Characterization of neutron stray fields for residual activation estimation around high-energy accelerators using spectrometric and Monte Carlo methods

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activation estimation around high-energy accelerators using spectrometric and Monte Carlo methods

Inauguraldissertation zur

Erlangung der Würde eines Doktors der Philosophie vorgelegt der

Philosophisch-Naturwissenschaftlichen Fakultät der Universität Basel

von

Roman Galeev

Basel, 2021

Originaldokument gespeichert auf dem Dokumentenserver der Universität Basel edoc.unibas.ch

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Genehmigt von der Philosophisch-Naturwissenschaftlichen Fakultät auf Antrag von

PD Dr. Daniela Kiselev, Prof. Dr. Bernd Krusche, Prof. Marco Caresana

Basel, 13.10.2020

______________________

Dekan der Fakultät, Prof. Dr. Marcel Mayor

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Abstract

Information about the neutron spectral energy distribution is useful for various purposes, in particular for radiation protection and dosimetry or for the determination of residual neutron-induced radioactivity in shielding materials of high-energy accelerators. A suitable device for spectrometric measurements of neutron fields is the extended range Bonner Sphere spectrometer (ERBSS). During this work, an ERBSS manufactured in Paul Scherrer Institute (PSI) was characterized and calibrated. Fur- thermore, state of the art measurement and data evaluation techniques based on Bayesian methods were adapted and optimized for the application in specific fields.

The neutron spectrum was measured with the ERBSS around the PSI high-intensity proton accelerator (HIPA). Results of these measurements were compared with results obtained by the Monte Carlo particle transport code (MCNP) to benchmark the models used for investigation of neutron radiation field properties and residual activation. For the application in a multi-source environment, the background subtraction method was developed. This method is based on the application of shadow object, Monte Carlo simulations and Bayesian data analysis. It was tested by measurements in a workplace field produced by the spent nuclear transport and storage cask in the interim storage (Zwilag).

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List of Figures

1.1 Plots of the elastic scattering cross section for¹H,¹²C,²⁰⁸Pb and²³⁵U [1] 6 1.2 Plot of the neutron capture cross section for³He(n,p)³H,¹⁰B(n,α)⁷Li

and⁵⁴Fe(n,γ)⁵⁵Fe [1] . . . 9 1.3 Neutron fluence to H^∗(10) conversion coefficients [2, 3] and the re-

sponse of the Berthold LB6411 neutron detector [4] . . . 13 1.4 Examples of the workplace spectra from different facilities [5] . . . 14 1.5 The example of the basic shapes combinations [6] . . . 17 1.6 Illustration of the surface splitting (blue arrows) and Russian roulette

(red arrows) with an example of 3 cells with different importance. Parti- cles are shown as a circles. Statistical weight of each particle is written on them. . . 19 2.1 Scheme of the TOF setup. Choppers are marked as "Ch" [7]. . . 22 2.2 Scheme of the recoil proton spectrometer with thin polyethylene foil as

the converter [8] This spectrometer is designed for the measurements at ITER facility [8]. . . 23 2.3 Scheme of the recoil proton spectrometer with liquid scintillator [9]Lis

a light output of scintillator. . . 24 2.4 Response functions for an scintillation detector for neutronsin the en-

ergy range between 1MeV and 19 MeV [10] . . . 25 2.5 Scheme of the spectrometer with nested moderators of cylindrical shape [11]. 26 2.6 The set of the moderators for BSS . . . 26 2.7 Scheme of the SP9³He filled proportional counter [12] . . . 27 2.8 Schematic illustration of the ionization chamber operation [13] . . . . 28 2.9 Schematic dependence of current on the applied voltage for a gas-filled

detector in the stray monoenergetic radiation field [14] . . . 29 2.10 The typical pulse height spectrum obtained with the³He counter [15] . 30 2.11 The exemplary response function for BSS (with activation foils) [16] . . 31 2.12 The exemplary data sets at the left calculated for different spectra at the

right (fission source (1), highely moderated fission source (2) or behind the shielding of high energy accelerator [5]) . . . 31

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3.1 Examples of the spectra around high energy accelerator facilities [5] . 36 3.2 Example of the parameterized model of the typical neutron spectrum be-

hind the shielding of high energy accelerators (top) and the comparison of the modeled spectrum with the simulations results (bottom) . . . 37 3.3 Example of the prior PDF assigned to the parameter and posterior PDF

obtained after evaluation with Gaussian fit, mean value and standard deviation (in the left data has a higher influence on the result than in the right) . . . 39 3.4 Plot of the correlation of the parameters for the high energy peak . . . 41 3.5 Example of the spectrum obtained from one data set with fixed and not

fixed position of the high energy peak . . . 42 3.6 Comparison of the integral values calculated from the spectra obtained

with parameterized model with different constrains, where HE is energy of the high energy peak . . . 43 3.7 Example of the unfolding of the artificially generated set of count rates

(with bare counter and without) . . . 44 3.8 Example of the spectrum in which the thermal peak is merged with the

intermediate region . . . 47 3.9 Example of the spectrum measured in reactor environment . . . 47 3.10 Examples of the highly moderated fields spectra [5, 17] . . . 49 3.11 Unfolding results for moderated²⁵²Cf source [5] with not modified model 49 3.12 Parameterized model for the spectrum unfolding with demonstration of

the additionally introduced parameters . . . 50 3.13 Spectra unfolded with BPE method with a parameterized model includ-

ing different parameters and with ME method (BPE results are used as a default for ME unfolding) . . . 51 3.14 Values of the fluence (left) and the ambient dose equivalent H^∗(10)

(right) calculated from the spectra unfolded with application of the parameterized models with different sets of parameters. Calculated values are normalized to the expected value derived from original spectrum.

