A method for measuring macroscopic cross-sections for thermal neutrons

Author’s Accepted Manuscript A method for measuring macroscopic crosssections for thermal neutrons A. El Abd, G. Taha, A.Y. Ellithi

www.elsevier.com/locate/apradiso

PII: DOI: Reference:

S0969-8043(16)31092-2 http://dx.doi.org/10.1016/j.apradiso.2017.07.036 ARI7988

To appear in: Applied Radiation and Isotopes Received date: 16 December 2016 Revised date: 20 May 2017 Accepted date: 19 July 2017 Cite this article as: A. El Abd, G. Taha and A.Y. Ellithi, A method for measuring macroscopic cross-sections for thermal neutrons, Applied Radiation and Isotopes, http://dx.doi.org/10.1016/j.apradiso.2017.07.036 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A method for measuring macroscopic cross-sections for thermal neutrons

A. El Abda*, G. Tahaa, A.Y. Ellithib

a

Reactor Physics Department, Nuclear Research Centre, Atomic Energy Authority, P.O.Box: 13759 Cairo, Egypt.

b

Physics department, Faculty of science , Cairo University , [email protected] [email protected]

*

Corresponding author. A. El Abd ,

Abstract A method was proposed for measuring macroscopic absorption and scattering cross-sections for thermal neutrons. It is based on a Pu-Be neutron source and He-3 neutron detectors assembly. A beam of neutrons was obtained from the source imbedded in a water tank. The He-3 detectors oriented inside the sample and at 1800 and 00 with respect to the incident neutron beam were used to register neutrons after interaction with the samples. Neutron count rates (detectors responses) were obtained for large (5.5 l) as well as small (1.3 l) volumes of standard samples. Sensitivities of the results obtained for the large and small samples were compared. A semi-empirical model was proposed to fit the results. It describes the relative detector responses in terms of a dimensionless variable which depends on the geometrical parameters and cross section of the standard samples used. The model successfully fits the results obtained. Advantages and limitations of the method were discussed.

Keywords: Macroscopic, scattering, absorption, neutrons , response, He-3 detector, semi-empirical

1.Introduction

The macroscopic thermal neutron cross section is the effective cross sectional area of a unit volume of material necessary for thermal neutron capture and/or scattering. It involves the volume fraction

1

weighted sum of the probabilities of the various elements which make up the substance within that volume [1]. The linear macroscopic thermal neutron cross sections for absorption, a (cm-1) of a mixture of n components can be calculated from the relation [1, 2]: a=



n i

m =  m , qi ia

1

where is the bulk mass density of the mixture, qi is the mass fraction of the i-th component ( in qi =1), and m ia

is the mass macroscopic thermal neutron cross-section for absorption (cm2.g-1) of the i-th component

m for any compound consisting of d and m is the density removed macroscopic cross section (cm2.g-1). ia elements is given by m = ia



d i

N av fi i , Ai

2

where Nav is Avogadro’s number and fi, Ai, and i are the mass fraction, atomic weight and thermal neutrons microscopic absorption cross-section at the standard neutron velocity, v0 (2200 m/s) of the i-th element, respectively. Similar equations can be written for calculating the linear macroscopic thermal neutron cross sections for scattering,s (cm-1) however in such case i is the thermal neutrons microscopic scattering cross-section. Both a and s of a medium are important parameters when transport of thermal neutrons in any system is considered. In oil well analysis, the knowledge of a and s of the materials surrounding a borehole penetrating a geological formation can be of great assistance in well evaluation. In addition, they enable the recognition of oil versus water and the identification of the oil/water interface in the formation. Moreover, both a and s are used in nuclear reactor calculations, radiations shielding, and mineral exploration [2-15]. Thus, reliable determination of both a and s are needed. Methods developed in literature were mainly for determining macroscopic absorption cross-section, a. These methods were based on either steady isotopic neutron sources such as Pu-Be, 252Cf , Am-Be and 124 Sb-Be [3-9] or pulsed neutron sources [2, 10-15]. All methods based on isotopic neutron sources for determining a are based on measuring the thermal neutron field perturbation caused by the examined standard samples of known a. Measured perturbed thermal neutron field (detector response) were carried using thermal neutron detector such as He-3 or BF-3. The detector response as a function of a , calibration curves, was used for determining unknown a of any samples. Experimental systems used for such measurements were essentially similar [3-9]. They included an isotopic neutron source, neutron detectors and a sample each placed in a moderator. The use of different moderators, neutron sources, neutron detectors and sample containers of different shapes and volumes combined with different source–sample– detector configurations resulted in various measurement devices and different interpretation procedures [39]. The idea of the pulsed neutron source based -methods for determining a [2, 10-15] for a sample is to irradiate a moderator enveloping entirely the sample, by a pulsed beam of fast neutrons. The neutron parameters including a of the moderator should be well known. The escaping die-away flux of thermal neutrons is detected by a thermal neutron detector. The fundamental mode of the decay constant λ0 derived from the recorded die-away curve (for a given fixed size of the sample) is performed for several values of the

2

moderator thickness R. In this way, the experimental curve λ0 (R) is known at several experimental points R. To obtain the absorption cross section a of the investigated sample, a theoretical curve *λ0 (R) has to be calculated using the diffusion equation in a two-medium bounded system. The intersection of the experimental curve λ0 (R) with the theoretical *λ0 (R) one at some value of the moderator thickness R gives the value of the sample thermal neutron absorption rate va, where v is the neutron velocity [13]. Other reactor based methods including neutron radiography were used to determine the so-called effective total macroscopic cross section [16, 17]. In addition, neutron activation analysis and time of flight (TOF) are the most common techniques for measuring microscopic cross sections for thermal as well as fast neutrons. Neutron TOF method [18-23] is mainly used for measuring total and/or scattering cross sections as a function of neutron energy. Total cross-sections are determined by measuring the transmitted neutron beam through a known amount of sample material and comparing this with the transmitted beam without sample. Neutron activation analysis techniques are mainly used for measuring neutron capture and/or absorption cross sections [24].

