Decay scheme of 50V
F. A. Danevich, M. Hult, D. V. Kasperovych, V.R. Klavdiienko, G. Lutter, G. Marissens, O. G. Polischuk, V. I. Tretyak
aa r X i v : . [ nu c l - e x ] A ug Decay scheme of V F.A. Danevich a, , M. Hult b , D.V. Kasperovych a , V.R. Klavdiienko a , G. Lutter b ,G. Marissens b , O.G. Polischuk a , V.I. Tretyak aa Institute for Nuclear Research of NASU, 03028 Kyiv, Ukraine b European Commission, Joint Research Centre, Retieseweg 111, 2440 Geel, Belgium
Abstract
Investigation of the V electron-capture to the 2 + Ti and searchfor β − decay of V to the 2 + Cr (both those decays are fourfoldforbidden with ∆ J ∆ π = 4 + ) have been performed using a vanadium sample of naturalisotopic abundance with mass of 955 g. The measurements were conducted with thehelp of an ultra low-background HPGe-detector system located 225 m underground inthe laboratory HADES (Belgium). The measured value of the half-life of V for electroncapture was T EC1 / = (2 . +0 . − . ) × yr. The β − -decay branch was not detected and thecorresponding lower bound of the half-life was T β / ≥ . × yr at the 90% confidencelevel. Keywords : V; Electron capture; Beta decay; Low-background HPGe γ spectrometry The isotope V is present in the natural mixture of vanadium with a very low abundance of0.250(10)% [1]. Taking into account the mass difference between V and Ti (2207 . ± . V and Cr (1038 . ± .
30 keV [2]), both electron capture (EC) of Vto Ti and β − decay of V to Cr are possible (the decay scheme of V is shown in Fig. 1).However, decays of V to the ground states of Ti and Cr are strongly suppressed by thevery large spin change ∆ J = 6 in both the cases. The only excited levels on which decay of V can undergo are the 2 + Ti, and the 2 + Cr. Boththe decay channels are fourfold forbidden non-unique (∆ J ∆ π = 4 + ). Since in both channelsdecay goes to the excited levels of daughter nuclei, de-excitation γ -ray quanta can be detectedby γ spectrometry of a vanadium sample. While the V electron-capture transition to the 2 + Ti is observed in several experiments, the β − decay of V to the 2 + Cr remains unobserved (despite two claims of detection that have been disprovedin the subsequent more sensitive investigations). The history of V decays investigations issummarized in Table 1 (see also recent review [15]).The decay of V is of especial interest since the transitions involve several different nuclearmatrix elements with the associated different phase-space factors multiplied by the axial-vector Corresponding author.
E-mail address: [email protected] (F.A. Danevich). g A [16]. This constant plays an important role in the neutrinoless double β decay probability calculations [17, 18, 19, 20, 21]. Recent calculations in nuclear shell model [16]result in the following (partial) half-lives for the two decay modes: T EC1 / = (5 . ± . . ± . × yr given for g A = 1 . . β − -decay branch, T β / = (2 . ± . . ± . × yr. + Ti + + V EC b - Q EC Q b - + Cr + Figure 1: Decay scheme of V. No confirmed observation of the β − decay of V to the 2 + Cr has yet been performed.2able 1: Half-lives of V relative to the electron capture to the 2 + Ti and β − decay to the 2 + Cr.Reference (year) Experimental technique Half-life (yr)Electron capture β − decayto 2 + + > . × > . × [4] (1957) Proportional counter,NaI(Tl) scintillation counter (4 . ± . × > . × [5] (1958) Proportional counter,NaI(Tl) scintillation counter (4 . ± . × –[6] (1961) NaI(Tl) scintillation counter > . × > . × [7] (1962) NaI(Tl) scintillation counter (8 . ± . × (1 . ± . × [8] (1966) NaI(Tl) scintillation counter > . × > . × [9] (1977) Ge(Li) γ spectrometry > . × > . × [10] (1984) HPGe γ spectrometry (1 . +0 . − . ) × > . × [11] (1985) HPGe γ spectrometry (1 . +0 . − . ) × > . × [12] (1989) HPGe γ spectrometry (2 . ± . × (8 . +13 . − . ) × [13] (2011) HPGe γ spectrometry (2 . ± . × > . × [14] (2019) HPGe γ spectrometry (2 . +0 . − . ) × > . × This work (2020) HPGe γ spectrometry (2 . +0 . − . ) × > . × In this work we report measurement of the V EC decay half-life and search for β − decayof the nuclide using HPGe γ spectrometry of a 955 g vanadium sample. A disk-shaped sample of metallic vanadium with diameter of 100.1 mm and thickness of 19.9mm with mass of 955 . ± .