The uncertainties are obtained by Bayesian parameter estimation method 52 3.15 Ratios of the partial fluxes of the unfolded spectra and partial fluxes

of original spectrum. The error bars represent the uncertainty coming from the evaluation method [18] . . . 53 3.16 Comparison of the original spectrum with the spectrum obtained with

unfolding by means of the Bayesian parameter estimation (modified model) . . . 54 3.17 Comparison of the integral values of the total neutron fluence (left) and

the ambient dose equivalentH*10(right) for original and unfolded spectra 55

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List of Figures

4.1 Functional scheme of the data aquisition system used for PSI BSS . . . 58 4.2 Cross section of the geometrical model of the BSS for response function

calculation [19] . . . 59 4.3 The variation of 12-inch spheres response assuming different PE densities 60 4.4 Simulated to measured ratios of the count rate for the 7-inch sphere for

two diameters and reduced³He pressure. The statistical uncertainty of the measurements is reasonably low and hence is neglected . . . 61 4.5 Layout of the GeNF irradiation facility [20] . . . 62 4.6 Comparison of the simulated and measured responses of proportional

counters in thermal field . . . 63 4.7 The voltage-current dependence estimated by measurements for the

detectors used with PSI BSS. The operating voltage is 820 V. . . 64 4.8 Layout of the accelerator facility used for the calibration of the neu-

tron measurement instruments with quasi-monoenergetic reference fields. T: target, SC2: scintillation detector for TOF measurements, SC1:

scintillation detector used as a monitor, NM: long counter with³He proportional counter, PLC: long counter with BF₃counter, He:³He proportional counter with moderator cap, GM: Geiger–Mueller counter used as a photon monitor, M: movable mounting stand for detectors under test, B: beam tube [21]. . . 65 4.9 Calibration facility for neutron measurement devices at the PTB [22] . 66 4.10 Simulated to measured ratios of the count rate for the BSS in quasi-

monoenergetic reference fields . . . 67 4.11 Final set of response functions for the PSI BSS. Response functions

for polyethylene moderators and bare counter at the top and for the spheres with a metallic layer at the bottom. The response functions for the spheres with a lead layer are indicated by dashed lines in the bottom plot . . . 68 4.12 The normalized spectral distribution of the neutron fields produced by

bare and moderated²⁵²Cf source at PSI calibration laboratory obtained by Monte Carlo simulations [23] . . . 69 4.13 Count rates measured with Bonner spheres with bare and moderated

252Cf source with polynomial fit . . . 70 4.14 Neutron spectrum measured with the bare and moderated²⁵²Cf source

of PSI calibration laboratory . . . 71 4.15 Comparison of the measured dose rate and reference value with bare

252Cf (left) and moderated²⁵²Cf source (right) . . . 71 4.16³He proportional counter used for PSI BSS [24] . . . 73 4.17 Vertical cross-section of the geometrical model used for the simulation 74

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4.18 Simulated count rate in the detector as a function of the distance between detector and source . . . 74 4.19 Americium-Beryllium neutron source with PSI inventory number 1056

with the threaded rod used for transportation . . . 75 4.20 Drawing of the central plates of the stand . . . 76 4.21 Detector in a cylindrical cover made of polyethylene . . . 77 4.22 Internal part of the stand with inserted detector and preamplifier . . . 77 4.23 Verification stand assembled with the detector in the reference position 78 4.24 Results of stability measurements conducted from November 2017 to

May 2018. Error bars represent expected deviation due to the manufacturing tolerances . . . 79 4.25 Measured pulse height spectrum given by a SP9³He detector (serial

number 0916-21) in the verification stand. The signals caused by the gamma particles do no interfere with the signals caused by neutrons . 79 4.26 Neutron and gamma dose rate behind the shielding with variable PE

thickness measured with LB 6411 neutron dose rate meter [4] and AD-B gamma dose rate meter [25] . . . 80 5.1 Scheme of the HIPA accelerator . . . 82 5.2 Vertical cross-section of the shielding above the Target M . . . 83 5.3 Ratio of the beam current monitor readings after and before the Target M 84 5.4 Distribution of the dose rate measurement results during 3 days with

Gaussian fit . . . 84 5.5 Area of the measurements above the Target M and positioning scheme.

WENDI-2 is on the left side. Other devices were used for testing purposes 86 5.6 The dose rate measured and estimated by Monte Carlo simulations. The

error bars for simulation result represent the statistical uncertainty only. 87 5.7 Measurement positions for the spectrum non-uniformity study . . . . 88 5.8 Relative values of the count rates obtained by different spheres for dif-

ferent positions . . . 89 5.9 Exemplary paramtrized spectra which make a difference within 6% in

the count rates for the speres used for spectrum non-uniformity study 89 5.10 Neutron spectrum measured above Target M together with normalized

simulations results (simulation is provided by Vadim Talanov, GFA PSI) [26] 92 5.11 Dose rates on top of the Target M shielding obtained with BSS and

WENDI-2 dose rate meter and dose rate estimated by Monte Carlo simulations. . . 92 5.12 Measurement system at the measurement position in PiM3 area next to

the muon beamline . . . 93

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List of Figures

5.13 Neutron spectral distribution measured at PiM3 area unfolded with BPE and ME method (normalized to 1 mA proton current) and scaled simulations results. Spectrum obtained by means of Monte Carlo particle transport is used as a default spectrum for unfolding [26] . . . 94 5.14¹⁵¹Eu neutron capture microscopic cross-section . . . 95 6.1 Geometrical model of the cask used for Monte Carlo simulation (pro-

vided by Nagra) and positions for spectrum measurements around the cask [17] . . . 98 6.2 The spectra unfolded with Maximum Entropy method, Bayesian Param-

eter Estimation and the normalized simulation result for position 1, 2 and 3 as numbered . . . 99 6.3 The spectra unfolded with Maximum Entropy method, Bayesian Pa-

rameter Estimation and the normalized simulation result for position 5 . . . 100 6.4 Spectral distributions used for investigation of the shielding cylinder

properties . . . 102 6.5 Scheme of the geometrical model used for the estimation of the shield-

ing properties of the shadow cylinder . . . 103 6.6 Spent nuclear fuel cask on the transport platform outside storage hall . 104 6.7 Measurement system in front of the cask inside the storage hall together

with shadow cylinder . . . 104 6.8 Scheme of the positioning for the measurements inside the storage hall 105 6.9 Comparison of the count rates measured outside andC R_{t ot al}-C R_{shad ow} 106 6.10 Horizontal and vertical cross-sections of the geometrical model used for

the Monte Carlo simulations . . . 107 6.11 Theαratio for different spheres defined for arbitrary suggested source

height (5.4 m) . . . 108 6.12 Count rates obtained after the application of the geometry related cor-

rection factor and count rates measured outside the storage hall . . . . 108 6.13 Comparison of theαratios for different source heights . . . 109 6.14 Comparison of theαratios for different spheres . . . 109 6.15 Count rates obtained after the application of the geometry related cor-

rection factor from both positions and count rates measured outside the storage hall . . . 110 6.16 Exemplary count rates with the 4th order polynomial fitting constraint 111 6.17 Polynomial fitting with different count rates of boundary spheres . . . 112 6.18 Fitted count rates obtained by the geometrical correction of the shadow

measurement (for the arbitrary source height) and the count rates measured outside the storage hall . . . 113