According to the authors’ knowledge, the use of steady neutron source based-methods for determining both a and s are rare [8, 25-27]. A few number of authors [8, 25-27] proposed a method for determining both a and s. Two neutron detectors were oriented inside the sample investigated to account for neutron scattering on detector response [8, 25-27]. Semi-empirical models were proposed to describe both absorption and scattering cross sections of the samples. These models used the so-called effective cross-section that depends on the detector orientation [8, 25-27]. They showed that if calibration measurements were made at two orientations, two simultaneous equations would result that can be solved explicitly for both a and s. In spite of these proposed methods provided the idea for determining both a and s experimentally, they were not applied in literature. Additionally, the effect the sample's density, on determining both a and s was not investigated before. Therefore, a method for simultaneous determination of both a and s for solid as well as liquid samples taking into account the sample's density is needed. The aim of the present work was the development of a method for determining both a and s for solid and liquid samples. The samples are characterized with different densities. The method was based on the use of a Pu-Be neutron source and He-3 neutron detectors assembly. Wide beams of neutrons were obtained from a Pu-Be neutron source immersed in a water shield. He-3 neutron detectors oriented around the samples examined and in different directions with respect to the incident neutron beams were used to register neutrons. The measurements were carried out using beams of neutrons above and below Cd cut-off energy (0.55 eV). A semi-empirical model was proposed. It describes the detector responses in terms of a dimensionless variable, which includes the physical, nuclear and geometrical properties of the sample. 2. Experimental details: The experimental set-up used in this work is shown schematically in Fig.1. It consists of an empty cylinder (made of polyethylene) of 70 cm diamter and 100 cm length. A tube of 10 cm diameter is fixed along axis of the cylinder. The cylinder is filled with water. The water cylinder was fixed on a wooden table (1 meter height above the ground). A Pu-Be neutron source (1 Curie) is stored below the wooden table in a special chamber, made of borated paraffine wax and surrounded by lead. The source is raised - through a tube - by a rope into the central tube such that distance between source and one face of the cylinder is 15 cm (exit face of neutrons). The other face of the tube is blocked by paraffine wax. The outlet face of neutrons is covered by Cd sheets of thickness 5 mm except an opening of ~10 cm diameter. Water surrounding the neutrons

3

source moderates emitted neutrons from the Pu-Be source. The water cylinder is surrounded by blocks of borated paraffine to minimize leakage of fast neutrons. Two cylindrical containers having volumes 5.5 liters (large volume) and 1.3 liters (small volume) were prepared to accommodate the samples investigated. 3He neutron detectors (LND-252172, operating voltage range is 750-1000 Volts, recommended operating voltage = 850 Volts) were fixed on the sample containers in three different positions as shown in Fig.1. The 3He neutron detectors 1, 2 and 3 are for the detectors orientations at 1800, inside the sample and 00 with respect to the direction of the incident neutron beam, respectively. To minimize neutron counts due neutrons reaching the detectors from surrounding, back sides of the detectors 1 and 3 were covered by Cd. A power supply (Canberra model 31060) providing high voltage to the He-3 detector via a preamplifier (Ortec-142PC) was used. The output signal from the preamplifier was fed to amplifier (Canberra Amp/TSCA 2015A) and subsequently to a counter (Ortec 772) for neutron counting. To check performance of the He-3 detectors, the output signal from the amplifier was fed to multichannel analyzer cart (MCA) cart with 8000 channels (NDS). The MCA cart was installed on a PC and was controlled by the Genie 2000 software package. The MCA cart was used for acquiring and analyzing spectra resulting from the neutron interactions with the He-3 detector. The neutron spectra were acquired, from time to time, showed that the performance of the detectors and electronics is stable, namely there is no drift. Since He-3 has a large capture cross-section for thermal neutrons, He-3 neutron detectors are sensitive to thermal neutrons only. They utilize the He-3 (n,p) H-3 reaction for the detection of thermal neutrons [28]. The reaction products (tritium 3H, and proton, p), sharing the 765-keV reaction energy, produce further ionizations inside the detector. The finally obtained signal from He-3 neutron detectors is proportional to the number of thermal neutrons interacting with the detector [28]. Standard bulk samples investigated in this works were two sets: the first set was consisting of commercial sand available for building (it was considered as a pure SiO2). Different percentages of boric acid (H3BO3) and Sodium Chloride (NaCl) were added to separate sand samples, such that different values of a and s are obtained (Table 1). This set was used in the large and small volume samples. Some liquid standard samples consisting water and fractions of NaCl and H3BO3 were prepared - these samples were used in the large volume samples. The second set of standard samples were sand (of well know chemical composition), TiO2 and double distilled water (H2O). Since TiO2 is available for us, it was used as a standard sample. The chemical composition of sand used in this set was determined by X-ray fluorescence (XRF). The concentration of SiO2 was found to be 92.69%, whereas the remaining impurities were Al2O3 (5.08%), Fe2O3 (1.80%), TiO2 (0.23%) and ZnO (0.20 %). This set was used in the small volume sample. A sand sample is mixed with a known amount of boric acid, and then detector responses were determined for such sample. After finishing the measurements, the concentration of the boric acid inside the sample was changed by replacing a known volume of the sample with a boric acid. The detector responses were determined again for this sample. This process was repeated till having a final sample of large cross sections (approaches those values of H3BO3). The TiO2 sample was treated in similar way as the sand sample in the second set. A lot of standard water samples were prepared. Three sets of water samples containing different weight fractions H3BO3, NaCl and both H3BO3 and NaCl were prepared. The macroscopic absorption and scattering cross sections (a and s ) of the two sets of the prepared standard samples were calculated using equations 1 and 2. According to these equations, a and s were calculated for the prepared standard samples with the knowledge of their bulk densities, which is measured for each sample, mass fractions of the constituting elements and/or compounds (Tables 1and 2), microscopic absorption and scattering cross sections [29-31], atomic weights and Avogadro’s number. Values of the

