Performance evaluation of the Boron Coated Straws detector with Geant4

The last decade has witnessed the development of several alternative neutron detector technologies, as a consequence of upcoming neutron sources and upgrades, as well the world-wide shortage of $^3$He. One branch of development is the family of $^{10}$B-based gaseous detectors. This work focuses on the boron coated straws (BCS) by Proportional Technologies Inc., a commercial solution designed for use in homeland security and neutron science. A detailed Geant4 simulation study of the BCS is presented, which investigates various aspects of the detector performance, e.g. efficiency, activation, absorption and the impact of scattering on the measured signal. The suitability of the BCS detector for Small Angle Neutron Scattering (SANS), direct chopper spectrometry and imaging is discussed.


Introduction
For many years 3 He-based detectors have been dominant in the field of neutron scattering science, as they satisfied scientific requirements and 3 He was available in sufficient quantities at an affordable price. The situation has changed in recent years due to the worldwide 3 He crisis [1,2] that necessitated the development of alternative neutron detector technologies based on 10 B 4 C [3,4,5,6,7,8,9], 6 LiF [10,11,12] and scintillators [13,14,15,16,17,18,19,20].
More importantly though, these new technologies are required to exceed the scientific capabilities of previous detectors, as imposed by future instrument upgrades and upcoming research facilities. Such a facility is the European Spallation Source (ESS) ERIC [21,22] that aspires to lead neutron scattering research.
The cutting edge neutron scattering instruments set high requirements for the detectors, that could otherwise become the bottleneck of the instrument's scientific performance. It is therefore important to understand every aspect of detector performance before qualifying it for a particular neutron technique.
Monte Carlo simulations could and should play a key role in the development and characterisation of detectors as a reliable, cheap and versatile tool [23]. Simulations not only make it easier to analyse and compare detectors and detector arrangements without building a physical prototype every time, but also enable the quantification of otherwise unmeasurable properties. The primary goal of this work is to perform a comprehensive characterisation of the BCS detectora promising 3 He detector replacement technology developed initially for homeland security applications -, using Monte Carlo simulations. The study includes the efficiency of the detectors, the absorption and activation of the materials thereof, and the impact of the material budget on scattering. A generic detector geometry is implemented in Geant4 [24,25,26], which can serve the needs of various neutron scattering techniques. The following sections introduce the detector specifics and the respective model, define appropriate figures of merit and discuss the evaluation of the BCS performance.

The BCS detector
BCS is a position sensitive 10 B-based gaseous neutron detector developed by Proportional Technologies, Inc. (PTI) [27]. It consists of a long thin-walled aluminium tube, containing seven copper straws arranged hexagonally with one in the centre (see Fig. 1). The inner wall of the straws is coated with a 1 µm thin B 4 C converter layer enriched in 10 B by 95%. The straws are filled with an Ar/CO 2 mixture (90/10 by volume) at 0.7 atm. A bias voltage is applied between the tube and resistive Stablohm wires tensioned in the center of each straw as anodes, making them work in proportional mode [28]. The charge is read out at both ends of the detector using charge division to acquire longitudinal position information along the straws.
The length and diameter of the straws, and therefore of the tubes, can vary depending on the application. It is claimed that a straw diameter of 2 mm up to 15 mm or even more can be achieved [5], but in most publications either 4 mm or 7.5 mm is used [29,30,31]. Generally, several BCS tubes are placed behind each other in successive layers in order to achieve the desired coverage, uniformity and detection efficiency. The main application field of the BCS detectors is homeland security and neutron imaging but they have the potential to be used as large area position-sensitive detectors for SANS and chopper spectrometers.  [27]. The copper straws inside the aluminium tubes are exposed.

