Evaluation of Natural Radioactivity Levels for Structural Material Used in the Construction of the Neutrino Detector

In this work, the evaluation of natural radioactivity and spontaneous fission rates was performed for 8 nuclides from the natural radioactive 238U, 235U and 232Th decay chains. For this purpose, three samples of structural materials of the neutrino detector, i.e. aluminum, titanium and glass were analyzed by gamma spectroscopy and by neutron activation analysis to quantify a specific radioactivity of the samples. According to the results of this investigation, glass and aluminum samples have maximum values of the mean uranium concentrations 7.3(7) × 10−4% and 3.1(6) × 10−5%, respectively, while the lowest value for mean concentration of the uranium was found in titanium samples to be 4.7(3) × 10−6%. Aluminum sample had maximum values of the mean thorium concentrations, 2.5(8) × 10−3%, while the lowest value for mean concentration of the thorium was found in titanium samples to be 6.2(3) × 10−7%.


Introduction
Practically all the neutron-rich nuclei are unstable due to an excess of neutrons in the nucleus.They decay by emission of electrons, beta decay, and generate the electron anti-neutrinos e ν .The quantity of the radioactive nuclei can be defined with the anti-neutrino flux in the reactor core.The anti-neutrino flux density distribution allows carrying out monitoring of the reactor core.
Depending on the neutrino flavour, there are several possible detection reactions in a liquid-scintillator detector.The most important ones are the inverse beta decay channel for e ν : Gamma radiation from capture of slow neutrons in 157 Gd is used as signal to neutrino registration after thermalization of fast neutrons in neutrino detector.The 158 Gd emits gamma-ray cascade with the total energy of 8 MeV ( ) n S 7937.33 keV = . The inverse beta decay reaction has a threshold of 1.8 MeV.It provides a delayed coincidence signal while the positron gives a prompt signal and then the neutron is captured by a free proton or 157 Gd in ~200 μs [1].The neutrino detector has to measure the desired signal at the input count rate of 300 day −1 under the assumption of the 0.5 m 3 detector volume, the 5 m distance between centers of the reactor core and the neutrino detector and reactor power of 17 MW.Due to the passive and active shielding the neutrino detector provides ultra-low background counting rate in the detector.The cosmic muon capture reaction ( ) on the heavy elements is source of the natural radiation background (fast neutrons).Lead is one of these elements usually used for the construction of the passive shielding.In fact, real counting threshold of the detector is determined by intrinsic radioactive contaminants.As 14 C is naturally abundant in organic scintillators, detection of neutrino is not possible below the end point 156 keV of the 14 C β-spectrum.
The isotopes from the natural uranium and thorium decay chains are intensive alpha and beta radioactive sources.At the same time, the 238 U, 235 U, 234 U and 232 Th are disintegrated via spontaneous fission process.The spontaneous fission rate is far less than the α-decay one.The 238 U, 235 U, 234 U, 232 Th and their daughter nuclei create signals in the liquid-scintillator detector in their natural α-and β-decays.These signals correlate with those from the fast neutrons which appear in the spontaneous fission of the 238 U, 235 U, 234 U and 232 Th.Nuclear characteristics of the 238 U, 232 Th and their daughter nuclei emitting neutrons in the spontaneous fission are given in the Table 1.Only nuclei of the 232 Th emit the neutrons after spontaneous fission in the radioactive 232 Th decay chain.The spontaneous fission probability SF of the 232 Th is 1.1 × 10 −9 % per decay.So, the neutrino detector, the passive and the active shielding should be built with materials in which natural radioactivity has ultra-low background.
The 235 U and its daughter nucleus 231 Th are important naturally occurring radioactive isotopes; they were used to determine the uranium concentration in the samples analyzed.The 235 U decays by 100% α-emission to levels in 231 Th.The recommended nuclear decay data of the 235 U and 231 Th are presented in Table 2.The decay data were taken from the LNHB (available at http://www.nucleide.org/NucData.htm).