4

microscopic absorption and scattering cross sections – at the neutron velocity of 2200 m/s - were taken from reference [29-31]. a and s were calculated for the sand sample (second set) taking into account the impurities found – namely, their mass fractions determined by XRF. Following the approximations given in reference [30, 31], the value of the microscopic scattering cross section for hydrogen at the standard neutron velocity of 2200 m/s, effective scattering cross section, of 57.73 b were used for calculating the macroscopic scattering cross sections for the hydrogenous compounds used in this work. The obtained results of the calculated mass macroscopic cross section, density removed macroscopic cross sections, sm and am and measured bulk densities are listed in Tables 1 and 2. The linear macroscopic cross sections can be easily calculated from equation 1 (a = am and s = sm ). According to error propagation theory [32,33], uncertainty (error) of calculating a parameter such as a ors is the quadratic sum of the uncertainties of the parameters or factors used to calculated it. Namely, uncertainties of the calculated a ands (using eqs 1 and 2) of the standard samples used in this work are due uncertainties in qi, Nav, fi, Ai, and i. These uncertainties were calculated and their values did not exceed 5% of either a ors. The sample containers were filled by the prepared standard samples. The measurements of neutron count rates (detectors responses) were carried out for every position at least three times- once the measurement was carried out for a position for a given sample, the detector was inserted inot another one. The measuring time was 100 seconds. These measurements were established using incident neutron beam of the whole neutron spectrum emitted by the Pu-Be neutron source that is consisting of fractions of thermal and epithermal neutrons including fast neutrons. The incident neutron fluxes on the investigated samples (at the outlet face of neutrons – see Fig.1) was calculated using MCNP5 computer cod based on the three dimensional model (Fig. 1). The thermal neutron flux (below neutron energy of 0.5 eV) was found to be 3.8x102 neutron/cm2.s, whereas the epithermal and fast neutron flux (above neutron energy of 0.5eV) was found to be 6.7x106 neutron/cm2.s. 3. Results and discussion: The detector response depends on its orientation, the incident neutron beam and both the values of a and s of the samples investigated. The incident beam consists of thermal, epithermal and fast neutron components. For such a kind of beam, the thermal neutrons interacting with the sample investigated consist of both the thermal neutron component, originally existed in incident the beam, and a component resulting from moderation of epithermal and fast neutrons. These thermal neutrons are either absorbed or scattered by the sample investigated. The obtained results of detector responses - neutron count rates- resulting from neutron reactions (absorption and scattering) were plotted versus the calculated values of a and s, for the first set of standard samples (large and small volumes) at the different orientations (positions) is shown in Figs.2a&2b. Sensitivities of detectors were calculated by dividing the range of the detector response (range of response = maximum value of detector response - minimum value) by the corresponding range of the values of a and/or s. These results are listed in Table 3. As one can see sensitivities of the large samples are the highest, especially for the inside detector. Moreover, sensitivities in terms of s are much better than those in terms of a. Sood et al. [27] have found that the rate of sensitivity change is appreciable up to a sample of volume 300 cm3. It can be noticed in the present work that sensitivities is improved by 20 % for the inside detector

5

via increasing the sample volume from 1.3 L to 5.5 L. Moreover, preparation of large samples needs large quantities of standard samples. Thus, our attention was paid to the small sample volumes (1.3 L). The obtained results of the detector responses versus a and s at the different orientations for the second set of standard samples (Table 2) are shown in Figs.3a and b. One should expect that the detector response for sand samples is different from that of the TiO2 samples, because these samples have different values of a , s and densities. This can be noticed for the detector responses in terms of s (Figs. 3b).The upper and lower results are for the sand and the TiO2 samples, respectively. The different behaviors of the detector responses may be explained in terms of the samples' densities. As one can see from Table 2, the densities of the sand samples are higher (high response) than those of the TiO2 samples (small response). The responses in terms of a (Fig. 3a) are different from those in terms of s (Fig. 3b). The responses collapse for the inside and 00 detectors (position numbers 2 and 3, respectively in Fig.1) however, with some deviations for the 1800 detector (number 1 in Fig.1) response. To determine unknown macroscopic cross section, especially s for any solid sample, its density must be of the same magnitude as the density of either the sand or the TiO2 samples. This is the main drawback of direct use the current results to determine s. On the other side, a can be determined directly for any solid sample independent of its density. Detector responses versus a and s for the liquid samples for the second set (water containing fractions of H3BO3, NaCl and both H3BO3 and NaCl) are shown in Figs. 4a and b. As one can see, as a increases, the responses decrease. The decrease of the responses depends on the NaCl, H3BO3 or both H3BO3 and NaCl content of the sample. However, as s increases the responses increase (Fig. 4b). Additionally, characteristics curves can be noticed for the three sets of water samples. The highest, the middle and the lowest responses are for the water samples containing NaCl, both H3BO3 and NaCl and H3BO3, respectively. This means a can be determined for any water sample independent of its content, however s cannot be determined. A few measurements were carried out for the large volume (liquid) samples. Responses of the detector at the different orientations are roughly similar for both volumes, however, for the large volume at position 1 (1800), the response is higher than the corresponding one for the small volume. Uncertainties of detector responses were estimated in this work by repeated measurement. It did not exceed 3% of the value of the response obtained. 3.1 A semi-empirical model for determining a and s In this work, a semi-empirical model was proposed. It describes the detector responses in terms of a dimensionless variable, which includes the physical, nuclear and geometrical properties of the sample. For a given geometry and sample dimension, the averages of the detector responses at the different orientations were calculated. The relative detector responses, R were calculated as the ratios of the average detector responses with respect are a reference thermal neutron flux and the microscopic absorption cross section inside sand,  (E ) and

are the thermal neutron flux and microscopic absorption cross

section inside the investigated samples, and E1 and E2 are the lower and upper limits of the thermal neutron spectrum. It should be noted that and are the cross section at the 2200 m/s .The values of  (E ) (which , is proportional to the detector response for the different samples) 0 ( E ) are lower than that of