Geant4 model
The Geant4 geometry model implemented for this study is a generic 1 m 2 detector arrangement that consists of 5 consecutive detector panels with 40 tubes in each (see Fig. 2). For higher uniformity in the conversion efficiency, the tubes are rotated by 20 • around their cylindrical axes and a relative horizontal shift of 10.16 mm is applied for adjacent panels (see Fig. 3) to avoid high differences in the path length in the B 4 C converter layer [32].       All materials are selected from the Geant4 database of NIST materials, except for Al and Cu. The latter are described with the use of the NCrystal library [34,35,23], as their crystalline structure is important for the correct treatment of their interaction with neutrons. The density of the NCrystal aluminium and copper are ρ Al =2.69865 g/cm 3 and ρ Cu =8.93484 g/cm 3 respec-tively. The Geant4 physics list used is QGSP BIC HP.
The detector system is illuminated with neutrons from a point source at a 5 m distance from the centre of the geometry in vacuum. The neutron source is an isotropic, monochromatic conical beam with an opening angle of 10.6 • ; this ensures that the direct beam crosses all 5 panels to minimise edge effects.
The model does not contain the anode wires in the straws and therefore neither the charge collection nor the readout are simulated. A detection event is recorded if a neutron's conversion products deposit more energy in the counting gas than a preset threshold applied to mimic discrimination of the gamma background. In different studies of BCS detectors, different thresholds are reported, e.g. 30 keV [36], 73 keV [5] and 200 keV [29]. Based on these values, in the simulations of this study an energy threshold of 120 keV is applied, which corresponds to an appropriate threshold for 10 B detectors to achieve sufficient γ/thermal neutron discrimination for neutron scattering applications [37,38,39].
The simulation of each neutron is completely independent so pile-up is not possible. If a neutron enters the copper straw in a BCS detector, it is counted as incident for that straw. If the neutron is converted in the B 4 C layer, it is counted as converted. The detection event's two coordinates perpendicular to the straw are defined by the virtual position of the wire in the center of the straw. In order to get the third, longitudinal coordinate, first the weighted average of the deposited energy by the conversion products is determined, then a Gaussian distribution with that mean value is sampled. The full width at half maximum (FWHM) for this smearing is set to 0.6 cm based on experimental results [29,32]. Although the longitudinal resolution for a tube detector depends on the position along its length (higher in the centre than closer to the ends [31]), and is very much a function of the analogue quality and signal treatment in the electronic readout, this study assumes uniform resolution.

Detector efficiency
Detection efficiency is one of the key performance parameters of a detector.
With new and stronger sources coming up it is important to fully exploit the high brilliance of a neutron pulse and accommodate a larger number of users.
This aspect of neutron detectors has come to focus with the replacement detector technologies. A simulation tool like Geant4 can shed a lot of light in the response of a complex geometry like that of BCS.
The functional unit of a BCS detector is a single straw. The straw detection efficiency can be expressed in several valid ways. In this work the following definition is used: • Detection efficiency is the number of neutrons detected in a straw over the number of incident neutrons in that straw from every direction. A neutron is counted as incident every time it enters the copper of the straw from the outside.
= # of detected neutrons in the straw # of incident neutrons in the straw .
The replacement of the number of detected neutrons with the number of converted neutrons in the nominators results in the respective conversion efficiencies.
Another relevant quantity is the detection to conversion ratio (DCR), that is the fraction of detected neutrons over converted ones. As previously mentioned, to get a detection event after a conversion, at least one of the conversion products has to leave the boron carbide layer and deposit enough energy in the counting gas to overcome the preset threshold. Detailed calculations of this exist [40,41,42] For BCS it is claimed that for 1 µm of B 4 C, one of the two charged conversion products has a 78% probability to escape the converter and ionise the counting gas in the straw [30]. This is the theoretical maximum for DCR, with no energy threshold. With the applied threshold of 120 keV, the simulated DCR is 70%, regardless of the wavelength of the converted neutrons, due to the small thickness of the B 4 C layer. This value also gives an upper limit for the detection efficiency, as it is the convolution of the conversion efficiency and the DCR. The higher the threshold is, the lower the DCR and therefore the detection efficiency will be. The optimal value depends on the gamma background of the measurement and ought to be chosen carefully.
The detection efficiency for each straw with monochromatic 0.6Å, 3Å and 11Å neutrons is depicted in Fig. 4. The efficiency of a single straw is quite low with an average of 3%, 12% and 31% respectively. This is why 7 of them are packed together in a BCS tube and this is why employing even more overlapping straws in consecutive panels of detectors is necessary for most applications. The detection efficiency of the straws is quite uniform for a particular wavelength across all panels. This is because of the monoenergetic neutron sources, but a previous study with polyenergetic neutrons demonstrated that the thermalisation of the neutron spectra can cause significant differences between the panels [33]. That is the reason for the slightly lower efficiencies in the last panels for 11Å, as the thermalisation through scattering leads to more and more neutrons with lower wavelength in the neutron spectrum and therefore lower average efficiency for the straws in the back. The results presented are derived from simulations with all 5 panels in place.
This means that efficiencies with fewer than 5 panels are somewhat overestimated because of the back-scattered neutrons from later panels, but the simulations with fewer panels showed that this effect means a <0.5% difference only.  It is worth mentioning that the thickness of the converter layer has an impact on the detection efficiency. As previously said, the latter results from the convolution of the conversion efficiency and the DCR. The conversion ef-ficiency could be increased by using a thicker conversion layer but that would lower the escape probability of the conversion products and consequently the DCR [5,6,40]. The cumulative effect of the converter layer thickness is wavelength dependent and not straightforward. The simulations show that for high wavelengths the global detection efficiency could be increased with lower B 4 C thickness due to the increase of DCR but for lower wavelengths the decrease of the conversion efficiency overrules it and the detection efficiency decreases.
In the other direction, the efficiency for low wavelengths can slightly benefit from thicker converter layers but for higher wavelengths where the conversion efficiency is already high, the lower DCR lowers the detection efficiency. In this study the commercial converter layer thickness of 1 µm is used. A more detailed investigation of converter thicknesses and efficiency optimisation is out of scope here.