Examination
The uranium mass concentration and absolute decay rate of the 235 U were measured with the gamma spectrometric method in samples analyzed (aluminum and titanium sheets and glass samples).
The gamma line of 235 U at the 185.7 keV was used in this case.In the same way the uranium mass concentration and the absolute decay rate of the 238 Uwere measured with the 234m Pa full absorption peaks at the 766.6 keV and 1001 keV, as the 234m Pa is daughter nucleus of natural radioactive 238 U.
The first two daughter nuclei of the radioactive 238 U decay chain ( 234 Th, 234m Pa) are very short-lived compared with 238 U so that radioactivity equilibrium is quickly achieved (about in three months) in the samples of natural isotopic composition which need not be subjected to special isotope separation.The 238 U, 234 Th, 234m Pa have the similar radioactivity.Absolute decay rate of 238 U, 234 Th, 234m Pa, 231 Th and uranium concentration were determined in the samples analyzed with the use of the gamma-rays listed in the Table 3.The decay data were taken from the ENSDF BNL-NCS-51655-01/02-Rev.
Three daughter nuclei of the equilibrium radioactive 232 Th decay chain ( 228 Ac, 212 Pb, 208 Tl) were used for the determination of the natural radioactive and the spontaneous fission rates of the 232 Th.The γ-ray energies and absolute γ-ray abundances of the 228 Ac, 212 Pb and 208 Tl are listed in the Table 4.The recommended decay data were taken from the ENSDF BNL-NCS-51655-01/02-Rev.
The concentration and natural radioactivity of potassium were measured with the use of the full absorption peak of the 40 K at the 1460.8keV E γ = in a gamma-ray spectrum of the samples analyzed.Nuclear data, the 40 K decay scheme and the 40 Ar excited level scheme are given in Figure 1 and Figure 2, respectively.
The 238 U, 235 U, 232 Th and their daughter nuclei have low-level radioactivity in the samples analyzed, therefore the big cylindrical samples have been used to achieve large statistical reliability.Masses of the aluminum, titanium samples and glass of the photomultiplier were about 1800 g, 1871 g, and 771 g, respectively.The concentrations of the other trace, minor and major elements have been measured with the instrumental neutron activation analysis.

Experimental Facility for Spectrometric Measurements
Experimental facility includes gamma-ray spectrometer and a passive shielding of a HPGe detector.The passive shielding consists of 0.5 mm of copper, 1 mm of cadmium and 9 cm of lead with 2.8(4) × 10 −3 s −1 counting rate of 210 Pb at the 46.5 keV.The usage of cadmium and copper as an inner layers of a multilayer shielding attenuates the bremsstrahlung and the X-rays (72.805 keV abundance is 2.75% and 74.969 keV abundance is 4.58%) induced by the beta-particles from the 210 Bi decay ( ) 1621 MeV E β = in the lead.A special effort was spent to reduce the background from the 41 Ar (counting rate is 1.3(2) × 10 −3 s −1 for the 1293.7 keV peak at the reactor power of 17 MW).Therefore the distance between the detector and the copper layer of the passive shielding was reduced up to 3 mm (see Figure 3).
The integral background normalized to the mass of the Ge crystal in the energy range from 40 keV to 2.7 MeV was determined to be 2.84 s −1 •kg −1 .This value is by a factor of 2.2 worse than that obtained at the installation of the Felsenkeller laboratory at the ground level [16].The shielding construction with the minimized gap of only 3 mm between detector and innermost copper increases the continuous background due to backscattering.However, in the energy range 100 -150 keV the reduction of the background by 3 mm gap exceeds the backscattering effect as long as the sample activity is lower than 3 Bq, as it is shown in the Table 5.A reference 60 Co gamma-ray source (3.2 kBq) was used to investigate the influence of the backscattering effect during sample      The decision threshold g in units of activity was determined using the full absorption peak at the signif- ic-ance level 0.025 α = ( ) where ε is the full energy peak registration efficiency for the sample-detector geometry, P γ is the gamma- ray emission probability, t is the measurement time and 0 R is the count rate in seconds both in a region of 2.5 FWHM beyond the peak.Shown in Figure 4 is the energy dependence of the counting detector efficiency for the size of reference gamma-ray source (62 mm in diameter, 100 mm height).The crystalline hydrate of uranyl nitrate UO 2 (NO 3 ) 2 •6H 2 O (750 g) was taken as the reference gamma-ray source.
Figure 5 shows the energy dependence of the decision threshold g under the assumption of 1 P γ = and 1 t = day for the sample geometry (diameter 62 mm, height 100 mm) used in routine analyses for the determi- nation of the sample natural radiation background.The decision threshold g achieves minimum (see Figure 5)  at energies of approximately 200 keV, where the counting detector efficiency is maximum (Figure 4).
The decision threshold n R * and the detection limit # n R in the units of counting rate at the selected energy were calculated as and respectively [17].The The area uncertainty of the full absorption peak is then calculated as [17]   ( ) where n N is the area of the full absorption peak and 7 shows the energy dependence of the area uncertainty (%) for measurement time of 1 t = day, and sample of size Ø 62 mm, height 100 mm.The Table 6 presents, for example, decision threshold g expressed in terms of activities for 235 U, 234 Pa and 208 Tl containing in the natural aluminum sample.The required decision threshold g for the aluminum sample can be reached at the measurement time of 7 d and the sample mass of 1.8 kg.
The gamma-ray spectra of samples analyzed and large standard reference gamma-ray-emitting sources were measured with the coaxial p-type HPGe-detector of 20% relative efficiency (CANBERRA GC2018) coupled   with "Lynx" multichannel digital analyzer (Canberra, USA).The germanium crystal of the detector has a diameter of 62 mm and a length of 30 mm, which is equivalent to a volume and mass of the active germanium of 90.6 cm 3 and 0.482 kg, respectively.The FWHM of the detector at the energy of 1.332 MeV was determined to be 1.7 keV.