6

0 ( E ) due to the thermal neutron self-shielding. The definition of equation 3 does not affect the calculation of the obtained results and it can take another form. Analysis of the obtained results showed that z can be written in the form:

 rh  z   t rh

 a     t 

m

(4)

where m = 0.85 and m=1.25 for the solid and liquid samples, respectively,  t =  a +  s , and r and h are the radius and height of the cylindrical sample containers, respectively. The proposed model was tested using the obtained results. The relative responses, R versus z are shown in Figs. 5a and b for the solid and liquid samples, respectively. As one can see, the results collapse to universal curves. The proposed model supported by the experimental results provides a method for determining both a and s for solid as well as liquid samples as follow: if the exponent m in equation 4 was set m =1, R(z) would depend on a and the dimension of the sample represented by the factor ((rh/(r+h)). The plots of R(z) versus z=((rh/(r+h))a are shown in Figs 6a and b for the solid and liquid samples, respectively. It can be seen that R(z) depends only on a . From such plots, a can be determined. With the knowledge of a,s can be determined from the results shown in Figs. 5a and b. Moreover, the sigmoid function give by :

R( z ) 

A1  A2  z  1    z0 

p

 A2

(5)

where A1, A2, Z0 and p are the fit parameters was used to fit the obtained results- the R-squared =0.99. Analytically, this formula can be used to for both determination of a and s. The results shown in Figs 5a, b, 6a and b are re-plotted in terms of the macroscopic mass absorption cross sections (density removed cross sections). They are shown in Figs 7a,b, 8a and b , respectively. In such case, the variable z has the unites of cm3 g-1. As one can see, the results collapse to master curves for the solid and liquid samples, however with some deviations. It can be noticed that, the results shown in Figs 5b and 6b and presented in terms of the macroscopic cross sections are comparable with those in Figs. 7b and 8b, for the liquid samples, respectively. However, the collapses of the corresponding ones for the solid samples (Figs 5a and 6a ) are better than those shown in Figs. 7a and 8a. Thus, macroscopic cross sections can be determined using both kinds of calibrations curves for the liquid samples, however, it would be better to use the results shown in Figs 5a and 6a for the solid samples. Previously, semi-empirical models were proposed to describe both absorption and scattering cross sections of the samples [8, 25-27]. According to these models an effective cross-section was related linearly with both a and s. Such models, failed to fit our results, because the experimental set-up used in this work is quite different from those in literature [8, 25-27]. Moreover, the current results cannot be compared with

7

those in literature not only because the different set ups used but also because of the lack of results for determining s for either solid or liquid samples. Additionally, the present work dealt with samples having different densities, however in literature the similar results does not exist. There is no problem from considering the commercial sand used as a pattern matrix in some experiments as a pure SiO2 [27] for the following reasons: 1) in most cases big additions of strong thermal neutrons absorbents has been used, and 2) the ratio of values of the average response of the neutron detectors for the commercial sand and that one of the well known chemical composition is ~3 %. It was noticed that the chemical composition of the sand sample analyzed by XRF and used in this work is different from that of the Ottawa Sand adopted in geophysics [13,30]. However, the values of macroscopic mass absorption and scattering cross sections for Ottawa sand are 0.00233 and 0.0959, respectively, agree with the corresponding values of the sand samples (0.0022 and 0.0957 ) - Table 2. The used geometry in the present work can be modified to increase sensitivity of the results obtained specially at higher values of both of a and s. At these values, response tends to saturate. This can be attributed to scattered neutrons from surroundings reaching detectors at positions 1 and 3. The positions of neutron detectors (180 0 and 00 orientations) in the present work were touching the outside surface of the sample's container. It means that only one side of each detector records neutrons resulting from the interaction with the samples examined. If these detectors were shifted to be inside the sample, they would receive neutrons from all sides leading to an increase in the sensitivity- see Fig. 9. Moreover, measurements can be carried out twice, one via wrapping the detector with Cd and the second without Cd. Detector responses due to pure thermal neutrons (resulting from the incident beam and neutron moderations) interaction with the examined samples is obtained by subtracting results obtained with Cd from those without Cd. The detector type (3He, BF3), filling pressure, diameter and length are important for thermal macroscopic cross section determinations [9]. Results of the Monte Carlo simulations [9] have shown that high-pressure 3He proportional counters offer much greater efficiency than BF3 detectors of the same size; however BF3 counters were characterized with better sensitivities. Additionally, sensitivity of the technique becomes better when a detector of a small diameter is used [9]. Thus, one may use BF3 counters and/or counters having small diameters in connection with the proposed geometry (Fig.9) to enhance sensitivity of the measurements. The volume of samples used in the work - not less than 1.3 liters - is too large for any core drilling applications. A proper solution can be achieved as follow: the volume of the small sample, of unknown cross sections, is increased to 1.3 liter by mixing it with a sample of known cross sections. The cross sections of the resultant sample are determined using procedure described in this work. The required cross sections of the smaller sample can be determined with the knowledge of its weight fraction. Additionally, some measurements are carried out for both samples of the volumes 0.6 and 1.6 liters, and the contribution of epithermal neutrons to response of the He-3 neutron detectors-this will be discussed in a forthcoming paper. The proposed model successfully described the results obtained. However, further measurements for other cylindrical volumes (different diameters and heights) are needed to support the present work. Additionally, the proposed model altogether with the obtained results be used not only for determining macroscopic cross sections but also self shielding [34, 35] for thermal neutrons in prompt gamma ray neutron activation analysis- this is left for a forthcoming paper.