02 g, provided by Goodfellow Cambridge Ltd was used in theexperiment. The vanadium disk was stored underground as soon as it was received by JRC-Geel in 2008 so that cosmogenic activation would be minimized. It was measured using an ultralow-background HPGe-detector system located 225 m underground in the laboratory HADES(Belgium). The detector system, named Pacman, consists of two HPGe-detectors facing eachother [22]. The experiment was realized in two stages with different amount of Perspex in theinner volume of the lead/copper shield. At the start not all Perspex was available but due totime constraints it was judged beneficial to start the measurements anyhow. A schematic viewof the two setups with HPGe detectors and the vanadium sample is shown in Fig. 2. The maincharacteristics of the HPGe detectors are presented in Table 2, more details can be found in[22, 23].At the first stage of the experiment in setup I the vanadium sample was measured for 34.74d, then the detectors were running for 38.16 d to measure background data without sample.The distance between the detectors Ge10 and Ge11 was 21 mm in setup I. The energy spectraaccumulated with the vanadium sample and without sample in setup I are shown in Fig. 3.3igure 2: (Color online) Schematic view of the inner shield (Pb not shown) of the two low-background setups with HPGe detectors and vanadium sample. H denotes distance betweenthe detectors Ge10 and Ge11, that can be adjusted taking into account a sample height.Then the experiment was continued in setup II for 110.55 d with the vanadium sampleand over 21.70 d to measure background without sample. The distance between the detectorsGe10 and Ge11 was 23 mm in setup II. Additional Perspex pieces were installed in setup II tominimize air inside so that to suppress background due to radon. The energy spectra gatheredin setup II are shown in Fig. 4. The insertion of the Perspex details decreased backgroundcaused by Rn daughters. In particular the counting rates in the γ -ray peaks of Bi withenergies 609.3 keV and 1764.5 keV were decreased by 3-5 times.4able 2: Properties of the HPGe-detectors used in the present experiment. FWHM denotesthe full width at half of maximum of γ -ray peak. HPAl = High Purity Aluminum. LB Cu =Low Background Copper Ge10 Ge11Energy resolution (FWHM) at 1332 keV 1.7 keV 1.9 keVRelative efficiency 62% 85%Crystal mass 1040 g 1880 gEndcap / Window material HPAl / HPAl LB Cu / LB CuOther characteristic Submicron outer Inverted endcapdeadlayer (i.e. the window facing down)5
500 1000 1500 2000
Lu, 201.8
Lu, 306.8511
Bi, 609.3
La, 788.7
Ac, 911.2
Ac, 969.0
La, 1435.8 K , . V 1553.8
Bi, 1764.5
I Ge11Energy (keV) C oun t s / k e V
500 1000 1500 2000
Lu, 201.8
Lu, 306.8511
Bi, 609.3
La, 788.7
Ac, 911.2
Ac, 969.0
La, 1435.8 K , . V 1553.8
Bi, 1764.5
I Ge10Energy (keV) C oun t s / k e V Figure 3: (Color online) The energy spectra accumulated in setup I with the vanadium samplefor 34.74 days by detectors Ge11 (upper panel) and Ge10 (lower panel) (solid lines). The dottedhistograms show background data measured without sample for 38.16 days by the detector Ge11(upper panel) and Ge10 (lower panel). The background spectra are normalized on the time ofmeasurements with the sample. Energy of γ -ray peaks are in keV.6
500 1000 1500 2000
Lu, 201.8
Lu, 306.8511
Tl, 583.2
Bi727.3
La, 788.7
Ac, 911.2
Ac, 969.0
La, 1435.8 K , . V 1553.8
Bi, 1764.5
II Ge11Energy (keV) C oun t s / k e V
500 1000 1500 2000
Lu, 201.8
Lu, 306.8511
Tl, 583.2
Bi727.3
La, 788.7
Ac, 911.2
Ac, 969.0
La, 1435.8 K , . V 1553.8
Bi, 1764.5