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6.19 Spectra obtained by the geometrical correction of the shadow measurement (for the arbitrary source height) and measured outside the storage hall . . . 113

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List of Tables

3.1 Relative values of estimated fluence and dose derived from the spectra 44 4.1 Technical parameters of the verification stand . . . 76 5.1 Ratios of the count rates for exemplary spectra . . . 90 5.2 Estimated values of the flux for different spectrum regions . . . 93 6.1 Neutron dose rates measured with BSS and two survey instruments . . 99 A.1 Geometrical dimensions of the PSI BSS moderators . . . 125

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Introduction

The fields of anthropogenic ionizing radiation can be found in different areas related to the industry, science or medicine. They are used for materials analysis, for patients treatment and diagnostics. In situations, where people can be exposed to ionizing radiation, it is necessary to follow the basic principles of radiation protection: justifi- cation, limitation and optimization [27]. Measurements of the radiation fields have to be in compliance with these principles and regulations. Furthermore, the information about radiation fields is used not only for radiation protection purposes, but also useful for radioactive waste management isses, as it determines the nuclide inventory.

At the Paul Scherrer Institute neutron radiation is of particular interest due to the operation of high energy accelerators, which produce neutron radiation for research purposes or as secondary radiation.

In this work, the properties of neutron fields are investigated by measurements, computer modeling or by the combination of these two methods with the emphasize on the measurement of the neutron spectral energy distribution.

The challenges accompanying measurements of neutron fields are the wide energy range of the particles covering up to 12 orders of magnitude. Furthermore, indirect ionization mechanisms of neutrons leads to the fact that the energy deposited in the detector is not always related to the energy of incoming neutron and further to a small detection efficiency of high energy neutrons. For the purposes of radiation protection, it is necessary to verify the compliance with the legal limits using com- mercially available devices with a single measurement, which should cover the whole energy range. The sensitivity of the available measurement devices does not always correspond to the energy dependent biological effect of the radiation, on which the legal limits are based [28]. This effects lead to the increase of the uncertainty of the neutron dose indications of survey instruments [4, 29]. Nevertheless, this uncertainty can be reduced using in-field calibration. This requires the reliable information about the neutron spectral energy distribution.

Besides the measurements, radiation fields can be also characterized using computational methods. The computational methods for radiation characterization described in this work can be applied, for instance, for the estimation of the residual activity

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of materials which are used to shield beam line components [30]. These methods are based on certain assumptions about the geometry configuration, material composition and beam losses. Often simplifications of the geometry are introduced.

Additionally, the results of the simulations depend on the applied physical models and evaluated cross-sections [31, 32]. It is desirable to benchmark the assumptions made for the simulations with the results of measurements. The state of the art spectrometric methods provide valuable information for this verification [33].

During the operation of high-energy accelerator facilities, the residual activity accu- mulates in beamline components and in shielding materials [34]. For the operation and maintenance of the facility, as well as for handling and release of this activated components, residual activity must be determined qualitatively and quantitatively according to licensing and clearance limits [35]. Since the activation level is dependent on the neutron flux and spectral energy distribution, reliable information about the neutron spectrum can improve its characterization.

To characterize the field in multi-source environment, it is desirable to isolate particular source by subtraction of the background. Additionally, this allows to estimate the contribution of a certain source to the dose received by workers.

All of this aims can be achieved by the application of the neutron spectrum measurement system. The suitable measurement system for that is the extended range Bonner spheres spectrometer (ERBSS) [36]. In order to evaluate the data measured with Bonner spheres spectrometer, a mathematically underdetermined problem has to be solved, what means that there are fewer equations than unknowns. This can be done by application of Bayesian methods, which however require the prior information about the measured field [37, 18]. For this work, an ERBSS comparable to the NEMUS spectrometer [38] was manufactured at Paul Scherrer Institute (PSI).

The project can be divided into two parts. The first part includes:

• Calibration of the ERBSS using the MCNP particle transport code [39].

• Verification of the ERBSS calibration in different reference fields.

• Stability assessment of the measurement system including the detector and the data acquisition system.

The second part contains:

• Further development and improvement of measurement techniques and data evaluation methods based on Bayesian analysis.

• Adaption of the improved methods for the application in specific neutron fields and measurement conditions.

• Investigation of the developed methods’ performance through measurements in different neutron fields and sensitivity studies.

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1 Basics

The nature of the particles-matter interaction defines the way of the detection of these particles. This chapter aims to explain the interactions of neutrons with matter in relation to neutron spectrometry and its applications. In the paragraphs that follow, the basics of the interactions between neutrons and matter will be described, including the physical properties of neutrons, an explanation of the interaction processes and the practical use and value of these processes.

Moreover, this chapter includes the description of the computational methods used for the definition of the neutron fields properties together with their theoretical basis.

The neutron radiation can have an affect on the human body, this effect has to be evaluated for a purpose of radiation protection and dosimetry. Due to this, following chapter contains the description of the methods of the radiation effects quantification.

1.1 Interactions of Neutrons with Matter

A neutron is a subatomic particle in a family of hadrons with no net electric charge and a mass of 1.675×10⁻²⁷kg. A free neutron outside of the nucleus is unstable and has a half-life 10.2 minutes.

A neutron is an indirectly ionizing particle, despite the absence of the interactions between the neutrons and electrons in an atomic shell, the products of the neutron nucleus reactions or the recoil nuclei can ionize the atoms of the absorbing material [40].