8

Conclusions A method was developed to determine both macroscopic absorption and scattering cross-sections for any sample in the form of powder or liquid. The inside detector sensitivity was fount to be better than those of the other detector orientations. A semi-empirical model was proposed to fit the results obtained. The model successfully fitted the results of both the solid and liquid standard samples.

References [1] K.H.Bekurts, k. Wirtz, 1964. Neutron physics, springer, Berlin. [2] K. Drozdowicz, B. Gabaǹska, E. Krynicka, U. Woźnicka, 2001. Influence of the grain size on the effective absorption cross-section of thermal neutrons in a medium containing highly absorbing centers, Annals of Nuclear Energy 28, 1485-1497. [3] C. Tittle, G. W. Crawford. 1983. Measuring the thermal neutron absorption cross sections of rocks”. The Log Analyst, May-Jun. 1983, pp. 12-15. [4] A. Kreft, A. Dydejczyk , J. Gyurcsak, 1984. Determining the Thermal Neutron Absorption Cross Section of Rocks, Int. J. Appl. Radit. Isot., 35(7) 573-575. [5] A. Kreft, A. Bolewski jr., J. Gyurcsak, M. Ciechanowski, 1987. Determining of the thermal neutron absorption cross section for small geological samples, Appl. Radit. Isot., 38(5) 365-369. [6] A. Kreft, A. Bolewski jr., M. Ciechanowski, 1989. An isotopic neutron source method for measuring the thermal neutron absorption cross section of rocks using small samples. Nucl. Geophys. 3 (4), 367–372. [7] G.N. Salaita, A system for measuring thermal neutron absorption cross section of small liquid and rock samples, SPWLA 26th Annual Logging Symposium Transactions, Paper Q, 1985. [8] J.Sun, R. Gardner, 2004. Optimization of the steady neutron source technique for absorption cross section measurement by using an 124Sb-Be neutron source. Nucl. Instrum. Methods B 213, 22–2.

[9] A. Bolewski Jr., M. Ciechanowski, A. Dydejczyk, A. Kreft, 2008. On the optimization of the isotopic neutron source method for measuring the thermal neutron absorption cross section: Advantages and disadvantages of BF3 and 3He counters, Applied Radiation and Isotopes 66 (2008) 457–462 [10] L. Allen, W. Mills, DC Stromswol, 1985. Determination of the thermal neutron absorption cross section of 1- liter rock samples by pulsed source technique, Nuclear Instruments and Methods in Physics Research Bl0/ll , 1033-1037. [11] K. Drozdowicz, B. Gabaǹska, A. Igielski, E. Krynicka, U. Woźnicka, 2001. A pulsed measurement of the effective thermal neutron absorption cross-section of a heterogeneous medium, Ann. Nucl. Energy 28, 519– 530 [12] J. Czubek, K. Drozdowicz, B. Gabanska, A. Igielski, E. Krynicka-Drozdowicz, U. Woznicka, 1991. Advances in absolute determination of the rock matrix absorption cross section for thermal neutrons. Nucl. Geophys.5,101–107. [13] J. Czubek, K. Drozdowicz, B. Gabanska, A. Igielski, E. Krynicka-Drozdowicz, U. Woznicka, 1996. Thermal

9

neutron macroscopic absorption cross section measurement applied for geophysics. Prog. Nucl. Energy30,295–303. [14] K. Drozdowicz, E. Krynicka, Woznicka, U. Woznicka, A. Kurowski, 2001. The thermal neutron absorption of mixtures of hydrogenous and non-hydrogenous substances measured in two-region geometry. INP Rep. No 1891/PN, Institute of Nuclear Physics, Krakow, www.ifj.edu.pl/ reports/2000.html. [15] U. Woznicka, E. Krynicka, K. Drozdowicz, M. Kosik, W. Janik, 2001. Influence of granulation of the diabase sample on the thermal neutron S a measurement. INP Rep. No 1893/PN, Institute of Nuclear Physics, Krakow, www.ifj.edu.pl/reports/2000.html. [16] H. Kobayashi, 1992. Macroscopic cross section measurements and defect detection in materials using neutron radiography technique, Journal of nuclear science and technology, 29,1045-1053. [17] E.A. Durisi, L. Visca, F. Albertin, R. Brancaccio, J. Corsib, G. Dughera,W. Ferrarese, A. Giovagnoli, N. Grassi, F. Grazzi, A. Lo Giudice, G. Mila,M. Nervo, N. Pastrone, F. Prino, L. Ramello, A. Re, A. Romero, R. Sacchi,F. Salvemini, A. Scherillo, A. Staiano, 2013. Characterization of a neutron imaging setup at the INES facility, Nuclear Instruments and Methods in Physics Research A 726, 31–36. [18] V.R. Skoy, T.F. Wang, G.N. Kim, Y.D. Oh, M.H. Cho, I.S. Ko, W. Namkun, 2009. Measurement of neutron total cross-section and resonance parameters of xenon, Nuclear Instruments and Methods in Physics Research B 267, 2351–2356. [19] Y. Danon, C. J. Werner, G. Youk, R. C. Block, R. E. Slovacek, and N. C. Francis, 1998. Neutron Total CrossSection Measurements and Resonance Parameter Analysis of Holmium, Thulium, and Erbium from 0.001 to 20 eV, Nuclear science and engineering,128, 61–69. [20] G.Kim,R.Machrafi,H.Ahmed, D.Son, V.Skoy, Y.Seok Lee, Moo-Hyun Cho, H.Kang, In Soo Ko, Won Namkung, Jong Hwa Chang, Kun Joong Yoo, 2003. Measurement of neutron total cross-section of Dy at Pohang Neutron Facility, Annals of Nuclear Energy 30 , 1123–1134 [21] K. Guckelsberger, W. Nistler, R. Scherm, M. Weyrauch, 2000. The total neutron scattering cross section of 3H, PhysicaB, 276-278, 75-976 [22] K. Drozdowic, Total cross section of plexiglass in the thermal neutron region, 1989, Ann.nucl. Energy, 16, 275-278. [23] G.J. Cue1,J.R. Santisteban, R.E. Mayer, J.R. Granada, 1995. Total neutron cross section of Teflon between 0.00038 and 590 eV, Nuclear Instruments and Methods in Physics Research A,357,519-523. [24] A. El Abd, 2010. Measurements of the thermal neutron cross-sections and resonance integrals for 186W (n,) 187W and 98Mo (n,) 99Mo reactions , Journal of radioanalytical and nuclear chemistry, 284(2), 321-326. [25] A. Bussian, W. Jetter, I. Supernow, 1991. A method of measuring thermal neutron absorption and transport cross sections, Nuc. Geo. 5(4),439-449. [26] S.Tallavarjula, Thermal neutron cross section measurement for geological materials, Ph.D. thesis, NCSU, 1995