Absorption in detector components
The previous section demonstrates that for achieving a higher detection efficiency it is necessary to use multiple panels of detectors. This does not only increase the number of conversion and detection events but as a consequence the undesired absorption in the non-converting materials of the detector, namely aluminium and copper also increases. However, it is not only these two materials that can absorb neutrons without leading to a detection but B 4 C too. As mentioned before, not all conversion events result in a detection event because in some cases the conversion products do not exit the converter layer or they do not deposit sufficient energy in the detector gas to overcome the applied threshold. In addition, there is a rather small amount of neutron absorption in carbon and 11 B without conversion products to trigger a detection event. These two event classes together are hereinafter referred to as absorption in B 4 C.
In a single Geant4 simulation it is possible to register the number of neutrons absorbed in aluminium, copper and B 4 C separately and compare the effect of these materials. The latter could also be done with multiple simulations using different models with the materials out of focus replaced with vacuum to eliminate their effect on each other, but these effects appeared to be minor so we present the results using the model with all materials in place. In Fig. 6 the relative absorption is depicted for simulations with five different neutron wavelengths. The relative absorption in any material or materials is defined as the number of neutrons absorbed in that material over the number of incident neutrons for the entire detector system.  Most of the undesired absorption occurs in the converter layer. This is not surprising with 30% of the converted neutrons not triggering a detection event (70% DCR). The absorption in the copper is higher than in aluminium except for the highest wavelength (11Å), but the difference is rather small in every case. This might be unexpected as the absorption cross-section of copper is approximately 16 times higher for these wavelengths (see Fig. 32 in appendix), but the total volume of aluminium is 17.6 times higher than that of copper, therefore the average path length of the neutrons in aluminium is much longer, an effect that compensates the cross-section difference.
It is possible to make a 'naive' analytical estimation of the absorption in a material using Eq. 2: where Σ a is the macroscopic absorption cross section given by Eq. 3 and l is the path length in a material.
where σ a is the microscopic absorption cross section, ρ A is the atomic density, ρ m is the mass density, M is the molar mass of the material and N A is the Avogadro number.
For a specific neutron wavelength each parameter is known except the path length in the materials. One way to estimate the latter is to assume that a neutron stops halfway through the detector system after crossing an aluminium wall 2 times and a copper wall 6 times frontally in each panel. Using the wall thicknesses provided in Tab. 1 the results are l Al =4.7 mm and l Cu =0.375 mm.
The path length of the neutrons is of course not constant even for a specific wavelength, as presented in Fig. 7. For aluminium, the beginning of the first peak in the histogram corresponds to the wall thickness of a tube, because that is the minimum distance in aluminium that a neutron has to pass to be absorbed in a straw. Due to the circular tube geometry and the conical beam, most of the neutrons do not enter the tube wall perpendicularly, so the neutrons absorbed in the first tube they enter can have a path length in aluminium longer than this minimum, that results in the first peak. The beginning of the second peak corresponds to three times the wall thickness of the tube, as the that is the minimum distance in aluminium for a neutron that is absorbed in the second tube it enters. The upcoming peaks are more and more blurred as the path length difference in different directions, and the number of scattered neutrons become more and more important. The last broad peak corresponds to the neutrons that pass through all panels without being absorbed and the rest of the histogram contains only scattered neutrons. Similar effects appear for copper because of the straws, but with more overlapping layers and complex geometry. With the average path length of the neutrons extracted from the simulations a more accurate estimate can be made proving the relevance of the formula in Eq. 2 and supporting the results. The relative absorptions from the two estimation methods and the results from simulation are presented in Table 2.
The estimations using the average path lengths are in very good agreement with the simulations. All results are within 2.5%, except for the the lowest wavelength but even there the difference is less than 13%. This shows how well such an easy formula describes the process of absorption in the detectors. The naive estimations also give a decent result, regarding the approximation of the estimation. Some numbers are off by a factor 3.3, but for medium wavelengths the difference is less than 70%. For wavelengths where the average path length is longer than the used fixed number, the results are underestimated, and the other way around, overestimated path lengths lead to overestimated absorptions.
More accurate estimations could be made with more sophisticated formula but even in this state, both estimations support the simulation results.     lengths 60-30 % of the neutrons leave the detector system even with 5 panels but for the highest wavelength this value drops below 0.5%. This high transmission number at lower and medium wavelengths emphasises the need for a shielding layer behind the panels. Proportion of absorption in aluminium and copper together is approximately 1.5% for low wavelengths and stays below 4.5% even for the highest wavelength. For the neutron wavelengths that are more relevant to neutron scattering techniques, the absorption of this scale is acceptable and justify the use of successive detection panels.
The obtained results correspond to pure unalloyed materials; alloyed materials and impurities may significantly increase the absorption due to the presence of isotopes with high absorption cross-section despite their low concentration.
For example, the macroscopic absorption cross section of Al5754 [43], an aluminium alloy typically used in nuclear science for mechanical structures, can be 18% higher than the pure aluminium mainly due to its manganese content.