Depending on the source type and on the area of application, neutrons with different energies ranging from 10⁻⁷eV to hundreds of GeV can be found. There are no fixed energy classifications for neutrons, but however for the practical measurements related to this work, neutrons can be divided by the following groups:

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• Cold. The neutrons with the energies lower than thermal. Particular type is ultracold neutrons, which has a velocity below 7 m/s and can be stored in vessels made of special materials [41]

• Thermal neutrons. These neutrons are in thermal equilibrium with the sur- rounding media. Kinetic energyE_kis about 2.5 meV.

• Intermediate neutrons. These neutrons have energiesE_khigher than thermal, but lower than approximately 0.1 MeV

• Fast neutrons. These neutrons, also called fission or evaporation neutrons, have energiesE_kbetween approximately 0.1 MeV to 20 MeV

• High energy neutrons. These neutrons, also called cascade neutrons, have energiesE_khigher than 20 MeV. Such neutrons can be found at high energy accelerator facilities or in cosmic rays.

These energy groups are used for the approximate separation of the energy regions in the spectral distribution and they have no strict boundaries.

1.1.1 Interaction Cross Sections

The cross section is the effective area that defines the probability of the interaction of a neutron with the matter. The cross sections for different reactions are dependent on the target nucleus, the energy of the neutron and the temperature of the target material. A cross section given for a single neutron-nucleus interaction is called microscopic cross section and is measured in units of area calledbarn(1 barn = 10⁻²⁸ m²). Cross sections are estimated by measurements or described by nuclear models.

To describe the likelihood of interaction for a certain material themacroscopiccross section is used. It is related to the microscopic cross section in the following way:

Σij=σij·N_j, (1.1)

whereΣijis the macroscopic cross section for the reaction of i in material j,σijis the microscopic cross section of the reaction of i with the nucleus of material j andN_jis the nuclear number density of material j.

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1.1. Interactions of Neutrons with Matter

1.1.2 Types of Neutron-Nucleus Interactions

In this section, a brief explanation of the different types of neutron-nucleus interactions are provided and examples relevant to the study are given. These particles are neutral and do not interact with the electronic shell of the atoms like photons or charged particles do, but can interact with the nuclei. Due to the lack of the experi- mental data, the neutron transport for energies higher than 20 MeV is usually based on the theoretical nuclear models. Several models are available (e.g., Bertini Intranu- clear Cascade (INC) model, Binary INC model, ISABEL model, pre-equilibrium model, Fermi break-up model, etc.) with particular advantages and disadvantages. The application of the different models may lead up to the 20% difference in results [31]. In this work, theoretically defined response of the spectrometric system also depends on the applied nuclear model. Currently the research work is conducted to define which of the models is more suitable for certain conditions.The different types of neutron-nucleus interactions can be divided into the following groups.

Elastic Neutron Scattering

The elastic neutron scattering process is the interaction of a neutron with the nucleus of the target material with change of the kinetic energy of the incoming neutron. In this case, the kinetic energy of the neutron and target nucleus is conserved. With inelastic scattering part of the energy results in the excitement of the nucleus or emission of particles. The phenomenon of elastic neutron scattering can be described by the collision of two balls in Newtonian mechanics. If a neutron with the mass m_n and an initial kinetic energy of E_K collides with a nucleus with a mass of M, then the nucleus will recoil with an angleθrespective to the direction of the initial neutrons motion. The kinetic energy transferred to the nucleus can be defined with the following expression[42]:

∆E_K=E_K m_nM

(m_n+M)²cos²θ. (1.2)

The maximum energy transfer is reached for an angleφequal to 0.

Elastic scattering is the main mechanism of energy loss in the moderation process, when the neutron looses energy by several scatterings. As is illustrated in equation 1.2, the energy transferred to the recoil nucleus is higher if the mass of the target nucleus is lower. It is for this reason that the most commonly used neutron moderators are materials with a low atomic number such as materials containing hydrogen, deuterium, carbon etc.

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The dependence of the elastic scattering cross section on the neutrons energy has a similar behaviour for different isotopes. An example of the elastic cross section plots for¹H,¹²C,²⁰⁸Pb and²³⁵U is delineated in Figure 1.1 [1]. On the plots for thermal

Figure 1.1 – Plots of the elastic scattering cross section for¹H,¹²C,²⁰⁸Pb and²³⁵U [1]

energies, the cross section decreases linearly with increasing energy (1/v behaviour, wherev is the velocity of the neutron). The intermediate region cross section does not significantly change with energy. In the fast region, the elastic scattering cross section decreases, which is caused by increase of the probability of inelastic interactions [43].

The resonances (shown as sharp peaks on the cross section plot [44]) may occur for different isotopes in the intermediate and fast regions.

Elastic scattering plays an important role in the measurements of the neutron fields:

as some of the neutron detectors are sensitive mostly to the thermal neutrons, the fast neutrons must be first moderated in order to be registered in the volume of these detectors. For this reason, in the neutron radiation survey instruments, the detector is surrounded by a moderator such as polyethylene [45].

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Inelastic interactions

In the process of inelastic interaction, the kinetic energy of the incoming neutron and target nucleus is not conserved and is partially transferred into the excitation of the nucleus or emission of particles. The inelastic scattering is going through two steps.

First, the energy is partially transmitted from neutron to the nucleus, than the excited nucleus vibrates and emittingγ, neutron or other particle [42, 46]. This process of the inelastic interaction with gamma emission is described by following equation:

n+Â_ZX→Â+1_Z X^∗→Â_ZX^∗+n⁰→Â_ZX^∗→Â_ZX+γ, (1.3) whereÂ_ZX is the target nucleus,Â_Z⁺¹X^∗is the excited compound nucleus,Â_ZX^∗is the excited target nucleus andγis the gamma particle.

Neutron Capture

Many types of neutron capture are possible for different isotopes. Radiative capture is a type of neutron absorption that is followed by the emission of a gamma particle. It is described by the following expression:

n+Â_ZX→Â_Z⁺¹X^∗→Â_Z⁺¹X+γ. (1.4)

This reaction probability increases with decreasing neutron energy due to the fact, that slower neutrons have more time to interact. The neutron capture may also lead to the deexcitation of the nucleus through the emission of an alpha particle. The equation for this reaction is:

n+Â_ZX→Â+1_Z X^∗→Â−4_Z−2Y+α. (1.5)

The reaction with the emission of the alpha particle is particularly useful for neutron detection in BF3filled detectors [47]. The incoming neutron provokes the reaction and the resulting fragments have enough kinetic energy to ionize the filling gas and to be detected. The reaction can unfold in two ways:

n+¹⁰₅ B→¹¹₅ B^∗→⁷₃Li+α+2.793 MeV, in 6% of cases,

n+¹⁰₅ B→¹¹₅ B^∗→⁷₃Li^∗+α+2.313 MeV, in 94% of cases (1.6) In the case, when Li is in an excited state, it relaxes normally with the emission of a gamma particle.