10

[27] A. Sood, R. Gardner, T. Groy, 2000. Steady neutron source measurements of a and s in geological samples, App.Radit.Isot.,603-616. [28] G. F. Knoll, 2010. Radiation detection and measurement, John Wiley & Sons, Inc. Hoboken, USA, 4 th Edition. [29] Mughabghab S.F., Divadeenam M., Holden N.E. Neutron Cross Sections, Vol. 1. Neutron Resonance Parameters and Thermal Cross Sections. Part A: Z = 1–60. Academic Press, New York, 1981. [30] K. Drozdowicz, E. Krynicka, Thermal Neutron Diffusion Parameters in Homogeneous Mixtures, IFJ Report, 1694/PN (1995), Institute of Nuclear Physics, Kraków, Poland, www.ifj.edu.pl [31] Drozdowicz K. (1998), A method to calculate thermal neutron diffusion parameters for hydrogenous mixtures. Nucl. Instrum. Meth. A 411, 121-129. [32] D.V. Lindley, 2006. Understanding Uncertainty. Published by John Wiley & Sons, Inc., Hoboken, New Jersey [33] M. Grabe, 2005. Measurement Uncertainties in Science and Technology, Springer- Verlag Berlin Heidelberg. Printed in the Netherlands. [34] Wenbao Jia , Can Cheng , Daqian Hei , Yongsheng Ling , Hongtao Wang , Da Chen. 2015. Method for correcting thermal neutron self-shielding effect for aqueous bulk sample analysis by PGNAA technique. J Radioanal Nucl Chem ,304,1133–1137. [35] E. Martinho, J. Salgado, I. F. Gonçalves,2004. Universal curve of the thermal neutron self-shielding factor in foils, wires, spheres and cylinders, J Radioanal Nucl Chem, 261 (3), 637–643.

11

Fig.1. Schematic diagram of the experimental set-up (side view - vertical projection). Not to scale. 1,2 and 3: the neutron detector positions at 1800, inside the sample and 00, respectively; 4 : sample; 5: water moderator; 6 : paraffin wax plug; 7 : a Pu-Be neutron house; 8: tube through which the source is raised during measurements; 9: neutron source, 10: wooden table; 11:borated paraffin ; 12: Cd sheets. The dashed dotted lines are symmetry axes. Fig.2a. Detector responses versus a for the first set of the large (5.5 L) and small (1.3 L) standard samples. Positions from 1 to 3 are for the detector orientations shown in Fig.1 Fig.2b. Detector responses versus s for the first set of the large (5.5 L) and small (1.3 L) standard samples. Positions from 1 to 3 are for the detector orientations shown in Fig.1. Fig.3a. Detector responses versus a for the second set (sand and TiO2) of standard samples: Volume = 1.3 L, Positions from 1 to 3 are for the detector orientations shown in Fig.1.Fig.3b. Detector responses versus s for the second set (sand and TiO2) of standard samples: Volume = 1.3 L, Positions from 1 to 3 are for the detector orientations shown in Fig.1. Fig.4a. Detector responses versus a for the liquid samples: Volume = 1.3 L, Positions from 1 to 3 are for the detector orientations shown in Fig.1. Fig.4b. Detector responses versus s for the liquid samples: Volume = 1.3 L, Positions from 1 to 3 are for the detector orientations shown in Fig.1. The lines drawn for the inside detector (position 2) are guides for the eye. The upper results (dashed line) are for H2O +NaCl samples, the middle (dashed dotted) are for H2O +NaCl+ H3BO3 samples, the lower results (solid line) are for H2O + H3BO3 samples. Fig.5a Relative detector responses (R) versus the dimensionless variable (z) for the solid samples along with the fit lines using equation 5. Fig.5b Relative detector responses (R) versus the dimensionless variable (z) for the liquid samples along with the fit lines using equation 5. Fig.6a Relative detector responses (R ) versus ((rh/(r+h))a for the solid samples. Fig.6b Relative detector responses (R) versus ((rh/(r+h))a for the liquid samples. Fig.7a Relative detector responses (R) versus the variable z (cm3.g-1) for the solid samples along with the fit lines using equation 5 Fig.7b. Relative detector responses (R) versus the variable z (cm3.g-1) for the liquid samples along with the fit lines using equation 5. Fig. 8a Relative detector responses (R) versus ((rh/(r+h))a (cm3.g-1) for the solid samples. Fig.8b Relative detector responses (R) versus ((rh/(r+h))a (cm3.g-1) for the liquid samples along with the fit lines using equation 5.

12

Fig.9. Schematic diagram proposed to improve detector sensitivity. 1: incident neutron beam; 2: moderator; 3: sample and 4: neutron detectors

Table 1. Calculated mass macroscopic absorption and scattering cross sections ( density removed macroscopic cross sections), bulk densities and sample compositions of the first set of standard samples – errors are within 5 % of the reported values..