II Ge10Energy (keV) C oun t s / k e V Figure 4: (Color online) The energy spectra accumulated in setup II with the vanadium sampleby detectors Ge11 (for 110.55 d, upper panel) and Ge10 (110.55 d, lower panel) (solid lines). Thedotted histograms show background data measured without sample by detector Ge11 (21.70 d,upper panel) and Ge10 (21.70 d, lower panel). The background spectra are normalized on thetime of measurements with the sample. Energy of γ -ray peaks are in keV.7he energy spectra measured in the two setups are rather similar. The majority of thepeaks could be assigned to K and nuclides of the
Th,
U, and
U decay chains. Besides,there are also clear peaks of
La and
Lu in the data taken with the vanadium sample thatis evidence of the V-sample contamination by La and Lu. No unidentified peaks were observed.The energy dependence of the energy resolution in the sum energy spectrum of the detectorsGe11 and Ge10 in setups I and II was estimated by using clear γ -ray peaks with energies E γ = 201 . Lu), 583.2 keV (
Tl), 609.3 keV and 1120.3 keV (
Bi),788.7 keV (
La), 911.2 keV (
Ac) as ( E γ is in keV):FWHM(keV) = 0 . q . × E γ − . × E γ . (1) Massic activities in the vanadium sample of K, La,
Lu, daughters of the
Th,
U,and
U decay chains were calculated with the following formula: A = ( S sample /t sample − S bg /t bg ) / ( η ε m ) , (2)where S sample ( S bg ) is the area of a peak in the sample (background) spectrum; t sample ( t bg )is the time of the sample (background) measurement; η is the γ -ray emission intensity of thecorresponding transition; ε is the full energy peak efficiency; m is the sample mass. Thedetection efficiencies were calculated with EGSnrc simulation package [24, 25], the events weregenerated homogeneously in the V sample. The calculations were validated using a liquidsolution containing Ba,
Cs,
Cs, Co, and
Eu. The standard deviation of the relativedifference between the simulations and the experimental data is 2 .
5% for γ -ray peaks in theenergy interval 53 keV–1408 keV for Ge10 detector, and is 4% for γ -ray peaks in the energyinterval 80 keV–1408 keV for Ge11 detector. The estimated massic activities of radioactiveimpurities in the vanadium sample are presented in Table 3.8able 3: Radioactive contamination of the V sample measured by HPGe γ -ray spectrometry.The upper limits are given at 90% confidence level (C.L.), the reported uncertainties are thecombined standard uncertainties.Chain Nuclide Massic activity (mBq/kg) K 3 . ± . V 2 . ± . La 18 . ± . Lu 22 . ± . Th Ra 16 . ± . Th 12 . ± . U U ≤ . Pa ≤ . Ac 11 . ± . U m Pa 41 ± Ra ≤ . .2 Electron capture decay of V to the + Ti There is a clear peak with energy 1553.8 keV in all the energy spectra accumulated with thevanadium sample that can be ascribed to the electron capture decay of V to the 2 + Ti. The peak is absent in the background data. In order to estimate the half-lifeof V for the EC decay channel the sum energy spectrum of all the measurements with thevanadium sample was analyzed. A part of the spectrum in the energy region of interest ispresented in Fig. 5. The exposure for V is (2 . ± . × nuclei of V × yr.The spectrum was fitted in the energy interval (1520–1585) keV by a sum of a first order poly-nomial function (to describe the continuous distribution near the peak) and by Gaussian func-tion (to describe the γ -ray peak). The fit with a very good value of χ / n.d.f. = 100.2/126 = 0.795(where n.d.f. is number of degrees of freedom) returns the following peak parameters: energyof the peak is 1553.90(12) keV (in a good agreement with the table value 1553.768(8) keV [26]),the FWHM = 2 . .
95 keV,see formula (1)), the area of the peak is 654(27) counts.
