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%.
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
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 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
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
DCh | Isotope | Т1/2 | Т1/2(SF) | SF (%) | nAbn | DM | BF (%) | Refs. |
---|---|---|---|---|---|---|---|---|
238U | 238U | 4.468(5) × 109y | 8.20(6) × 1015 y | 5.45(4) × 10−5 | 1.98(3) | α | 100 | [ |
234Th | 24.10(3) d | β− | 100 | [ | ||||
234mPa | 1.159(11) min | <1 × 10−9 | β− IT | 99.85(1) 0.15(1) | [ | |||
234Pa | 6.70(5)h | <3 × 10−10 | β− | 100 | [ | |||
234U | 2.455(6) × 105y | 1.5(0.2) × 1016y | 1.6(2) × 10−9 | 1.63(15) | α | 100 | [ | |
230Th | 7.54(3) × 104 y | <4 × 10−12 | α | 100 | [ | |||
232Th | 232Th | 1.402(1) × 1010 y | 1.22 × 1021 y | 1.1 × 10−9 | 2.13(20) | α | 100 | [ |
228Ac | 6.15(3) h | β− α | 100 5.5(22)・10−6 | [ | ||||
212Pb | 10.64(1) h | β− | 100 | [ | ||||
208Tl | 3.053(4) min | - | β− | 100 | [ |
Т1/2 is the half-life time, Т1/2(SF) is the spontaneous fission half-life time, SF is the spontaneous fission probability per decay (%), nAbn is the neutrons perunitfission, BF is branching factor of the radioactive decay (%), DM is decay mode, Refs. are references, DCh is Decay chain.
Isotope | Т1/2 | Т1/2(SF) | SF (%) | nAbn | Decay mode | BF | Reference |
---|---|---|---|---|---|---|---|
235U | 7.04(1) × 108 y | 0.98(28) × 1019 y | 7.0(2) × 10−9 | 1.86 | α | 100 | [ |
231Th | 25.52(1) h | - | β- | 100 | [ |
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
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
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
The concentration and natural radioactivity of potassium were measured with the use of the full absorption peak of the 40K at the
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
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 [
Decay chain | Analytical isotope | Gamma-ray energy(keV) | Absolute emission intensity (%) |
---|---|---|---|
238U | 234Th | 63.29(2) | 4.4(9) |
234mPa | 766.36(2) | 0.207(30) | |
234mPa | 1001.03(3) | 0.59(8) | |
234U | 53.20(2) | 0.123(2) | |
235U | 235U | 185.715(5) | 57.2(8) |
231Th | 84,214(3) | 6.71(10) |
Isotope | Energy(keV) | Absolute emissionintensity (%) |
---|---|---|
212Pb | 238.625(6) | 43.4(3) |
212Pb | 300.09(1) | 3.3(1) |
228Ac | 338.322(2) | 11.25(3) |
208Tl | 583.191(2) | 84.4(7) |
228Ac | 911.205(4) | 26.6(7) |
228Ac | 968.971(10) | 16.1(3) |
228Ac | 1588.210(30) | 3.27(10) |
208Tl | 2614.532(13) | 99.9(4) |
L, (mm) | I, (s−1) | |
---|---|---|
With 60Co (3.2 kBq) | Without 60Co | |
3 | 38.3 | 0.30 |
50 | 36.0 | 0.33 |
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
where
at energies of approximately 200 keV, where the counting detector efficiency is maximum (
The decision threshold
and
respectively [
The area uncertainty of the full absorption peak is then calculated as [
where
The
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
Nuclide | Pγ | ε | E (keV) | g (Bq) |
---|---|---|---|---|
235U | 10.960 | 0.00646 | 143.75 | 0.178 |
235U | 5.080 | 0.00663 | 163.33 | 0.250 |
235U | 57.200 | 0.00701 | 185.68 | 0.073 |
235U | 5.010 | 0.00734 | 205.27 | 0.225 |
234Pa | 20.000 | 0.00634 | 131.2 | 0.135 |
234Pa | 11.400 | 0.00781 | 227.2 | 0.139 |
234Pa | 10.200 | 0.00624 | 569.5 | 0.149 |
234Pa | 15.000 | 0.00456 | 883.24 | 0.154 |
234Pa | 12.000 | 0.00403 | 946 | 0.190 |
208Tl | 99.830 | 0.0000243 | 2614.82 | 7.988 |
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
where the subscripts
where
Given in the
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 (
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.