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In the (n,p) capture process, the excited nucleus emits the proton after the neutronis absorbed. The equation of this reaction is as follows:

n+Â_ZX→Â+1_Z X^∗→Â−1_Z₋₁Y+p. (1.7)

The example of the application of (n,p) reaction is the detection of the neutrons with

3He filled proportional counters. The detection mechanism is similar to the one with BF₃. The reaction is displayed as follows :

n+³₂He→⁴₂He^∗→³₁H+p+0.764 MeV. (1.8)

Other types of captures including the production of multiple neutrons (2 or 3) or the production of the neutron and alpha particle together [48]. Examples of the different neutron capture cross sections are shown in Figure 1.2 (³He(n,p)³H,¹⁰B(n,α)⁷Li and

54Fe(n,γ)⁵⁵Fe) [1].

Moreover, the neutron capture reactions contribute to the neutron activation process.

The build-up of the isotopes produced as a result of the neutron capture leads to the induced radioactivity of the absorbing material. For example, the production of²²Na,

52Mn,⁶⁰Co,¹³⁴Cs,³H,⁵⁵Fe and¹⁵²Eu isotopes occurs in the concrete shielding around nuclear and accelerator installations (particularly by caused thermal neutrons) [49].

The residual activity of the certain isotope after the neutron irradiation is described by following equation:

A_{r es}=λΣc(E)Φ(E)³

1−e^−λt^{i r r}´

·e^−λt^{d ec}, (1.9)

whereA_{r es}is the residual activity after irradiation timet_{i r r} and decay timet_{d ec},Σc(E) is an energy dependent macroscopic capture cross-sectionΦ(E) is an energy dependent neutron flux,λis a decay constant of the given isotope. Practically, the estimation of the residual activity can be performed using Monte Carlo particle transport codes, like FLUKA [50] or by transmutation codes like Cinder’90 [51], SP-FISPACT [52] or ORIHET-3 [53] coupled with Monte Carlo simulations.

Spallation

Nuclear spallation is the disintegration of the target into smaller fragments as a result of an interaction with a high energy particle such as neutron, proton or heavy ion. De- pending on the target nucleus, the amount, and the type of fragments can be different and include protons, neutrons, alpha particles, and smaller nuclei. The process of

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Figure 1.2 – Plot of the neutron capture cross section for³He(n,p)³H,¹⁰B(n,α)⁷Li and

54Fe(n,γ)⁵⁵Fe [1]

spallation has two stages: intranuclear cascade and de-excitation [54].

In the first stage, the high energy particle interacts with the nucleons within the nucleus, after which the nucleus is left in a highly excited state. The nucleus then relaxes by emitting the particles or disintegrates into smaller nuclei, which may also relax through the emission of particles [55].

While the cross sections of capture and scattering decrease with increasing energy, the spallation reaction becomes dominant in the high energy region for heavy nuclides [56].

Spallation reactions can be used for the detection of high energy neutrons with energies higher than 20 MeV. Layers of high density materials (like lead or tungsten) are included in the moderators of the survey instruments, to produce slower neutrons through spallation. This approach is widely used for the dosimetry purposes at high energy accelerator facilities [57]. The same principle is applied for the spectrometric measurements with the Bonner spheres spectrometer.

Fission

Nuclear fission is the neutron-nucleus interaction induced by the bombardment of heavy nuclei (mostly Z≥92) by neutrons [42]. As a result of this interaction, target

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nuclei are split into two lighter nuclei with the emission of several fast (prompt) neutrons.

The fission fragments, which are still in the excited state, emit several evaporation (delayed) neutrons. The typical mass ratio of the fission fragments is about 2:3. The most spread fissile nuclides are:²³⁵U,²³³U and²³⁹Pu.

The fission reaction is used in nuclear power plants and research reactors. The phenomenon of neutron induced nuclear fission is also used for neutron detection. The type of the detectors based on the fission reaction is called fission chambers [58].

1.2 Radiation Protection And Dosimetry

Even though the neutron radiation is not directly ionizing, it still has an effect on the human body through the interactions described in Section 1.1, which has to be quan- tified for a purpose of dosimetry and radiation protection. To regulate the exposure by the fields of the ionizing radiation and to quantify it, three sets of quantities are used.

Namely, physical quantities, protection quantities and operational quantities [59].

1.2.1 Physical quantities

The physical quantities used for radiation measurement and radiation protection are directly measurable quantities selected by the International Commission on Radiation Units and Measurements (ICRU). They are universally accepted for the characterization of the ionizing radiation fields. For radiation protection, three physical quantities are of relevance:

• Fluence - This is the number of particles incident on a sphere divided by the cross section area of this sphere. The unit of the fluence ism⁻².

• Absorbed dose - This is a fundamental dosimetric quantity, defined as:

D= dε

d m, (1.10)

wheredεis the mean energy transferred by the ionizing radiation to the matter with the mass d m. The SI unit of the absorbed dose is joule per kilo- gram (J×kg⁻¹) or Gray (Gy).

• Kerma. This abbreviation stands forKinetic Energy Released in Matterand is equal to the sum of the kinetic energies of the charged ionizing particles (d E_{c p}) liberated by the uncharged particles (photons or neutrons) in material of mass

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1.2. Radiation Protection And Dosimetry

d m:

K =d E_{c p}

d m . (1.11)

1.2.2 Protection quantities

Similar doses of different types of ionizing radiation can cause biological effects on different levels [60]. Moreover, there are different biological sensitivities to radiation for different tissues and organs [61]. Due to this, the physical quantities are not always representative, and they cannot be used for legal limitation purposes. For the definition of the dose limits theprotection quantitiesare used taking into account the radiation weighting factorsandtissue weighting factorsintroduced by International Commission on Radiological Protection (ICRP) [61]. The radiation weighting factors are up on the type and the energy of the particles. The tissue weighting factors are multipliers related to certain organs and tissues considering their sensitivities to the different kinds of ionizing radiation. A more detailed description and specification of the weighting factors can be found in the corresponding ICRP documents (e.g.

publication 92). The protection quantities used for external dose assessment are equivalent doseandeffective dose.

