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. 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:

Gamma radiation from capture of slow neutrons in ¹⁵⁷Gd is used as signal to neutrino registration after thermalization of fast neutrons in neutrino detector. The ¹⁵⁸Gd emits gamma-ray cascade with the total energy of 8 MeV. 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 ¹⁵⁷Gd 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 m³ 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 ¹⁴C is naturally abundant in organic scintillators, detection of neutrino is not possible below the end point 156 keV of the ¹⁴C β-spectrum.

The isotopes from the natural uranium and thorium decay chains are intensive alpha and beta radioactive sources. At the same time, the ²³⁸U, ²³⁵U, ²³⁴U and ²³²Th are disintegrated via spontaneous fission process. The spontaneous fission rate is far less than the α-decay one. The ²³⁸U, ²³⁵U, ²³⁴U, ²³²Th 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 ²³⁸U, ²³⁵U, ²³⁴U and ²³²Th. Nuclear characteristics of the ²³⁸U, ²³²Th and their daughter nuclei emitting neutrons in the spontaneous fission are given in the Table 1. Only nuclei of the ²³²Th emit the neutrons after spontaneous fission in the radioactive ²³²Th decay chain. The spontaneous fission probability SF of the ²³²Th 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 ²³⁵U and its daughter nucleus ²³¹Th are important naturally occurring radioactive isotopes; they were used to determine the uranium concentration in the samples analyzed. The ²³⁵U decays by 100% α-emission to levels in ²³¹Th. The recommended nuclear decay data of the ²³⁵U and ²³¹Th are presented in Table 2. The decay data were taken from the LNHB (available at http://www.nucleide.org/NucData.htm).

Т_1/2 is the half-life time, Т_1/2(SF) is the spontaneous fission half-life time, SF is the spontaneous fission probability per decay (%), n_Abn is the neutrons perunitfission, BF is branching factor of the radioactive decay (%), DM is decay mode, Refs. are references, DCh is Decay chain.

The uranium mass concentration and absolute decay rate of the ²³⁵U were measured with the gamma spectrometric method in samples analyzed (aluminum and titanium sheets and glass samples).

The gamma line of ²³⁵U at the was used in this case. In the same way the uranium mass concentration and the absolute decay rate of the ²³⁸Uwere measured with the ^234mPa full absorption peaks at the 766.6 keV and 1001 keV, as the ^234mPa is daughter nucleus of natural radioactive ²³⁸U.

The first two daughter nuclei of the radioactive ²³⁸U decay chain (²³⁴Th, ^234mPa) are very short-lived compared with ²³⁸U 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 ²³⁸U, ²³⁴Th, ^234mPa have the similar radioactivity. Absolute decay rate of ²³⁸U, ²³⁴Th, ^234mPa, ²³¹Th 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 ²³²Th decay chain (²²⁸Ac, ²¹²Pb, ²⁰⁸Tl) were used for the determination of the natural radioactive and the spontaneous fission rates of the ²³²Th. The γ-ray energies and absolute γ-ray abundances of the ²²⁸Ac, ²¹²Pb and ²⁰⁸Tl 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 ⁴⁰K at the in a gamma-ray spectrum of the samples analyzed. Nuclear data, the ⁴⁰K decay scheme and the ⁴⁰Ar excited level scheme are given in Figure 1 and Figure 2, respectively.

The ²³⁸U, ²³⁵U, ²³²Th 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 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 ²¹⁰Pb 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 ²¹⁰Bi decay in the lead. A special effort was spent to reduce the background from the ⁴¹Ar (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 ⁶⁰Co gamma-ray source (3.2 kBq) was used to investigate the influence of the backscattering effect during sample

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.

The decision threshold in units of activity was determined using the full absorption peak at the signific-ance level ,

where is the full energy peak registration efficiency for the sample-detector geometry, is the gamma- ray emission probability, is the measurement time and 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 UO₂(NO₃)₂・6H₂O (750 g) was taken as the reference gamma-ray source.

Figure 5 shows the energy dependence of the decision threshold under the assumption of and day for the sample geometry (diameter 62 mm, height 100 mm) used in routine analyses for the determination of the sample natural radiation background. The decision threshold achieves minimum (see Figure 5)

at energies of approximately 200 keV, where the counting detector efficiency is maximum (Figure 4).

The decision threshold and the detection limit in the units of counting rate at the selected energy were calculated as

and

respectively [17] . The and are the quantiles of the normal distribution for the error probability of the type I and for the error probability of the type II, respectively (, ,), is the number of counts below the full absorption peak in the spectrum, the is full width at half maximum (FWHM) of the full absorption peak, the is the width of the full absorption peak, the is measurement time in the Equations (2) and (3). The energy dependences of and are shown in the Figure 6.

The area uncertainty of the full absorption peak is then calculated as [17]

where is the area of the full absorption peak and. Figure 7 shows the energy dependence of the area uncertainty (%) for measurement time of 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 ²³⁵U, ²³⁴Pa and ²⁰⁸Tl 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 cm³ and 0.482 kg, respectively. The FWHM of the detector at the energy of 1.332 MeV was determined to be 1.7 keV.