Experiment
The concentration and specific radioactivity of potassium, uranium, thorium and their daughter nuclei were measured with the gamma spectrometric method.The concentrations of As, Ce, Co, Cr, Fe, Hf, La, Na, Sb, Sc, Sm, Th, U, Zn have been measured with the instrumental neutron activation analysis.

1) Relative gamma spectrometric technique
The relative gamma spectrometric technique was used to measure the absolute decay rate and the spontaneous fission rate of the natural radioactive elements in samples analyzed.Here the specific activity s SA of a radioi- sotope is obtained by direct comparison with the activity st A of the same radionuclide given in a reference gamma-ray-emitting-source by the following equation [18]   ( ) ( ) where the subscripts sm and st mark the value belonging to the sample and the reference source, respec- tively, the sm m is sample mass and S is the area of the full absorption peak.The t is measurement time of a gamma-ray spectrum.The sm µ and st µ are gamma-ray transmission coefficients of the sample and reference source materials, respectively.The energy dependence of the gamma-ray transmission coefficient assuming a R = can be calculated according to expression ( ) where ( ) E τ is the total linear absorption factor of the sample or reference source, respectively.Figure 8 shows the registration geometry of the gamma-ray with the Ge detector.The x and y are distances travelled by γ -ray through the detector and the sample, respectively, the a and R are the detector and the sample radii, re- spectively, the b and l are the detector and the sample heights, respectively, the 0 h is the detector-sample dis- tance in Figure 8 and in Equation (6). ) were taken as large calibration gamma-ray sources.The reference data were taken from the LNHB (available at http://www.nucleide.org/NucData.htm)and are presented in the Table 7.
The samples analyzed and the standard reference gamma-ray-emitting-sources had the same sizes.For measurement the time period were taken from 7 to 32 days.The full absorption 208      The decay data were taken from the LNHB (available at http://www.nucleide.org/NucData.htm).

2) Instrumental neutron activation analysis technique
Instrumental neutron activation analysis technique was used to measure the concentrations of 14 trace elements in the samples.The aluminum, titanium, glass samples and comparison standard (IAEA 433 standard reference material) were packed in high-purity quartz glass ampoules.The sample and the comparison standard mass were about 30 -50 mg.The samples and comparison standard were irradiated in a water channel of the WWR-M reactor for two hours at thermal ).The gamma ray spectra were measured after 3, 6 and 20 days of cooling time.The analysis results of the sample and the nuclear characteristics [15] of the nuclides used to determine the concentrations are shown in the Table 8.Equation (7) shows the time dependence of the daughter nucleus amount for an equilibrium 238 U decay chain: where the 1,0 100 is the number of the uranium nuclei in the samples analyzed, the λ is decay constant, the A N is Avogadro number, the AW is atomic weight, the a is the isotopic abundance, the sm m is sample mass.U C is the mass concentration (%) of uranium in the sample that was measured with the in- strumental neutron activation analysis.The time period when the activity of the daughter nuclei reaches a maximum was calculated with the equation ( ) . The activity of the daughter nucleus is any time t with the initial condition 0 i N = at 0 t = .In our case the time t is equal to m t .