Material | Isotope | T½ | Absolute decay rate (Bk) | Decay mode | Particle energy (keV) | Particle emission intensity (%) |
---|---|---|---|---|---|---|
UO2(NO3)2・6H2O | 238U | 4.468(5) × 109 y | 4.3(3) × 106 | α | 4198 | 77.5(5) |
4151 | 22.3(5) | |||||
4038 | 0.13(3) | |||||
235U | 7.04(1) × 108 y | 69.9(2) × 103 | α | 4397.8 | 57.19(20) | |
4366.1 | 18.30(13) | |||||
4214.7 | 5.95(12) | |||||
4596.4 | 4.74(6) | |||||
4556.0 | 3.79(6) | |||||
4322 | 3.33(6) | |||||
4414.9 | 3.01(16) | |||||
4502.4 | 1.28(5) | |||||
234U | 2.455(6)・105 y | 522(2) × 03 | α | 4774.6 | 71.37(2) | |
4722.4 | 28.42(2) | |||||
4603.5 | 0.210(2) | |||||
228Th | 1.9126(9) y | 1.70(8) × 103 | α | 5423.24(22) | 74.0(6) | |
5340.35(22) | 26.0(8) | |||||
KBr | 40K | 1.407(7) × 109 y | 5.7(2) × 103 | β− | 1311.09 | 89.25(17) |
11.90(11) × 109 y | EC | 1504.9 | 10.55(11) |
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
Equation (7) shows the time dependence of the daughter nucleus amount for an equilibrium 238U decay chain:
where the
constant, the
imum was calculated with the equation
any time t with the initial condition
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
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
Element | Nuclide | Eγ (keV) | γ-ray abundance | T1/2 (d) | CAl (%) | CTi (%) | Cglass (%) |
---|---|---|---|---|---|---|---|
As | 76As | 559.1 | 45 | 1.078 | 1.9(1) × 10−3 | ||
Ce | 141Ce | 145.44 | 48.29 | 32.5 | 2.3(3) × 10−4 | ||
Co | 60Co | 1332.49 | 99.98 | 1925 | 2.2(1) × 10−4 | 7.2(8) × 10−5 | |
Cr | 51Cr | 320.08 | 9.91 | 27.7 | 2.31(2) × 10−2 | 1.95(2) × 10−2 | |
Fe | 59Fe | 1099.25 | 56.5 | 44.5 | 2.2(2) × 10−1 | 6.8(7) × 10−2 | |
Hf | 181Hf | 482.18 | 80.5 | 42.39 | 3.9(4) × 10−5 | ||
La | 140La | 1596.21 | 95.4 | 1.68 | 3.2(3) × 10−4 | 1.6(4) × 10−6 | |
Na | 24Na | 1368.63 | 99.99 | 0.623 | 1.14(2) × 10−2 | ||
Sb | 124Sb | 602.73 | 97.79 | 60.2 | 1.5(6) × 10−5 | 9.7(6) × 10−5 | |
Sc | 46Sc | 889.28 | 99.98 | 83.79 | 3.3(1) × 10−5 | ||
Sm | 153Sm | 103.18 | 29.25 | 1.928 | 9.7(8) × 10−6 | ||
Th | 233Th | 311.90 | 38.50 | 26.97 | 6.1(9) × 10−4 | ||
U | 239U | 106.12 | 26.3 | 2.357 | 3.1(6) × 10−5 | 4.7(3) × 10−6 | 7.3(7) × 10−4 |
Zn | 65Zn | 1115.54 | 50.6 | 244.3 | 4.66(9) × 10−2 | ||
K | 40K | 9.7(2) × 10−2 |
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
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
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-
Nuclide | T1/2 | Eγ (keV) | γabn (%) | Al | Glass | Ti | |||||
---|---|---|---|---|---|---|---|---|---|---|---|
Аcalc (Bk∙g−1) | Аmeas (Bk∙g−1) | I (s−1 g−1) | Аcalc (Bk∙g−1) | Аmeas (Bk∙g−1) | I (s−1∙g−1) | Аmeas (Bk∙g−1) | I (s−1∙g−1) | ||||