The equivalent doseH_Tis defined as:

H_T=D_T·w_R, (1.12)

whereD_Tis the absorbed dose of radiation type R averaged over the tissue of organ T, w_Ris the radiation weighting factor for radiation type R.

In case where the radiation field consists of the radiation of different types with different weighting factors, the equivalent dose is defined as:

H_T=X

R

D_T·w_R. (1.13)

The unit of the equivalent dose is J·kg⁻¹, termed the Sievert (Sv) to indicate the adaption by the weighting factor.

The effective doseEis the sum of the equivalent doses for all the tissues and organs considering the appropriate tissue weighting factors (w_T):

E=X

T

w_T·H_T (1.14)

As well as for equivalent dose the unit of the effective dose is Sv.

The protection quantities are used for the definition of the legal dose limit values, but

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they cannot be directly measured. It is possible, with adequate detailed information about the irradiation conditions, to calculate exposure in terms of protection quantities (e.g. by means of simulations). However, this does not offer the practical use for operational radiation protection [59].

1.2.3 Operational quantities

For application in operational radiation protection, the ICRU has defined directly measurable quantities calledoperational quantities. These quantities are defined in such a way to provide a reasonable estimate of the protection quantities. Operational quantities are based on thedose equivalent at a certain point in a tissue or tissue equivalent material.

Three operational quantities are used for the external dose assessment. Namely these are, ambient dose equivalentH^∗(10) used for strongly penetrating radiation, directional dose equivalentH^∗(0.07) used for weakly penetrating radiation, and personal dose equivalentHp(10) used for strongly penetrating radiation andHp(0.07) used for weakly penetrating radiation. The first two are used for area monitoring and the third is used for the individual monitoring. For the purpose of this project, we will focus on ambient dose equivalent.

According to the ICRP publication 103, the ambient dose equivalentH^∗(d) is the dose equivalent at a point in a radiation field that would be produced by the corresponding expanded and aligned field in the ICRU sphere at a depth d on the radius vector opposing the direction of the aligned field [62]. For strongly penetrating radiation, the depth d=10 mm is recommended. ICRU sphere is the sphere with a diameter of 30 cm consisting of the tissue-equivalent material (76.2% oxygen, 11.1% carbon, 10.1%

hydrogen, and 2.6% nitrogen) [63]. The unit of the dose equivalent is Sv.

Relation of Radiation Protection Quantities and Energy Dependent Biological Ef- fect

To relate the three groups of the quantities used for radiation protection, different conversion coefficients were developed by ICRP and ICRU. The conversion coefficients from the physical quantities to the operational quantities are interesting and relevant to this study since the physical quantities are measured to be applied for dosimetric purposes.

Energy dependent fluence to dose conversion coefficients for the determination of theH^∗(10) were defined with radiation transport codes using an ICRU sphere [2]. To calculate the ambient dose equivalentH^∗(10), measured energy spectral distribution of the particle field is multiplied by the corresponding energy dependent conversion

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1.2. Radiation Protection And Dosimetry

coefficients. The plot of the conversion coefficients together with the response of the Berthold LB6411 neutron detector [4] are shown in Figure 1.3 [2, 3]. As it can be seen from the plot, dependence of the coefficients on the energy is not linear and they do not increase uniformly and variety of the different spectral distributions can be found depending on the workplace conditions (type of source, shielding etc.). Moreover, there is significant difference between the detector response and the conversion coefficients, which can lead to overestimation or underestimation of the measured dose in specific fields.The examples of spectra from the different facilities are shown in Figure 1.4 [5]. Due to this, devices used for neutron dosimetric measurements must be sensitive to the neutrons with energies from meV up to GeV.

Figure 1.3 – Neutron fluence toH^∗(10) conversion coefficients [2, 3] and the response of the Berthold LB6411 neutron detector [4]

A challenging factor arises from the energy dependent fluence to dose conversion coefficients. To provide the adequate information about the dose, the energy dependent sensitivity of the measurement device should be as close as possible to the conversion coefficients. That leads to additional difficulties in developing and manufacturing the measurement devices. The other option is to apply a field calibration factor to the certain device if energy spectral distribution of the field is known. For this purpose, neutron spectrometry can be applied.

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Figure 1.4 – Examples of the workplace spectra from different facilities [5]

1.3 Computational Methods for Radiation Field Estima- tion

In order to estimate the behaviour of neutrons under certain conditions, this study has made use of Monte Carlo simulations. In particular, the response functions of the PSI BSS are obtained using Monte Carlo particle transport code. The foundations of the Monte Carlo simulations for particle transport are detailed in the following chapter.

The common computer codes used for Monte Carlo simulations of the neutron fields are, MCNP(X), FLUKA, GEANT4 [64]. In this project, MCNP code is used due to its good performance in thermal energy region [39, 65]. This choice is done because the code is applied for the simulations of the detectors sensitive mostly to thermal neutrons.

1.3.1 Physical Principle of Particle Transport

The general physical quantity used in radiation protection and dosimetry to describe a particle field is a "particle phase space density", also known as "angular flux" [66].

Particle phase space density defines the number of particles in the infinitely small volume of phase space and can be described as a derivative of fluence with respect to

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1.3. Computational Methods for Radiation Field Estimation

all coordinates of the phase space including time, energy and direction:

~Ψ= ∂Φ

∂t∂E∂~Ω, (1.15)

whereΨis the angular flux at a certain point,Φis a particle fluence,t is the time period, E is the energy of the particles and~Ωis the solid angle. Angular flux is a differential quantity, while fluenceΦis an integral quantity, and can be described by the following equation:

Φ= Ñ

E~ΩtΨd E d~Ωd t=nv t, (1.16)

wherenis a particle density andv is a velocity. The particle fluence is the total length travelled by all free neutrons per unit volume.