Discussion
Natural uranium contains 99.274% of 238 U, 0.720% of 235 U, and 0.0055% of radiogenic 234 U.The 238 U, 235 U and 234 U decay via alpha emission to 234 Th, 231 Th and 230 Th, respectively.The alpha decay energies Q α of the 234 U, 235 U, 238 U are equal to 4858.5, 4678.7, and 4270 keV [7], respectively.The total radioactivity of the natural uranium connected with 238 U and 234 U for the aluminum, titanium and glass samples shown in the Table 9 can be divided half-and-half between 234 U and 238 U, as the 235 U contribution to the radioactivity of the natural uranium can be neglected.The 238 U absolute decay rate is more than 235 U rate by the factor of 15.1(30) and 30 (12) in the aluminum and glass samples, respectively.The natural radioactivity and spontaneous fission rates of the 238 U, 235 U, 234 U, 232 Th and their daughter nuclei were measured with the relative gamma spectrometric technique and were calculated using the INAA data according to Equation (7).In the Table 9 the radioactivities measured А meas , calculated А calc and spontaneous fission rates I for these radionuclides are listed.Radioactivity of 238 U was calculated to be the average of the measured 234 Th and 234m Pa activity values.The 238 U half-life is 1.41 × 10 17 seconds, therefore 5.58 × 10 −4 g of the 238 U have absolute alpha decay rate of 6.8(9) s −1 and produce the same number of 234 Th nuclei in the aluminum sample (1800 g).The number of the daughter nuclei with the exception of the 206 Pb is decreased with the time but the mass ratio of the daughter nuclei remains constant after the radioactive equilibrium is achieved.If absolute decay rate of 238 U is equal to 6.8(9) Bq, then 5.58 × 10 −4 g of the 238 U enclose 2.07 × 10 7 nuclei (7.97 × 10 −15 g) of 234 Th in the equilibrium radioactive 238 U decay chain inside the aluminum sample.Mass concentration of 232 Th was calculated according to Equation ( 9), where 0.3594 a = is alpha decay branching of 212 Bi, the A sp is specific radioactivity of 208 Tl.Mass concentrations and specific activities of 232 Th, 234 Th and 234m Pa in the samples analyzed are listed in the Table 10.
The 230 Th does not have suitable analytical gamma lines for measuring its radioactivity.The radioactivity and neutron emission by spontaneous fission of 230 Th were not measured because 238 U does not go to radioactivity equilibrium with its daughter nucleus 230 Th.The contribution of 230 Th in the neutron emission of the sample is negligible since the spontaneous fission probability per decay of 230 Th is less than 4 × 10 −12 %.The fast neutron radiation intensity normalized to the sample mass was calculated.The intensity values are given in the Table 11.

Conclusion
In this work, the evaluation of the gamma and neutron emissions were performed for eight nuclides, from the natural radioactive 238 U, 235 U and 232 Th decay chains for aluminum, titanium and glass.The integral gamma radi-   ation background normalized to the mass of sample in the energy range 40 keV to 2.7 MeV was determined to be 0.34, 0.084 and 0.81 s −1 •kg −1 for aluminum, titanium and glass, respectively.The background of fast neutrons normalized to the sample mass is determined mainly by spontaneous fission of 238 U and is equal to 7.3(11) × 10 −6 , 1.19(46) × 10 −5 and 6.3(5) × 10 −7 s −1 •kg −1 for aluminum, glass and titanium, respectively.The 234 U radioactivity has not been evaluated in the titanium sample.Therefore, the 234 U radioactivity was taken to be equal to 238 U radioactivity for equilibrium radioactive 238 U decay chain in the titanium sample.If the value of the spontaneous fission intensity normalized to the sample mass of the titanium is 9.3(16) × 10 −15 s −1 •g −1 assuming the spontaneous fission branching of 234 U is only 1.6(2) × 10 −9 (%) then the radiation intensity of fast neutrons normalized to the sample mass is 1.51(4) × 10 −10 s −1 •g −1 .