Activation
Neutron absorption in the detector materials potentially has another negative effect besides lowering the detection efficiency, namely the neutron activation of these materials. Activation might interfere with the normal operation of the detectors in two ways. Firstly, the gamma rays and particles emitted by the excited nucleus and the decay products might form a background during measurements in addition to that of prompt gammas. Secondly, after the measurements, the radiation coming from the radioactive nuclei might not allow anyone to get close to the detectors (e.g. for maintenance) owing to the high gamma dose rate. The purpose of this section is both to determine whether the background from the activation is significant for the measurements, and to find out how much time one has to wait after the measurements to be safe to approach the detectors. This is intended to be a generic study, therefore the activation is calculated for pure aluminium and copper instead of a specific alloy. The activation of the previously mentioned aluminium alloy is already investigated in [44]. In that work it is also concluded that the activation of the Ar/CO 2 is a minor effect compared to the same of the aluminium-housing, and the beta radiation is negligible both in terms of background and radiation protection, so these aspects are not addressed here.
The calculations are performed for a constant flux of 10 9 n/cm 2 /s on a 1 cm 3 cubic sample, assuming 5% of neutrons are scattered toward the detectors. These numbers represent a worst case scenario for an intended SANS application [33] but the results to be presented scale linear with the flux, making it is easy to adopt them to any other particular application. This assumption gives an incident flux of 5 · 10 3 n/cm 2 /s for the 1 m 2 detector system, that mean a neutron intensity of 5 · 10 7 n/s. Using this number as source intensity for the previously introduced simulation arrangement, the intensity of neutron absorption in each material can be calculated for different monoenergetic beams using the relative absorption results from where I a is the neutron absorption intensity and λ is the decay constant of the regarded isotope. Pure aluminium contains only the 27 Al isotope, but copper has two natural isotopes -63 Cu and 65 Cu, so the absorption intensity is shared between them with respect to the their natural abundance and absorption crosssection. Neutron activation of the activation products (secondary activation) is neglected due to the low probability of the multiple neutron capture by the same nucleus. The irradiation time for the calculations is 10 6 s (≈11.5 days), that will be approximately an operation cycle for ESS.
The activity of an isotope after irradiation and cooling time t c is given by where a 0 is the activity reached by the end of the irradiation.
In order to express the results in activity concentration, the total activity of the isotopes are normalised with the total volume of the respective material. The volume of aluminium and copper for the five detector panels are V Al =14447 cm 3 and V Cu =822 cm 3 . The activity concentration of the isotopes of interest during irradiation and cooling are presented in Fig. 9. The results show that the activity concentration of the produced radionuclei saturates by the end of irradiation time. These end values are used to calculate the decay gamma emission of these radionuclei from a unit volume per second. In this study the gamma efficiency is approximated conservatively with 10 −7 [5,38] for all photon energies. Due to the constant gamma efficiency, only the total number of photons per decay has to be determined regardless of the photon energies. In order to do that, the yields of the possible decay gamma lines presented in Table 3 are summed, resulting in a gamma yield of  Table 3: Decay gamma lines of the activated isotopes with their production yield per decay [45] and the flux to dose conversion factor corresponding to the photon energy [46]. and I d,Cu−66 =17.5 s −1 for a unit volume. For the total volume of aluminum and copper, the gamma intensity is I γ Al =7.55·10 5 s −1 and I γ Cu =2.70·10 5 s −1 . The total decay gamma intensity for the whole detector system is I γ d =1.025·10 6 s −1 .
The prompt gamma intensity (I γp ) for aluminium and copper is calculated as the product of the neutron absorption intensity and the total prompt gamma yield per absorption (γ p ) for each material (see Eq. 6).
The number of prompt gammas per absorption is estimated as the ratio of the sum of the gamma line specific cross-sections (σ γi ) and the absorption crosssection (σ a ) [47]. Due to the gamma cascades, this ratio is not unity, the resulting yields are γ p,Al =1.978 and γ p,Cu =2.665. The prompt gamma intensities are I Al =1.493·10 6 s −1 , I Cu =2.345·10 6 s −1 and the total prompt gamma intensity is The total prompt and decay gamma intensity of aluminium and copper is As already mentioned, the obtained results correspond to pure unalloyed materials; alloyed materials and impurities may significantly increase the activity and dose rate due to isotopes with high cross-section or long half-life. This investigation assumed cold neutrons and single neutron activation, but for fast neutrons other reaction, like 63 Cu(n,α) 60 Co or 63 Cu(n,p) 63 Ni must be taken into consideration.