Bi, 1509.2 V, 1553.8
Ac, 1588.2
Energy (keV) C oun t s / . k e V Figure 5: (Color online) The sum energy spectrum accumulated with the V sample in the vicin-ity of the 1553.8 keV γ -ray peak of V. The fit of the data by a sum of Gaussian peak (effect)and a straight line (background) is shown. The background energy spectrum, normalized onthe time of measurements with the sample is shown by dots. Energy of γ -ray peaks are in keV.The detection efficiencies for different detectors in the two setups for γ -ray quanta withenergy 1553.8 keV were simulated with the help of the EGSnrc package [24, 25]. The detectionefficiencies are given in Table 4.The half-life of V relative to the electron capture to the 2 + Ti ( T / )was calculated by using the following formula:10able 4: Monte Carlo simulated full energy peak detection efficiencies for 1553.8 keV γ -rayquanta, live-times of the measurements, areas of the 1553.8 keV peak, V half-life values( T EC1 / ) for different detectors in the two setups. The standard statistical errors of the detectionefficiencies, areas of the peak and half-life values are given.Setup Detector Detection efficiency Live-time of 1553.8 keV T EC1 / measurement (s) peak area × (yr)I Ge11 0 . . +0 . − . I Ge10 0 . . +0 . − . II Ge11 0 . . +0 . − . II Ge10 0 . . +0 . − . T / = N ln 2 X ( η i t i ) /S (3)where N is number of V nuclei in the sample [ N = 2 . × ], η i and t i are detectionefficiencies and times of measurement for the two detectors in the two setups (given in Table 4), S is area of the peak with energy 1553.8 keV obtained by the fit of the data of the sum energyspectrum shown in Fig. 5 ( S = 654 ±
27 counts). By using these data the half-life of V hasbeen calculated as T EC1 / = [2 . +0 . − . (stat)] × yr.In addition to the ≈ .
2% statistical uncertainty of the Monte Carlo simulated detectionefficiency we conservatively assess a 4% systematic uncertainty on the calculated detectionefficiency of the detector system to the 1553.8 keV γ -ray quanta. An indirect confirmation of arather small systematic of the detection efficiency can be seen in Table 4 and Fig. 6 where the T EC1 / values determined from the data of measurements with two different detectors in setupsI and II are presented. The difference between the half-life values is well within the statisticalerrors, that does demonstrate stability of the half-life result and its independence neither onthe detector nor the experimental setup.Variation of the energy interval of fit from 1520–1540 keV (starting point) to 1570–1585 keV(final point), changes T EC1 / up to 1.1%. Finally, we account 4.0% for uncertainty in the numberof V nuclei in the sample due to the accuracy of the representative isotopic abundance of theisotope [1]. The summary of the systematic uncertainties is given in Table 5.Table 5: Estimated systematic uncertainties of the EC decay half-life (%).Number of V nuclei 4 . . . . . See discussion of the difference between the simulations and the experimental data used for the validationof the simulations in Sec. 3.1. .42.62.833.2 I Ge11 I Ge10 II Ge11 II Ge10 H a l f- li f e ( y r) Figure 6: (Color online) Half-life of V relative to the electron capture to the 2 + Ti determined from the data of measurements with the detectors Ge10 and Ge11 insetups I and II (points, see also Table 4). The final result of the present work, obtained byanalysis of the sum spectrum of the detectors in the two setups, is shown by a square. Theerror bars represent the statistical errors, while the box around the final value show the errorscalculated by summing in quadrature the statistical and systematic uncertainties.Adding all the systematic uncertainties in quadrature, the half-life is T EC1 / = [2 . +0 . − . (stat) ± . × yr.By summing in quadrature the statistical and systematic uncertainties the half-life of Tirelative to the electron capture to the 2 + Ti is T EC1 / = (2 . +0 . − . ) × yr.A historical perspective of half-life of V is presented in Fig. 7. It is interesting to notethat early experiments claimed too short half-lives. That can be explained, first of all, byutilization of rather low energy resolution detectors like proportional counters and NaI(Tl)scintillation counters (see Table 1). Other possible reasons for obtaining a too short half-lifecan be using nonpure samples, high background with possible interferences of γ rays of differentorigin (including cosmogenic activation, since most of the earlier experiments were performed inlaboratories on the ground level), less good electronics, stability problems of long measurements.The latter point is especially crucial in conditions of a poor energy resolution.12 von Ileintze 1955Glover 1957Bauminger 1958McNair 1961Watt 1962Sonntag 1966Pape 1977Alburger 1984 Simpson 1985Simpson 1989Dombrowski 2011Laubenstein 2019 Present studyPublication date H a l f- li f e ( y r) Alburger 1984Simpson 1985Simpson 1989Dombrowski 2011Laubenstein 2019
