Neutron capture and nuclear constitution”, Nature, 137, 344 (1936)

[26] H. A. Bethe, “Nuclear Physics, B. Nuclear Dynamics, Theoretical”, Rev. Mod. Phys., 9 (2), 69-244 (1937)

[27] J. E. Lynn, E. R. Rae, “The analysis of neutron spectrometer resonance data”, J.

Nucl. Energy I, 4, 418-444 (1957)

[28] W. E. Lamb Jr, “Capture of Neutrons by Atoms in a Crystal”, Phys. Rev., 55, 190-197 (1939)

[29] J. E. Lynn, “The Theory of Neutron Resonance Reactions”, The International Series of Monographs on Physics, Eds. W. Marshall and D.H. Wilkinson, Clarendon Press, Oxford, 1968

[30] K.H. Beckurts and K. Wirtz, “Neutron Physics”, Springer-Verlag Berlin, 1964 [31] C. Kittel, “Introduction to Solid State Physics”, 7th_{Ed., Wiley, 1996}

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2. Chapter Two

The NRCA technique: experimental details

Abstract

In this chapter the GELINA experimental facility, where NRCA experiments were performed, is described, followed by the definition of the time-of-flight (TOF) method and the neutron-energy resolution function and its experimental verification. Subsequently, γ-ray detection is discussed and the NRCA detection set-ups are described. Finally, the way the data are handled is outlined.

2.1 The GELINA pulsed neutron source

In order to perform measurements in the field of neutron physics, a neutron source that covers a wide spectrum of neutron energies is often required. As already mentioned, the neutron energy is to be determined by the TOF technique. Therefore a pulsed source with a “white” spectrum is necessary. Several white spectrum neutron sources are available. These may be based on a nuclear reactor or on an accelerator. In the first case, usually a pulsed thermal and epithermal beam originates from a steady-state reactor with the use of a chopper. Accelerator based neutron beams can be pulsed as well; the time resolution is usually very high rendering them adequate for TOF measurements. Accelerator-based neutron beams may be generated in a variety of ways. In cyclotrons they are produced through a (p, n) reaction. In high-energy (ca. 800 MeV) proton-based machines they arise from spallation processes, resulting in highly energetic neutron beams. Finally, in electron based sources, neutrons are produced via Bremsstrahlung in a heavy nucleus, since the cross section for the process is proportional to Z2_{. The}

Bremsstrahlung photons then induce photonuclear reactions (γ, n) that produce neutrons. If

the target is fissionable, photofission reactions (γ, f) take place as well. The energy

distribution of the arising neutrons is centred on a few MeV and goes up to the energy of the incident electrons. This fast neutron spectrum may be slowed down by collisions in a

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moderator with low Z, e.g. hydrogen in the form of water. In this way, the accelerator can provide neutrons with energies varying from a few meV to several tens of MeV [1].

The Geel Electron Linear Accelerator (GELINA) produces neutrons with a pulsed electron beam and a uranium target. It was built in 1965 and subsequently upgraded in 1976, 1984 and 1994. A further upgrade is being actualised at the moment of writing of this thesis. In the following a short description of the machine is given; for more information, reference can be made to [2] and [3].

The accelerating section is shown in Figure 2.1. This is powered by three klystrons with an average power of 20 kW each. Electrons with energy of 100 keV are injected by a triod gun that produces bursts with a pulse length of about 10 ns. The electrons then go through three accelerating sections: the first one is a 2-m long tube with stationary electromagnetic waves, where the electrons are accelerated to a velocity close to the velocity of light (20 MeV). The further two sections are 6-m long and are traversed by travelling electromagnetic waves. When the electrons exit the accelerating sections, the electric field has divided the electron burst in 30 microbunches, separated by 0.33 ns, with energies progressively decreasing from 140 MeV to 70 MeV. The time difference between the first and the last microbunch corresponds to 10 ns. The electron beam is focussed by magnetic quadrupoles placed between the sections and at the accelerator exit. Beam divergences are eliminated by solenoids placed along the sections.

e

-

_beam

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Exiting the accelerating section, the 10 ns wide electron beam enters the target hall (Figure 2.2). In order to perform very accurate TOF measurements, the 10 ns pulse width should be reduced. This is achieved with a compression system, installed in 1984 [4]. It consists of a 360° bending magnet of diameter 2.5 m, which produces an average magnetic field of 0.37 Tesla. The magnet produces a non-uniform magnetic field so that electrons only make one tour inside the magnet. Electrons with higher energy cover a larger circular trajectory in the magnet, whereas the less energetic ones travel on a smaller circle. As a result, at the exit of the magnet all the microbunches are grouped in a pulse of about 1 ns which is appropriate for accurate TOF measurements.