Figure 2 .
Figure 2. Excited level scheme of the 40 Ar.

Figure 4 .
Figure 4.The efficiency calibration curve of the GC2018 HPGe detector.

Figure 5 .
Figure 5. Decision threshold g versus the energy for measurement time of 1 day and the normalized emission probability of P γ = 1.
of the normal distribution for the error probability α of the type I and for the error probability β of the type II, respectively ( N is the number of counts below the full absorption peak in the spectrum, the l is full width at half maximum (FWHM) of the full absorption peak, the 2 b l = is the width of the full absorption peak, the t is measurement time in the Equations (2) and (3).The energy dependences of n R * and # n R are shown in the Figure 6.

Figure 6 .
Figure 6.The energy dependence of * n R and # n R of GC2018 HPGe detector for measurement time t = 1 day and for the sample geometry of Ø 62 mm, height 100 mm.

Figure 7 .
Figure 7.The area uncertainty (%) versus the energy of the full absorption peak at the measurement time of t = 1 d, and sample geometry of Ø 62 mm, height 100 mm.

Figure 8 .
Figure 8. Gamma-ray registration geometry for a large sample with HPGe detector.
Tl 510.77 keV, 583.19 keV, 40 K 1460.82 keV and 214 Bi 1729.59 keV, 1764.5 keV peaks registered in the gamma-ray spectra of the samples analyzed given in Figures 10-12.

Figure 9 .
Figure 9.The energy dependences of the gamma-ray transmission coefficient for the Al, Ti, KBr, the UO 2 (NO 3 ) 2 •6H 2 O and quartz glass samples for R = 3.1 cm, l = 10 cm.

Figure 10 .
Figure 10.The full absorption 208 Tl peaks 510.77 keV, 583.19 keV in the radioactive equilibrium 232 Th decay chain registered in the gamma-ray spectra of the samples analyzed.

Figure 11 .Figure 12 .
Figure 11.The full absorption 208 Tl peak 2614.55 keV in the radioactive equilibrium 232 Th decay chain registered in the gamma-ray spectra of the samples analyzed.
After irradiation the ampoules were washed out with the 0.5 M HNO 3 aqueous solution and the distilled water.The total sample and the comparison standard was measured with the 20% coaxial HPGe detector (Canberra, FWHM 1.7 keV at 1332.5 keV E γ =

Table 1 .
Nuclear characteristics of the 238 U, 232 Th and their daughter nuclei.

Table 2 .
The nuclear data of the 235 U and 231 Th.

Table 3 .
Main gamma-rays of the radioactive equilibrium 238 U and 235 U decay chains.

Table 4 .
Main gamma-rays of the radioactive equilibrium 232 Th decay chain.

Table 5 .
Effect of the detector-shielding distance L to the counting rate I of the detector in the energy range from 100 keV to 150 keV.L, (mm) I, (s −1 )measurements.The energy range 100 -150 keV is just above the K X-ray absorption edge of the multilayer Pb-Cd-Cu shielding because these elements have corresponding edges at the energies of 87.95 keV, 26.712 keV and 8.982 keV.

Table 6 .
The decision thresholds g for 235 U,234Pa and 208 Tl for the aluminum sample at the relative detector efficiency of 20%, the measurement time of 7 d and the sample mass of 1.8 kg.

Table 7 .
Characteristics of the standard reference gamma-ray-emitting sources.

Table 8 .
Mass concentrations of elements determined measured with NAA technique in Al, Ti and glass samples.

Table 9 .
The natural radioactivity A and spontaneous fission rate I of 238 U, 235 U, 234 U, 232 Th and their daughter nuclei normalized to the sample mass.

Table 11 .
Neutron radiation intensity normalized to the sample mass.