Scattering
Another side effect of the increased detector material budget due to the multi panel layout is the scattering of neutrons. In contrast to absorption, scattering can degrade the detector performance by producing intrinsic background, which in turn can impact the signal to background ratio. The latter is a driving requirement in particular for inelastic neutron instruments and has to be carefully considered in the detector design process.

Quantities of interest
The following raw (in boldface font) and derived quantities are of interest for the scattering study: • X: position along the straws (along the wire).
• Y: position perpendicular to the straws.
• TOF: neutron time of flight from the source until the detection.
• Θ: polar angle calculated from the source and the detection event X and Y positions.
• Φ: azimuthal angle calculated from the source and the detection event X and Y positions.
• λ: neutron wavelength calculated from the distance between the source and the detection event position (SDD) and the TOF, using Eq. 7 as where h is the Planck constant, m is the neutron mass and υ the velocity.
• Q: scattering vector calculated from Θ and λ, using Eq. 8 (SANS definition):   The effect of the discrete Y and Z detection coordinates also appears for λ. The ideal λ is calculated from the TOF and the source to detection point distance (SDD) according to Eq. 7, but for the simulated λ, the distance between the source and the detection event wire coordinates (SWD) is used. The maximum difference between source to detection point distance and source to detection event's wire coordinates distance is the inner radius of the straw. The resulting ∆λ difference for a non-scattered neutron is calculated using Eq. 9 For all quantities where the limits are defined by the parameters of the fitted Gaussian function, the mean is at least 3 orders of magnitude lower than the standard deviation, so for simplicity zero is used instead. This means that the range for any δ quantity, within which a detection event is considered as signal is ± the corresponding limit. The width of all signal ranges are presented in Tab. 4 and Tab. 5. The figures showing the limits visually, similarly as for δX (Fig. 11) and δY (Fig. 12), are placed in appendix (see Fig. 33

Impact of scattering on spatial resolution
The FWHM of the δX distribution is 0.67 cm, which is the result of the detection coordinate approximation with the weighted average of the deposited energy by the conversion products and the applied smearing with a FWHM of 0.6 cm. Small local scatterings could also cause the broadening of the peak. In order to evaluate this effect, the δX distribution is shown in Fig. 13 consecutively The figure on the right shows only δX for the conversion point in the centermost range with finer binning to reveal the shape of its peak. The lines are only joining the points.   that for these neutrons TOF generally increases due to scattering and so does the resulting λ. Going for longer initial wavelengths, the negative side becomes more and more significant. This proves that shorter measured TOF and λ as a result of scattering can be just as important as longer.

Impact of panels and material budget
The change in the measured λ due to scattering inside the detector can be expressed in terms of change in the measured neutron energy, that can be important when observing energy transfer in real samples.