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10 ns pulse

1 ns pulse

compression

magnet

e

-

_beam

Figure 2.3. The principle of the compression magnet (after [1]).

From the compression magnet, the electron beam hits a mercury cooled uranium rotating target, shown in Figure 2.4. The target rotation helps distributing the beam power along the target volume: the beam diameter is only a few millimetres and, if the target would be fixed, the electron energy would be concentrated in a very small volume and melt the uranium. With this solution, the beam power is dissipated along most of the target volume. Stopping electrons produce Bremsstrahlung, a process that is favoured by the high atomic number of uranium. The Bremsstrahlung initiates photonuclear reactions (γ, n)

and (γ, 2n) and, in minor quantity photofission reactions (γ, f) [5]. The energy distribution

of the neutrons produced shows a peak around 1-2 MeV, the intensity of the low energy neutrons being rather small. In order to increase the number of neutrons with energy lower than 100 keV, the neutrons need to be partially moderated. This is accomplished with two 4-cm thick beryllium containers filled with water. High-energy neutrons lose part of their energy by scattering with nuclei, nuclei with a low atomic number being more efficient: hydrogen and beryllium are thus ideal neutron moderators. The partially moderated neutrons have a Maxwellian energy distribution with average energy of 0.025 eV and a tail with approximately a 1 E shape.

The neutrons are emitted in all directions and enter into 12 flight paths with lengths between 8 and 400 m. These consist of evacuated aluminium tubes 50 cm in diameter with collimators made of either borated wax or copper. At specific points along the flight paths the pipe is interrupted around the measuring stations where the experiments are set up. Each flight path can be individually shielded against gamma rays and neutrons coming directly from the target with a lead / copper shadow bar. The area around the target is shielded by a 3-m thick concrete wall surrounding the target hall at a distance of 3.1 m from the target, as depicted in Figure 2.2. The same figure also shows the flight path numbers. The better energy resolution is achieved at flight paths perpendicular to the moderator, i.e. forming an angle of 90° with respect to the electron beam, because they view the moderator material under the smallest angle.

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Figure 2.5 gives an overview of the accelerator building and the flight paths built around it. The flight paths are situated around a line at a 90° angle to the electron beam at intervals of 9° or 18° between each other.

Figure 2.4. The uranium target [6].

Beam line

Measurement station

Target hall and accelerator building

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2.1.1 GELINA parameters and neutron flux

According to the user’s needs, the accelerator may be run with various parameter configurations. The most common settings are reported in Table 2.1.

Table 2.1. Common GELINA parameters. Pulse length

[ns] Frequency [Hz] Peak current [A] Mean current [µA]

Mean power

[kW] Mean neutron rate [n/s] without pulse compression

5 800 12 48 5.3 1.8 x 1013

10 800 12 96 9.6 3.2 x 1013

10 100 12 12 1.2 4.0 x 1012

2000 50 0.22 22 2.2 7.3 x 1012

with pulse compression

1 800 100 75 7.5 2.5 x 1013

The parameters most frequently used are those in the last row, because the 1 ns pulse length yields the best time resolution with high beam intensity. The lower frequencies (50-100 Hz) are useful for measurements with epithermal or thermal neutrons, as overlap of adjacent pulses for low energy neutrons is avoided at longer flight path lengths. This goes at the expense of a lower neutron rate. The total neutron flux is continuously monitored by BF3 proportional counters. The output is referred to in the text as CM1 (Central

Monitor 1).