238U | 4.468 × 109 y | 3.8(7) × 10−3 | *6.8(9) × 10−3 | 3.7(5) × 10−9 | 8.9(9) × 10−3 | *1.1(4) × 10−2 | 6(2) × 10−9 | *5.8(3) × 10−4 | 3.1(2) × 10−10 | ||
234Th | 24.1 d | 63.3 92.59 112.85 | 4.47 2.562 0.2562 | 3.8(7) × 10−3 | 5.9(15) × 10−3 | 9.0(9) × 10−3 | 8.2(2) × 10−3 | 6.5(2) × 10−4 | |||
234mPa | 1.17 min | 766.6 1001 | 0.207 0.589 | 3.8(7) × 10−3 | 7.7(2) × 10−3 | <7.7 × 10−14 | 9.0(9) × 10−3 | 1.4(4) × 10−2 | <1.4 × 10−13 | 5.0(4) × 10−4 | <5 × 10−15 |
234Pa | 6.70 h | 131.2 926.7 880.5 | 20 22 4 | 6.2(9) × 10−6 | 5.3(4) × 10−6 | <1.6 × 10−17 | 1.4(1) × 10−5 | 1.9(6) × 10−5 | <5.7 × 10−17 | Not found | |
234U | 2.455 × 105 y | 53.2 | 2.2 | 1.6(3) × 10−3 | 6.5(14) × 10−3 | 1.1(3) × 10−13 | 3.6(4) × 10−3 | 7.6(7) × 10−3 | 1.2(3) × 10−13 | Not found | |
230Th | 7.538 × 104 y | ||||||||||
232Th (208Tl) | 1.405 × 1010 y | 2614.9 583.25 510.89 | 99.16 85.1 22.8 | 3.7(11) × 10−2 | 4.1(12) × 10−13 | 1.32(5) × 10−3 | 1.5(1) × 10−14 | 9.1(4) × 10−6 | 1.0(1) × 10−16 | ||
235U | 7.038 × 108 y | 185.7 | 54 | 1.8(3) × 10−4 | 4.5(3) × 10−4 | 3.2(3) × 10−14 | 4.1(4) × 10−4 | 3.7(1) × 10−4 | 2.6(2) × 10−14 | 7.2(2) × 10−5 | 5.1(3) × 10−15 |
40K | 1.277 × 109 y | 1460.8 | 10.67 | - | 13.2(3) × 10−2 | - |
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. γabn― γ-ray abundance.
Sample | Asp (Bq g−1) | C (%) | ||||
---|---|---|---|---|---|---|
232Th | 234Th | 234mPa | 232Th | 234Th | 234mPa | |
Al | 3.7(11) × 10−2 | 5.9(15) × 10−3 | 7.7(2) × 10−3 | 2.5(8) × 10−3 | 6.8(17) × 10−16 | 5.0(2) × 10−22 |
Ti | 9.1(4) × 10−6 | 6.5(2) × 10−4 | 5.0(4) × 10−4 | 6.2(3) × 10−7 | 7.5(3) × 10−17 | 3.2(3) × 10−23 |
Glass | 1.32(5) × 10−3 | 8.2(2) × 10−3 | 1.4(4) × 10−2 | 9.1(3) × 10−5 | 9.5(3) × 10−16 | 9.1(26) × 10−22 |
Decay chain | Nuclide | Т1/2 | Т1/2(SF) | SF (%) | nAbn | Ffast s−1∙kg−1 | ||
---|---|---|---|---|---|---|---|---|
Al | Glass | Ti | ||||||
238U | 238U | 4.468(5) × 109 y | 8.202(60) × 1015y | 5.45(4) × 10−5 | 1.98(3) | 7.3(11) × 10−6 | 1.19(46) × 10−5 | 6.3(5) × 10−7 |
234Th | 24.10(3) d | |||||||
234mPa | 1.159(11) min | <1 × 10−9 | ||||||
234Pa | 6.70(5) h | <3 × 10−10 | ||||||
234U | 2.455(6) × 105y | 1.5(0.2) × 1016 y | 1.6(2) × 10−9 | 1.63(15) | 1.7(7) × 10−10 | 1.98(61) × 10−10 | ||
230Th | 7.54(3) × 104 y | <4 × 10−12 | ||||||
235U | 235U | 7.04(1) × 108 y | 0.98(28) × 1019y | 7.0(2) × 10−9 | 1.86 | 5.9(6) × 10−11 | 4.9(3) × 10−11 | 9.5(5) × 10−12 |
232Th | 232Th | 1.402(1) × 1010 y | 1.22 × 1021 y | 1.1 × 10−9 | 2.13(20) | 8.7(34) × 10−10 | 3.1(4) × 10−11 | 2.1(3) × 10−13 |
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.