Water (H2O) soluble samples

Bulk samples: SiO2 + additional admixture SiO2+ weight fraction (%)

s

a

m

2

-1

(cm .g )

m

Bulk 2

-1

(cm .g )

H2O+

density

weight fraction (%)

s

a

m

2

-1

(cm .g )

m

Bulk 2

-1

(cm .g )

-3

density -3

(g.cm )

(g.cm )

SiO2

0.1066

0.0017

1.72

H2O

3.986

0.0222

1

SiO2 + 0.053% H3BO3

0.1073

0.0057

1.72

H2O+0.900% H3BO3

3.964

0.0895

1

SiO2 + 0.105% H3BO3

0.1081

0.0096

1.72

H2O+1.257% H3BO3

3.955

0.1161

1

SiO2 + 0.316% H3BO3

0.1112

0.0254

1.71

H2O+1.610% H3BO3

3.947

0.1424

1

SiO2 + 0.473% H3BO3

0.1135

0.0372

1.71

H2O+0.182% NaCl

3.979

0.0228

1

SiO2 + 0.787% H3BO3

0.1182

0.0606

1.71

H2O+0.362% NaCl

3.972

0.0234

1

SiO2 + 1.046% H3BO3

0.1220

0.0800

1.70

H2O+1.256% NaCl

3.939

0.0264

1.010

SiO2 + 1.201% H3BO3

0.1243

0.0916

1.70

H2O+2.048% NaCl

3.909

0.0290

1.016

SiO2 + 1.561% H3BO3

0.1296

0.1186

1.70

H2O+4.600% NaCl

3.815

0.0373

1.036

SiO2 + 1.612% H3BO3

0.1303

0.1224

1.70

SiO2+ 2.070% H3BO3

0.1371

0.1567

1.68

SiO2+ 2.570% H3BO3

0.1445

0.1945

1.68

SiO2 + 2.070% NaCl

0.1100

0.0090

1.70

SiO2 + 3.560% NaCl

0.1124

0.0142

1.68

100% H3BO3

1.5821

7.4872

0.85

13

Table 2. Calculated mass macroscopic absorption and scattering cross sections ( density removed macroscopic cross sections), bulk densities and sample compositions of the second set of standard samples – errors are within 5 % of the reported values.

Bulk samples: SiO2 , sand and TiO2 + additional admixture Bulk sample + weight fraction (%)

sm

a

Water (H2O) soluble samples m

Bulk

H2O+ weight fraction (%)

sm

am

Bulk

2 -1 2 -1 (cm .g ) (cm .g ) density

2 -1 2 -1 (cm .g ) (cm .g ) Density

-3

(g.cm )