Measurements of the neutron flux at GELINA showed that, above thermal energies, the flux at distance L is described by the following expression [6]:

( )

0.92 2 K E

E L

Φ = [cm-2_{, s}-1_{, eV}-1_{] (2.1)}

where E is expressed in eV and L in m; the value of the constant K depends on the operating power of the linac [6].

For the set-up used at flight path 5 (FP5) with a flight path of 14 meters, and 800 Hz 1 ns pulses, the flux per eV per cm2 _{may be approximated by the following expression [6]:}

( )

0.92

3600

E

Φ ₌ _{× E}− _[cm_-2_{, s}_-1_{, eV}_-1_{] (2.2)}

where E is again expressed in eV.

The neutron flux was monitored at FP5, just before the beam reaches the sample. Figure 2.6 represents such a measurement. The dips in the neutron flux are caused by the bismuth filter placed in the beam line (see Section 2.4).

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10 100 1000 10000 100000 1E-10 1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 Energy [eV] Yield [1/eV ]

Figure 2.6. Neutron flux per neutron produced measured at FP5.

2.1.2 The time-of-flight method

The time-of-flight (TOF) method is a very suitable technique to determine the energy of neutrons coming from a pulsed beam with a wide energy range. It is based on the measurement of the time a neutron takes to travel a known distance. From the time of flight the neutron energy can be calculated. For non-relativistic neutrons, i.e. of energy below 350 keV, the following expression is valid

2 2 1 2 n L E m t = (2.3)

where mn is the neutron mass, L the path length and t the time of flight measured. Inserting the neutron mass into Equation (1.8), the expression becomes:

2 2 5227.039 L E t = × cor [E in eV, L in m and t in µs] (2.4) The time of flight is measured by the difference between the starting time, t0, and the

arrival time, tn. In practice t must be corrected for the delay in the electronics and cables,

tcor. This may done by measuring the intense γ-radiation, called the γ -flash, travelling at the speed of light, coming from the neutron production target. t is thus given by

0

n

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For neutron capture measurements at GELINA, the signal for t0,indicating the begin of the neutron pulse, is given by the accelerated electrons passing trough a coil; tn is given by the detection of the γ-ray emission resulting from the neutron capture event. The time scale of the γ-ray emission after neutron capture is much smaller than the neutron flight time and can thus be neglected.

From Equation (2.3) it is understood that the sources of experimental uncertainty are correlated to the measurement of time and the measurement of length. The relative standard deviation in the energy value can be calculated from the following

1 2 2 2 2 E t L E t L ⎡ ⎤ ∆ _{= ×} ⎛∆ ⎞ ₊⎛∆ ⎞ ⎢⎜ ⎟ ⎜_⎝ _⎠ _⎝ ⎟_⎠ ⎢ ⎥ ⎣ ⎦⎥ (2.6)

Using Equation 2.4 the expression becomes 1 2 2 2 2 5227.039 E E t L E L ∆ _{= ×}⎡ _{× ∆ + ∆} ⎢⎣ ⎦ ⎤ ⎥ (2.7)

From this expression it is clear that the flight path length plays an important role in the energy resolution; the contribution to ∆L/L of the moderator thickness and sample

thickness can be reduced by increasing L, however, the neutron flux density decreases substantially with increasing distance (see Equation (2.1)). This factor should be taken into account when choosing the flight path length: a compromise should be made between resolution and intensity. The sources of uncertainty in the measurement are [1, 7, 8]:

- the duration of the neutron burst, which is not instantaneous but takes a certain amount of time, increasing the uncertainty in the time measurement

- the neutron target dimension

- the moderation time, that is the time the neutrons spend in the moderator. This depends on the dimensions of the moderator and on the angle between the path length and the moderator

- the sample thickness, which obviously gives an uncertainty in the flight length. Further, in thick samples, multiple scattering takes place: the neutrons lose their energy by being scattered from different nuclei in the sample, before being captured and the resulting γ-radiation detected. Neutrons with an energy slightly higher than the resonance energy are thus detected within the resonance region, resulting in a shoulder on the high-energy side of the resonance peak

- the promptness of detector response. For some detectors the variability in the time of response could be of importance, especially for short flight times.