The particle transport process is described in the Boltzmann equation as the balance between particle "production" and particle "reduction". For neutron transport this equation takes the following form:

1 v

∂Ψ(~x)

∂t +~Ω·~∇Ψ(~x)+ΣtΨ(~x)−S(~x)= Ï

~ΩEΨ(~x)Σs(~x⁰→~x)d~x⁰, (1.17) where~x=(E,~Ω,t) is the combination of all of the phase space coordinates. The terms of the Boltzmann equation can be described in the following way:

• _v¹^∂Ψ_∂⁽_t^~^x) is time dependent density change;

• ~Ω·~∇Ψ(~x) describes the translational motion: change of the position without the change of energy;

• ΣtΨ(~x)) is an absorption term, whereΣt is total macroscopic cross section, proportional to the inverse of the mean free path. The mean free path is the average distance between subsequent interactions;

• S(~x) is the particle source

• Î

~ΩEΨ(~x)Σs(~x⁰→~x)d~x⁰is the scattering, change of the energy and/or direction without changing the position. Σs is the total macroscopic scattering cross section.

The complexity of this multidimensional equation increases with the complexity of the considered geometry which is defined by the dimensions and material composition of the media.

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The solution of the Boltzmann equation by means of the Monte Carlo particle transport code is executed in the following way. Each simulated particle is tracked through its way and the outcome of the interaction and the free path before the interaction are determined by random selection from the pre-defined probability distributions. The secondary particles (if produced) are transported before the start of the new particle history. This process is Markovian, which means that the behaviour of the particle depends only on its actual properties, without considering previous interactions.

Additionally, the interactions between the simulated particles are neglected.

1.3.2 Basics of the Monte Carlo Approach

To determine the characteristics of the neutron field, such as flux and dose in a certain area, the particle transport process should be understood. The suitable way to investigate this process is the simulation of the neutron field by utilizing the Monte Carlo method. The Monte Carlo method is a technique of numerical analysis based on the use of random numbers to sample the properties of the particle (e.g. trajectory, free path, reaction probability etc.) [67]. The mathematical foundation for the Monte Carlo approach is explained by the Central Limit theorem [66].

One advantage of the method is that every step of the approach corresponds to a similar step of the simulated physical process. Neutron transport is a physical process described by probabilities, while the probabilities of particle-nucleus interaction are defined by the reaction cross section. For example, the particle could be absorbed or scattered with different angles and different energy losses.

1.3.3 Geometrical Models of the Particle Fields Simulations

Although the algorithms to build the geometry are different for the different codes they have similar features. The geometrical models for the simulations are described by the combination of surfaces and volumetric bodies called "cells". They could be built in the visual editor or defined by text input [68, 69]. For the description of the complex geometry, the principles of the combinatorial geometry are used, and the logical operations of the union, subtraction and intersection are applied to the bodies and surfaces. With this method, basic convex shapes like cylinders, spheres and parallelepipeds are combined to describe more complex shapes [6]. The example of the basic shapes combinations is shown in Figure 1.5. In this case "+" is equivalent to the operator of intersection∩, "-" is equivalent to subtraction of the intersection.

Each cell of the geometrical model has an isotropic composition of the material and density.

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Figure 1.5 – The example of the basic shapes combinations [6]

1.3.4 Variance Reduction And Biasing

The statistical error plays an important role in the analysis of the data obtained by the simulations. The reliability of the result depends on the input parameters provided by the user and the assumptions made in particular transport code. It was empirically defined that with the value of the variance (σ) higher than 0.5 is considered as not meaningful. Ifσis between 0.2 and 0.5, the fluctuation of the result may be a factor of few. From 0.1 to 0.2 the result is considered questionable. If the result is below 0.1, it is considered reliable. These values are listed in the MCNP manual [70]. The statistical uncertainty of the simulation depends on the amount of the simulated primary particles (otherwise known as the number of histories). The "efficiency" of the simulation is described by a value called afigure of merit:

F OM=σ²t, (1.18)

whereσ²is the variance (dependent on the amount of the simulated particles) andt is the CPU time needed per primary particle. To make the simulation more efficient, variance or simulation time should be reduced. There are several ways to reduce the figure of merit such as the application of the energy cut-offs, thresholds or biasing.

Cut-offs are used to reduce computing time by limiting certain characteristics of the transported particles. For instance, a low energy cut-off may be applied to the parti-

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cles when information about these particles below a certain energy is not relevant for the simulation or the result. Then, if particle energy becomes lower than the cut-off, further transport will not be performed.

In the case of high energy neutron transport, the energy cut-off can be applied for the photons with energies below photo-nuclear reaction energy threshold, since they do not induce neutron production. This method should not be used when contribution of the secondary particles can not be neglected or the production of the secondary particles can be even prevented.

There are different types of biasing used for simulation’s optimization. The Boltzmann equation (1.17) consists of the phase space densityΨ(x) and different operators acting upon it. Both could be biased by assigning thestatistical weightto the phase space density. Then,Ψ(x) is replaced by an artificial densityΨ⁰(x). The weightwshould be assigned in such a way thatΨ(x)=w(x)Ψ⁰(x) and the product of the weight and the number of particles remains constant. For example, the interaction cross section can be artificially increased but particles produced as a result of the interaction will have a lower statistical weight. Thus, the amount of the simulated particles is increased and leads to the reduction of the varianceσ².

The operators based on probability distribution functionsP(x), such as source speci- fications or cross sections, can also be biased by the application of the artificial probability density function (PDF)P⁰(x) with different statistical weights. In this case, the product of the weight and probability must remain the same, so thatP(x)=w(x)P⁰(x).

For instance, for a given source energy distribution, particles with a certain energy are produced more often, but with reduced statistical weight.

Surface splitting and Russian roulette

One of the commonly used biasing techniques for variance reduction is called importance biasing. Importance biasing changes the particle density in a certain region of the phase space according to its contribution to the result. The most used types of importance biasing aresurface splittingandRussian roulette. Surface splitting reduces the variance and increases the CPU time, while Russian roulette reduces the CPU time, but increases the variance. For both of these methods, importance is assigned to different geometry regions.