-3

(g.cm ) SiO2

0.1066

0.0017

1.7200

H2O

3.986

0.0222

1.00

SiO2 + 0.22 %H3BO3

0.1099

0.0184

1.7200

H2O+0.760 % NaCl

3.957

0.0248

1.01

SiO2 + 0.67 % H3BO3

0.1164

0.0516

1.7100

H2O+1.510 % NaCl

3.929

0.0272

1.01

SiO2 + 0.89 % H3BO3

0.1196

0.0681

1.7100

H2O+2.255 % NaCl

3.902

0.0297

1.02

SiO2 + 2.33 % H3BO3

0.1409

0.1761

1.6800

H2O+2.985 % NaCl

3.874

0.0320

1.02

SiO2 + 3.96 % H3BO3

0.1649

0.2978

1.6500

H2O+3.700 % NaCl

3.848

0.0344

1.03

SiO2 + 75.41% H3BO3

0.9537

4.2992

1.0800

H2O+5.110 % NaCl

3.796

0.0390

1.04

SiO2 + 0.94% NaCl

0.1081

0.0050

1.7100

H2O+6.475 % NaCl

3.745

0.0435

1.05

SiO2 + 2.37% NaCl

0.1105

0.0100

1.6900

H2O+7.143 % NaCl

3.694

0.0480

1.06

SiO2 + 16.80 % NaCl

0.1342

0.0603

1.5500

H2O+9.785 % NaCl

3.571

0.0589

1.08

SiO2+ 37.76 % NaCl

0.1688

0.1335

1.3800

H2O+15.464 % NaCl

3.340

0.0793

1.12

100% H3BO3

1.5820

7.4872

0.8500

H2O+20. 680 % NaCl

3.217

0.0902

1.16

Sand

0.0957

0.0022

1.5700

H2O+0.763 % H3BO3

3.967

0.0792

1.00

Sand + 0.5130 % NaCl

0.0966

0.0040

1.5700

H2O+1.510 % H3BO3

3.949

0.1353

1.00

Sand + 2.060 % NaCl

0.1002

0.0111

1.5500

H2O+2.255 % H3BO3

3.931

0.1906

1.00

Sand + 7.250 % NaCl

0.1126

0.0357

1.5100

H2O+2.985 % H3BO3

3.914

0.2451

1.00

Sand + 14.37 % NaCl

0.1354

0.0810

1.4600

H2O+3.700 % H3BO3

3.896

0.2987

1.00

Sand + 14.31 % NaCl + 0.45 % H3BO3

0.1275

0.0856

1.4600

H2O + 2.24 % NaCl + 0.75%H3BO3

3.880

0.0853

1.02

Sand + 14.21 % NaCl + 1.12 % H3BO3

0.1373

0.1356

1.4500

H2O + 0.71 % NaCl + 0.11%H3BO3

3.697

0.1261

1.06

Sand + 14.08 % NaCl + 2.02 % H3BO3

0.1504

0.2022

1.4400

H2O + 9.64 % NaCl + 1.52%H3BO3

3.591

0.1672

1.08

Sand + 13.88 % NaCl + 3.36% H3BO3

0.1701

0.3022

1.4300

H2O + 15.12 % NaCl+2.24%H3BO3

3.370

0.2394

1.12

14

Sand + 13.70 % NaCl + 4.70% H3BO3

0.1896

0.4017

1.4200

Sand + 13.37 % NaCl + 6.93% H3BO3

0.2223

0.5679

1.3900

Sand + 12.73 % NaCl + 11.43%H3BO3

0.2880

0.9024

1.3500

Sand + 11.76 % NaCl + 18.15%H3BO3

0.3861

1.4014

1.2900

Sand + 8.34 % NaCl + 42.00% H3BO3

0.7341

3.1421

1.1200

Sand + 2.37 % NaCl + 83.52% H3BO3

1.3413

6.2621

0.9100

100 % H3BO3

1.5821

7.4872

0.8500

TiO2

0.0875

0.0459

0.8100

TiO2 + 0.807 % H3BO3

0.0996

0.1060

0.8100

TiO2 + 1.610 % H3BO3

0.1116

0.1655

0.8110

TiO2 + 2.400 % H3BO3

0.1234

0.2245

0.8110

TiO2 + 3.187 % H3BO3

0.1352

0.2831

0.8110

TiO2 + 9.69 % NaCl + 2.88 % H3BO3

0.1484

0.2896

0.8291

TiO2 + 9.45 % NaCl + 5.17 % H3BO3

0.1823

0.3887

0.8296

TiO2 + 9.16 % NaCl + 8.16 % H3BO3

0.2264

0.6812

0.8302

TiO2 + 8.80 % NaCl + 11.78 %H3BO3

0.2797

0.9490

0.8310

TiO2 + 8.11 % NaCl + 18.71 %H3BO3

0.3820

1.4625

0.8325

TiO2 + 5.58% NaCl + 44.08 % H3BO3

0.7566

3.3431

0.8379

H2O + 20.07 % NaCl+2.96%H3BO3

Table 3. Detector sensitivities ( cm-1.S-1) for the large and small solid samples.

Detector response

Sample

/

Large

Small

D1 /a

10

6.4

D1/s

38

19

15

3.168

0.3092

1.16

D4 /a

16

13

D4/s

62

50

D3 /a

5.3

4.0

D3/s

20

15

Highlights    

A method was proposed for measuring macroscopic cross-sections for thermal neutrons. A Pu-Be neutron source and He-3 neutron detectors assembly were used. A new semi-imperial model was proposed and successfully fitted the results obtained. Macroscopic cross sections can be determined for solid and liquid samples.

11 12 5 6 3

2

9

1

4 8

10

11

5

7 10

Fig.1

16

Detector response (counts.sec-1)

100

position 1 (Large) position 1(Small) position 2 (Large) position 2 (Small) position 3 (Large) 10

position 3 (small)

0.001

0.01

0.1

1

a(cm-1)

Detector response (counts.sec-1)

Fig. 2a

100

position 1 (Large) position 1(Small) position 2 (Large) 10

position 2 (Small) position 3 (Large) position 3 (small)

1

s(cm-1)

Fig. 2b

17

10

120

position 1 ( sandsamples) position 1 ( TiO2samples) position 2 (sand and TiO2samples)

Detector response (counts.sec-1)

100

position 3 (sand samples) position 3 (TiO2 samples)

80

60

40

20

0 0.001

0.01

0.1

1

10

a(cm-1)

Fig. 3a

120

position 1 ( sandsamples) position 1 ( TiO2samples) position 2 (sand and TiO2samples)

Detector response (counts.sec-1)

100

position 3 (sand samples) position 3 (TiO2 samples)

80

60

40

20

0 0.1

1

s(cm-1)

Fig. 3b

18

400

position 2: H2O+NaCl, H2O+NaCl+H3BO3, and H2O+H3BO3 samples

Detector response(counts.sec-1)

position 1: H2O+NaCl, H2O+NaCl+H3BO3, and H2O+H3BO3 samples position 3: H2O+NaCl, H2O+NaCl+H3BO3, and H2O+H3BO3 samples

300

200

100

0 0.01

0.1

1

a(cm-1)

Fig. 4a

400 position 2 (H2O+NaCl) position 2 (H2O+NaCl+H3BO3) position 2 (H2O+H3BO3)

Detector response(counts.sec-1)

position 1 (H2O+NaCl) position 1 (H2O+NaCl+H3BO3) position 1 (H2O+H3BO3)

300

position 3 (H2O+NaCl) position 3 (H2O+NaCl+H3BO3) position 3 (H2O+H3BO3)

200

100

0 3.7

Fig. 4b

19

3.8

s (cm -1)

3.9

4

1.2

1.3 liter 5.5 liter

Relative response (R)

1

0.8

0.6

0.4

0.2 0.01

0.1

1

10

100

z

Fig. 5a

Relative response (R)

1

1.3 liter 5.5 liter 0.8

0.6

0.4

0.2 0

0.2

0.4

0.6

z

Fig. 5b

20

0.8

1

1.2

1.3 liter 5.5 liter

Relative response (R)

1

0.8

0.6

0.4

0.2 0.01

0.1

1

r*hr+h)*a

10

100

Fig. 6a

Relative response (R)

1

1.3 liter 5.5 liter 0.8

0.6

0.4

0.2 0

Fig. 6b

21

0.4

0.8

r*hr+h)*a

1.2

1.6

1.2

1.3 liter 5.5 liter

Relative response (R)

1

0.8

0.6

0.4

0.2 0.01

0.1

1

10

100

z (cm3.g-1)

Fig. 7a

Relative response (R)

1

1.3 liter 5.5 liter 0.8

0.6

0.4

0.2 0

0.2

0.4

0.6

z (cm3.g-1)

Fig. 7b

22

0.8

1

1.2

1.3 liter 5.5 liter

Relative response (R)

1

0.8

0.6

0.4

0.2 0.001

0.01

0.1

1

10

100

r*hr+h)*a (cm3.g-1)

Fig. 8a

Relative response (R)

1

1.3 liter 5.5 liter 0.8

0.6

0.4

0.2 0

Fig. 8b

23

0.4

0.8

r*hr+h)*a (cm3.g-1)

1.2

1.6

Fig. 9

24