Definition of fractional scattering
Signal and background relation can be characterised by several quantities.
A common way to express it in neutron scattering is the peak-to-tail ratio, that can be visually extracted from the presented figures. However, this ratio does not quantitatively reflect the total amount of signal or background and in addition it is sensitive to the histogram binning. Instead, a different figure of merit is used that provides fractional scattering in terms of integrals, as defined by Eq. 10: where S and B denote the number of detected neutrons considered as signal and background respectively. Although the shape of signal and background varies for the observed δ quantities, Fig. 24 demonstrates that the integrals of the previously defined signal ranges are similar within less than a 3% range. This means that any of the δ quantities and the signal limits thereof lead to essentially the same fractional scattering values. The following results are acquired using δΘ for signal-background separation.  shown before that additional panels not only increase the signal, but the scat-tered background as well as, via the detection of more scattered neutrons and the back-scattering of neutrons to upstream panels. This result shows that the ratio of signal to background degrades with the additional panels, because the fractional scattering increases monotonously. This is more notable for low wavelengths, where the differences are higher, but the tendency is the same for 11.0 A. For the same number of panels, fractional scattering is always higher for neutrons with shorter initial λ.    The thickness of the PE layer is 50 mm.
The highest gain from the back-scattering of transmitted neutrons is achieved for low wavelengths. Fig. 29 demonstrates the impact of the additional PE layer on δΘ for the lowest observed wavelength, λ=0.6Å. This result shows a significantly increased background with a slightly increased signal. Fig. 30 demonstrates that the PE layer has a different effect on the different δ quantities. The signal defined by the limits for δΘ is 6.3% higher than for δλ.
This difference is more than double of any previously experienced. This implies that the fractional scattering depends much more on the signal definition.
The focus here is on the case with the highest gain, so the fractional scattering results presented in Fig. 30 are calculated with the highest signal from δΘ. Even with this favourable definition, the ratio of the scattered background appears to be higher with the back-scattering layer than without it. For the highest wavelength there is no difference but going to lower λ where the PE should help, the fractional scattering becomes significantly worse.

Conclusions
A generic BCS detector model is implemented for Geant4 simulations. With this, a complex analysis is carried out in order to evaluate various aspects of the BCS detector performance. This study is made in the context of most realistic applications that might be envisaged. The aim is to have a complete set of generally applicable results.
The detection efficiency of a single straw, and even of complete detector tubes with seven straws are found to be low. Therefore, overlapping layers (panels) of detectors are needed to achieve a decent efficiency. The cost-efficient number of panels depends on the application and the relevant neutron wavelength range.
The absorption (not resulting in conversion to detectable particles) in B 4 C is 6.5-8 times more than in Al and Cu combined. The absorption from these two mechanical materials in the detector is in the range of 1.5-4.5% of the incident neutrons depending on the wavelength. Pure unalloyed material was modeled in the study; alloyed materials and impurities may significantly increase this and need to be considered. At smaller wavelengths the fraction of neutrons transmitted through the detector is high (50-60% at 0.6Å) and therefore absorbant shielding behind the detector is a must for applications below 5Å.
The activation analysis of such a detector has been implemented. The activation is dominated by copper, as expected, with a cooling time of a few days.
The radiation background from activated materials will not interfere with the data acquisition. The activation during operation at ESS is not expected to be a limitation for maintenance. The calculated numbers have been presented in a fashion that could be scaled to real applications.
The scattering has been studied in detail, namely its effect on δX, δY, δTOF, δΘ, δΦ, δλ, δE and δQ in terms of the fraction of neutrons that end up as signal, scattered background, transmission through the detector or absorbed an non-detected. The effect of the detector geometry on the natural shape of the resolution function is shown. Scattering is highest at low wavelengths and is significant below the Bragg cut-off. It can be considered to be at acceptable levels for applications such as SANS, diffraction and imaging, however, may be considerable for applications which are highly sensitive to it such as spectroscopy.
Any application for spectroscopy would need detailed consideration of its effect on performance.
A polyethylene "afterburner" block placed behind the detector was inves-tigated and found to increase signal by up to 4%, however, background correspondingly increased up to 15%. Therefore this is not a good solution for most applications. It also re-emphasises the need for the layer of shielding closest to the detector to be made of materials with very low neutron albedo.
The capabilities of Geant4 are enhanced by the NCrystal library [34,35] in order to treat the thermal neutron transport correctly in crystalline materials by taking into account the material structure and effects of inter-atomic bindings.
With this tool aluminium and copper are treated as crystalline materials with the cross-sections presented in Fig. 32.