Surface splitting is performed when transported particles cross the cell boundary from a region with lower importanceI₁to a region with a higher importanceI₂. In these instances, each particle is artificially split intoI₂/I₁particles and the weight of the new particle is multiplied byI₁/I₂. This procedure can compensate the particle losses due to attenuation in material. Nevertheless, the amount of particles created due to

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splitting should not be higher than the amount of particles lost due to attenuation, otherwise no additional information will be gained, even with low variance. If the amount of particles in the cell with lower importance, before surface splitting, is not sufficient, the artificial multiplication after surface splitting will not compensate this lack of information what leads to the wrong result. Additionally, particles produced as a result of the split of other specific particles are not statistically independent. An example of surface splitting is illustrated in Figure 1.6.

The Russian roulette is applied when the transported particle travels from a cell with

Figure 1.6 – Illustration of the surface splitting (blue arrows) and Russian roulette (red arrows) with an example of 3 cells with different importance. Particles are shown as a circles. Statistical weight of each particle is written on them.

higher importanceI₂into a cell with a lower importanceI₁. In this case, the particle is killed with the probabilityI₁/I₂. If the particle survives, its weight is multiplied byI₂/I₁. This procedure leads to the decrease of the number of particles, whilst the product of the weight and the number of particles remain constant. That allows to decrease the calculation time by the reduction of the particle number in certain regions with increasing statistical uncertainty in reasonable limits.

1.3.5 Particle Field Estimators

To obtain the results of the simulations, certain properties of the particles field must be recorded. There are different types of estimators, called "tallies" in MCNP, that are commonly used in different Monte Carlo transport codes. This work makes use of the

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following three estimators:

• Surface crossing estimator, which is used to record the fluence or current of the particles crossing the boundary between two cells

• Track length estimator, which is used to record the fluence averaged over the volume of the cell

• Mesh estimator, which is used to record the fluence, energy deposition or other quantities in a volume divided by the mesh (grid) specified by the user, generally independent from the tracking geometry

1.3.6 Statistical Errors

The variance (square of the relative error) of an estimated quantityx, calculated inN batches, is:

σ²= 1 N−1

" PN 1 n_ix_i²

n −

Ã PN 1 n_ix_i

n

!2#

, (1.19)

wheren_i is the number of histories in the batchi,nis the total number of histories in theNbatches,x_i is the average ofxin the batchi. In the case, whenN=n,n=1, this formula applies to single history statistics [66].

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2 Neutron spectrometry

Information regarding neutron energy spectral distribution can be used for a variety of applications. This information can be obtained by measurements based on the different physical principles depending on the area of application. In the following chapter, the advantages and limitation of each method are described including the Bonner Spheres Spectrometer.

2.1 Fields of application

The measurement of the neutron spectrum is used for various applications in different types of facilities. Most commonly, it is used in the following areas:

• Laboratories. Including calibration facilities, research laboratories for neutron experiments and the cross sections measurements [71].

• Workplaces. Where the professional activities are accompanied by neutron irradiation including nuclear and accelerator facilities. The neutron spectrum there is the object of interest for the dosimetry and radiation protection [72].

• Accelerator environments. Where the neutron spectrum measurements are used for the benchmarking of calculations as a check of the results for the radioactive waste volume estimation [73]

• Reactor environments. Close to the reactor core or outside the reactor vessel for the investigation of the integrity of the materials [74].

• Other areas. Such as fusion setups or medical facilities for the measurements of the secondary neuron fields [75]

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2.2 Basic Methods of Neutron Spectrometry

2.2.1 Time of flight method

One of the basic methods used for neutron spectrum measurements, is the time of flight method (TOF) [76]. This approach is ordinarily used in the laboratory environment and is based on the measurement of the time between the moment when a neutron is passing a certain point and the moment when it is registered by the detector in a specific distance. A variety of the detectors, depending on the area of application and energy range of the neutrons, are used for this kind of the measurements: from the proportional counters sensitive to the thermal neutrons to the scintillators or the lithium glass detectors mostly sensitive to the fast neutrons. The start point of the neutrons for TOF is a pulsed source or mechanical chopper device The exemplary scheme of the TOF setup is shown in Figure 2.1. This method is applied in a defined directional beam. The distance between the starting point and the detector can vary

Figure 2.1 – Scheme of the TOF setup. Choppers are marked as "Ch" [7].

from several meters to a few hundred meters. This method is applied in research and calibration facilities all around the world, e.g. in PIAF of PTB (Germany), n_TOF in CERN (Switzerland) and SENJU in J-PARC (Japan) [22, 77, 78].

2.2.2 Proton recoil spectrometry

In the method called proton recoil spectrometry, n-p scattering reaction is used to determine the neutron spectral energy distribution. This method is mostly used for the spectrometry of fast neutrons (appr.1 MeV and higher). Fast neutrons are interacting

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2.2. Basic Methods of Neutron Spectrometry

in a converter containing hydrogen and producing free recoil protons. The energy of the recoil protons can be measured with scintillators or with semiconductor detectors.

The exemplary scheme of the recoil proton spectrometer with the thin polyethylene foil as a converter is shown in Figure 2.2. Another type of the spectrometer based on

Figure 2.2 – Scheme of the recoil proton spectrometer with thin polyethylene foil as the converter [8] This spectrometer is designed for the measurements at ITER facility [8].

the n-p scattering is the device, where the function of the converter and the proton detector is performed both by the scintillator. There the energy of the recoil proton is measured by the scintillator is related to the energy of incoming neutron. The exemplary scheme of the neutron spectrometer based on the liquid scintillator is shown in Figure 2.3 [9]. The response functions of this spectrometer for different neutron energies are shown in Figure 2.4 [10].

The discrimination between signals produced by the protons and photons are performed by the pulse-shape analysis as is illustrated in the right side of Figure 2.3.

2.2.3 Spectrometry combining different moderators

The neutron fields work places often cover up to 12 orders of magnitude of the energy range. The way to cover such a wide energy range is to apply a set of detectors with different sensitivities for different energies. The data obtained with these detectors should be then deconvoluted to define the shape of the neutron spectrum. The multisphere spectrometer, also called Bonner Spheres Spectrometer (BSS), is the most used device suitable for this application [79]. This measurement system includes the neutron detector which is extremely sensitive mostly to the thermal neutrons and a set of spherical moderators with varying diameters and material compositions. Different