Publication date H a l f- li f e ( y r) Figure 7: (Color online) A historical perspective of half-life of V relative to the EC decay as afunction of the publication date (references to the publications are as follows: von Ileintze 1955:[3], Glover 1957: [4], Bauminger 1958: [5], McNair 1961: [6], Watt 1962: [7], Sonntag 1966:[8], Pape 1977: [9], Alburger 1984: [10], Simpson 1985: [11], Simpson 1989: [12], Dombrowski2011: [13], Laubenstein 2019: [14]). The results are presented by dots, while the limits areshown by arrows. The early positive claims of EC decay in V with too short half-lives wereobtained with low resolution detectors: proportional and NaI(Tl) scintillation counters [4, 5],NaI(Tl) scintillation counter [7]. The half-lives measured with the help of HPGe detectors inworks [10, 11, 12, 13, 14] and in the present study are in a reasonable agreement.13 .3 Limit on β − decay of V to the + Cr There is no peak with energy ≈
783 keV in the sum energy spectrum that can be interpretedas β − decay of V to the 2 + Cr. Thus, we have set a lower half-lifelimit on the decay with the following formula:lim T / = N ln 2 X ( η i t i ) / lim S, (4)where N is the number of V nuclei in the sample, η i and t i are detection efficiencies (for783.3 keV γ -ray quanta) and times of measurement for the two detectors in the two setups,and lim S is the number of events of the effect searched for which can be excluded at a givenconfidence level. The detection efficiencies for different detectors were simulated with the helpof the EGSnrc package [24, 25].To estimate the value of lim S the sum energy spectrum with exposure (2 . ± . × nuclei of V × yr was fitted by a background model that includes the effect searched for (a peakcentered at 783.3 keV with a fixed FWHM = 1 .
69 keV), several Gaussian peaks to describebackground γ -ray peaks of La,
Bi (daughter of the
Th subchain from the
Th chain),
Bi and
Pb (daughters of
Ra from the
U chain),
Ac (daughter of the
Ra subchainfrom the
Th chain), m Pa (daughter of
U), and a straight line to describe the continuousbackground. While the areas and positions of intensive peaks (766.4 keV of m Pa, 768.4 keVof
Bi, 785.4 keV of
Bi, 788.7 keV of
La, 795.0 keV of
Ac) were free parameters ofthe fit, the areas and positions of weak peaks (772.3 keV and 782.1 keV of
Ac, 786.0 keV of
Pb, 786.3 keV of m Pa, 786.4 keV of
Bi), superimposed on nearby intensive peaks, werefixed taking into account their relative intensities in the sub-chains. All the peak widths werefixed taking into account the dependence of the energy resolution on energy of γ -ray quanta(1).The best fit, achieved in the energy interval 761–818 keV with χ / n.d.f.= 0 . . ± . The fit and excluded peak are shown in Fig. 8. According to [27] we took lim S = 28 . γ -ray quanta (given inTable 6), obtain the following limit on the β − decay of V to the 2 + Cr: T β / ≥ . × yr at 90% C.L. The estimations of the lim S value includes only the statistical uncertainty, and any systematic contributionshave not been considered. γ -rayquanta for different detectors in the two setups.Setup Detector Detection efficiencyI Ge11 0.014986I Ge10 0.018497II Ge11 0.014140II Ge10 0.01848115 Ac, 755.3
Pa, 766.4
Bi, 768.4
Ac, 772.3
Ac,782.1 V,783.3
Bi,785.4
Pb, 786.0
Pa,
Bi, 786.3
La, 788.7
Ac, 795.0
Energy (keV) C oun t s / . k e V Figure 8: (Color online) Part of the sum energy spectrum accumulated with the vanadiumsample in the vicinity of the expected β − decay 783.3 keV γ -ray peak. Fit of the data byseveral γ -ray peaks and by a straight line to describe the continuous background is shown bysolid line, while an excluded peak expected in the β − decay of V is presented by dashed line.The background energy spectrum, normalized on the time of measurements with the sample isshown by dots. Energy of γ -ray peaks are in keV.The limit is approximately two times weaker than the limit T β / ≥ . × yr reported in[14]. The sensitivity of the present experiment is lower mainly due to a rather high radioactivecontamination of the vanadium sample that produce background in the region of interest.Therefore, an advanced experiment should utilize a radio-pure vanadium sample. A possi-bility of a deep purification of vanadium from radioactive impurities has been demonstrated in[14]. Thus, aiming to estimate requirements to experiments able to detect the decay, we assumea level of background already achieved in setup II without sample (see Fig. 4). We considertwo vanadium containing samples: a metallic vanadium of the natural isotopic compositionwith the sizes and geometry the same as in the present experiment, and a second one in formof vanadium oxide (V O ), enriched in the isotope V to 50%. We assume the bulk densityof enriched vanadium oxide sample to be 0.5 of the solid V O density (3.36 g/cm ). To getthe same number of V nuclei (2 . × ), the size of the enriched sample was chosen tobe ⊘ × .