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2.2 The neutron-energy resolution function: an example and its experimental verification

In an NRCA experiment the measured line width is broadened by a variety of experimental factors, as indicated in the previous section. For some practical applications,

e.g. the calculation of the detection and quantification limits in specific measuring

conditions, the resonance peak width as observed in the TOF spectrum must therefore be evaluated. In the following the procedure followed to build the neutron energy resolution function is presented and subsequently verified with experimental results.

In this work, the approach proposed by Moxon for the program REFIT [10] is followed. It consists of employing a resolution function, which is defined as the probability of detecting a neutron of energy E at time t. The function is constructed by convolution of several functions, each representing a specific component of the time dependence. The following are the components employed:

- the pulse shape of the initial neutron burst - the target material and geometry

- the time uncertainty introduced by varying residence times of neutrons during the slowing down process in the moderator

- the angle between the fight path and the source - the sample thickness

- the time jitter in the detector signal

The first two components were assumed to be independent of neutron energy, while the remaining were considered energy dependent.

Below, the components are described in detail. The functions presented were not normalised, so they are not probability functions. Since the result of interest in this chapter is the peak width, normalisation is irrelevant.

2.2.1 The initial pulse

The initial pulse produced by the GELINA may be approximated by a trapezium. It is defined by a half width at half maximum of 1.5 ns and a top to bottom ratio tb/tB = 0.7. Figure 2.1 represents the initial pulse produced by the GELINA.

2.2.2 The target

It is assumed that the neutrons emitted by the uranium target have an exponential decaying component due to the finite time to cross the target and the multiple scattering therein. The half life is thus proportional to the time employed by a fast neutron to cover a mean free path in the target material, the decay time. For the source of the GELINA it is 3.5 ns. The decay obtained is depicted in Figure 2.8.

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0 1 2 3 4 0.0 0.2 0.4 0.6 0.8 1.0 1.2 t_B t_b 1.5 ns A m plitude [a.u.] Time [ns]

Figure 2.7. The initial pulse of the GELINA.

0 10 20 30 40 50 0.0 0.2 0.4 0.6 0.8 1.0 Amplitude [a.u.] Time [ns]

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2.2.3 The moderator

The time distribution due to the moderation of fast neutrons in a hydrogenous moderator is represented by the following equation:

( )

Vt 2 Vt I t e λ λ − ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ (2.8)

( )

I t represents the intensity at time t after the neutrons entered the moderator, V is

the outgoing-neutron velocity and λ is the neutron effective mean free path in the moderator. The mean free path is mostly determined by the hydrogen content of the moderator. For an infinite polyethylene moderator and for non-relativistic neutrons, the mean free path has been estimated in the order of 6.2 mm [10]. This value has been employed for the GELINA moderator. The time dependence of neutrons emitted from the moderator with energy 10.833 keV is represented in Figure 2.9.

0 10 20 30 40 50 0.0 0.2 0.4 0.6 Am pl itude [a.u.] Time [ns]

Figure 2.9. The time dependence of neutrons emitted from the moderator with energy 10.833 keV.

2.2.4 Angle of the flight path to the moderator surface

The flight path is viewing the moderator at a particular angle θ with the normal to the moderator surface, causing an additional uncertainty in the resolution function because of resulting variation in flight path length. The response at time t is:

New neutron-based isotopic analytical methods; An explorative study of resonance capture and incoherent scattering

New neutron-based isotopic analytical methods

An explorative study of applications of

resonance capture and incoherent scattering

New neutron-based isotopic analytical methods

An explorative study of applications of

resonance capture and incoherent scattering

Table of contents

List of symbols

(

) (

)(

)

(

)

(

)

( )

( )

( )

( )

( )

( )

( )

(

)

List of abbreviations

1.Prologue

1.Chapter One

Neutron Resonance Capture Analysis

(NRCA)

σ

σ

( )

X

X

X

X

( )

(

)(

)

(

)

( )

( )

( )

(

)

(

)

(

)

(

)

( )

(

)

(

)

∫

(

)

(

)

( )

( )

2.

Chapter Two

The NRCA technique: experimental details

e

beam

10 ns pulse

1 ns pulse

compression

magnet

e

beam

( )

( )

_beam

_beam