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 of a radioisotope is obtained by direct comparison with the activity of the same radionuclide given in a reference gamma-ray-emitting-source by the following equation [18]

where the subscripts and mark the value belonging to the sample and the reference source, respectively, the is sample mass and S is the area of the full absorption peak. The t is measurement time of a gamma-ray spectrum. The and are gamma-ray transmission coefficients of the sample and reference source materials, respectively. The energy dependence of the gamma-ray transmission coefficient assuming can be calculated according to expression

where 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 -ray through the detector and the sample, respectively, the a and R are the detector and the sample radii, respectively, the b and l are the detector and the sample heights, respectively, the is the detector-sample distance in Figure 8 and in Equation (6).

Given in the Figure 9 are the energy dependences of the gamma-ray transmission coefficient for the Al, Ti, KBr, the UO₂(NO₃)₂・6H₂O and quartz glass samples of size, used in the routine analyses for the determination of radioactivity of the natural radioactive elements.

To carry out measurements the reference gamma-ray-emitting-sources of ⁴⁰K, ²²⁸Th, ²³⁸U, ²³⁵U, ²³⁴U and their daughter nuclei with the accurately known the absolute decay rates were prepared. The UO₂(NO₃)₂・6H₂O (,) and KBr (,) 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 ²⁰⁸Tl 510.77 keV, 583.19 keV, ⁴⁰K 1460.82 keV and ²¹⁴Bi 1729.59 keV, 1764.5 keV peaks registered in the gamma-ray spectra of the samples analyzed given in Figures 10-12.

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 and epithermal neutron fluxes. After irradiation the ampoules were washed out with the 0.5 M HNO₃ 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). 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 ²³⁸U decay chain:

where the is the number of the uranium nuclei in the samples analyzed, the is decay

constant, the is Avogadro number, the is atomic weight, the a is the isotopic abundance, the is sample mass. is the mass concentration (%) of uranium in the sample that was measured with the instrumental neutron activation analysis. The time period when the activity of the daughter nuclei reaches a max-

imum was calculated with the equation. The activity of the daughter nucleus is at

any time t with the initial condition at. In our case the time t is equal to.

Natural uranium contains 99.274% of ²³⁸U, 0.720% of ²³⁵U, and 0.0055% of radiogenic ²³⁴U. The ²³⁸U, ²³⁵U and ²³⁴U decay via alpha emission to ²³⁴Th, ²³¹Th and ²³⁰Th, respectively. The alpha decay energies of the ²³⁴U, ²³⁵U, ²³⁸U are equal to 4858.5, 4678.7, and 4270 keV [7] , respectively. The total radioactivity of the natural uranium connected with ²³⁸U and ²³⁴U for the aluminum, titanium and glass samples shown in the Table 9 can be divided half-and-half between ²³⁴U and ²³⁸U, as the ²³⁵U contribution to the radioactivity of the natural uranium can be neglected. The ²³⁸U absolute decay rate is more than ²³⁵U 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 ²³⁸U, ²³⁵U, ²³⁴U, ²³²Th 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 ²³⁸U was calculated to be the average of the measured ²³⁴Th and ^234mPa activity values.

The ²³⁸U half-life is 1.41 × 10¹⁷ seconds, therefore 5.58 × 10⁻⁴ g of the ²³⁸U have absolute alpha decay rate of 6.8(9) s⁻¹ and produce the same number of ²³⁴Th nuclei in the aluminum sample (1800 g). The number of the daughter nuclei with the exception of the ²⁰⁶Pb 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 ²³⁸U is equal to 6.8(9) Bq, then 5.58 × 10⁻⁴ g of the ²³⁸U enclose 2.07 × 10⁷ nuclei (7.97 × 10⁻¹⁵ g) of ²³⁴Th in the equilibrium radioactive ²³⁸U decay chain inside the aluminum sample. Mass concentration of ²³²Th was calculated according to Equation (9), where is alpha decay branching of ²¹²Bi, the A_sp is specific radioactivity of ²⁰⁸Tl. Mass concentrations and specific activities of ²³²Th, ²³⁴Th and ^234mPa in the samples analyzed are listed in the Table 10.

The ²³⁰Th does not have suitable analytical gamma lines for measuring its radioactivity. The radioactivity and neutron emission by spontaneous fission of ²³⁰Th were not measured because ²³⁸U does not go to radioactivity equilibrium with its daughter nucleus ²³⁰Th. The contribution of ²³⁰Th in the neutron emission of the sample is negligible since the spontaneous fission probability per decay of ²³⁰Th 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.

In this work, the evaluation of the gamma and neutron emissions were performed for eight nuclides, from the natural radioactive ²³⁸U, ²³⁵U and ²³²Th decay chains for aluminum, titanium and glass. The integral gamma radi-

The asterisk ^* marks the average of the measured ²³⁴Th and ^234mPa activity values because they are daughter nuclei of the natural equilibrium radioactive ²³⁸U decay chain. γ_abn― γ-ray abundance.

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 ²³⁸U 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 ²³⁴U radioactivity has not been evaluated in the titanium sample. Therefore, the ²³⁴U radioactivity was taken to be equal to ²³⁸U radioactivity for equilibrium radioactive ²³⁸U 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 ²³⁴U 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.