57 mm, with a distance between the detectors H = 3 mm. Expected backgroundcounting rates and the Monte Carlo simulated detection efficiencies of the Pacman setup withthe samples are given in Table 7. 16able 7: Characteristics of experimental setups to estimate sensitivity to the β − decay of V. H denotes distance between the detectors Ge10 and Ge11 (see Fig. 2), BG det is backgroundcounting rate of the detectors (achieved in setup II without sample), BG EC is Monte Carlosimulated counting rate due to the EC decay of V, η is detection efficiency to γ -ray quantawith energy 783.3 keV. Sample, BG det BG EC η Experimental geometry (counts/day/keV) (counts/day/keV)Ge10 Ge11 Ge10 Ge11 Ge10 Ge11V metal, naturalisotopic composition ⊘ ×
20 mm, H = 21 mm 0.1291(8) 0.1176(8) 0 . . O , enriched in V to 50% ⊘ × .
57 mm, H = 3 mm 0.1291(8) 0.1176(8) 0 . . The background of the detectors dominates in the experimental conditions, with the contri-bution from the EC process in V an order of magnitude smaller. While the assumed enrichedsource contains the same number of V nuclei as the metallic one with the natural isotopiccomposition, the detection efficiency with the enriched source is about three times higher. As aresult, an experiment with enriched source has a higher sensitivity [see Fig. 9, (a)]. Moreover,utilization of enriched V would allow to observe clearly the β − decay of V (assuming thetheoretically predicted half-life T β − / = 2 × yr [16]) with a 3 σ accuracy over about 200 dof data taking, while an experiment utilizing a V-sample of natural isotopic composition needsmore than three years to detect the process with a similar accuracy (see Fig. 9, (b)).17 T (a) Time of measurement (days) li m / ( y r) (b) Time of measurement (days) N u m b e r o f s Figure 9: (Color online) Sensitivity of possible experiments to detect the β − decay of V[expressed as: (a) a lower half-life limit at 90% C.L.; (b) a number of σ for accuracy of theexpected 783.3 keV peak area, assuming the half-life T β − / = 2 × yr] depending on time ofmeasurement in two experimental conditions: (1) in the geometry of the present experiment(with a V-sample ⊘ ×
20 mm and distance between the detectors Ge10 and Ge11 H = 21mm); (2) with a V O -sample enriched in the isotope V to 50% with sizes ⊘ × .
57 mmand H = 3 mm. Only background without sample together with contribution due to the ECdecay of V are assumed. 18
CONCLUSIONS
The half-life of V relative to the EC to the 2 + Ti is measured as T EC1 / = (2 . +0 . − . ) × yr. The value is in agreement with the result of the recent experiment[14] and the theoretical predictions [16]. The β − decay of V to the 2 + Cris limited as T β / ≥ . × yr at 90% C.L. The limit is about 2 times weaker than thatset in the work [14]. Further improvement of the experiment sensitivity could be achieved byutilization of highly purified vanadium samples. Moreover, using of a sample enriched in Vwould allow detection of the β − decay. The accuracy of T EC1 / will also be improved with a sourceenriched in V both thanks to improvement of statistics and reduction of the uncertainty inthe V isotopic abundance.
This work received support from the EC-JRC open access scheme EUFRAT under Horizon-2020, project No. 22-14. D.V.K. and O.G.P. were supported in part by the project “Investiga-tion of double beta decay, rare alpha and beta decays” of the program of the National Academyof Sciences of Ukraine “Laboratory of young scientists” (the grant number 0120U101838).F.A.D. greatly acknowledges the Government of Ukraine for the quarantine measures that havebeen taken against the Coronavirus disease 2019 that substantially reduced much unnecessarybureaucratic work.
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