Development of Photonuclear Method for Hidden (N;C)-Concentrations Detection

1. L.Z. DzhilavyanInstitute for Nuclear Research, Russian Academy of Sciences, 117312 Moscow, RussiaE-mail: dzhil@cpc.inr.ac.ru DEVELOPMENT IN THE PHOTONUCLEAR METHOD FOR DETECTION OF HIDDEN (N; C)-CONCENTRATIONS WITH REGISTRATION OF INDUCED (12N; 12B)-ACTIVITIES

2. Contentof the report • Introduction. • The nuclear reactions involved in the method. • The (12N; 12B)-producing photonuclear reactions. • The involved background nuclear reactions. • Emission of -quanta, electrons, and positrons from irradiated objects at decays of 12N and 12B produced in these objects. • Radiation safety problems in the method. • Detectors for registration of (12N; 12B)-activities at pulsed electron accelerators. • Model descriptions for attempts to realize the method. • Conclusions and acknowledgements. 10.10.2018 L.Z. Dzhilavyan 17/2

3. Introduction • The photonuclear method [L.W.Alvarez.The USA-patent: US No. 4756866 (1988)]; [E.A.Knapp, R.B.Moler, A.W.Saunders, W.P.Trower. Appl. Rad. Isotopes 53, 711 (2000)]; • [L.Z.Dzhilavyan, A.I.Karev, V.G.Raevsky, Bull. Russ. Acad. Sci.: Phys. 75, 257 (2011)]; • [A.I.Karev, V.G.Raevsky, L.Z.Dzhilavyan, L.J.Brothers, L.K.Wilhide. RF-patent: RU 2444003C1 27.02.2012 Bull. №6] • [A.I.Karev, V.G.Raevsky, L.Z.Dzhilavyan, L.J.Brothers, L.K.Wilhide. USA-patent: US 8,582,712 B2. Nov, 12, 2013]. was suggested for external detection of hidden explosives and narcotic drags using registration of induced activities of the produced short-lived radioisotopes 12N (-decay; the maximal kinetic energy of -particles E max 16.3 MeV; the half-life T1/2 11.0 ms) and 12B (-decay; E max 13.4 MeV; T1/2 20.2 ms). It is assumed that (12N; 12B)-production takes place during each beam pulse of a pulsed electron accelerator, while registration of induced (12N; 12B)-activities occurs in time intervals between these pulses. • 12N and 12B are practically unique among those radioisotopes which have T1/2 ≈ (380) ms and may be produced in photonuclear reactions with thresholds Ethr~50 MeV when there are no more than 3 nucleons knocked out from some stable target-isotope with its natural abundance is>1%.The T1/2-values of12N and 12B are attractive for a desirable significant improvement in operational time at photonuclear detection of (N; C)-concentrations in comparison with what is available in the more traditional activation analysis with registration of the (13N; 11C)-activities from the (, n)-reactions, for which T1/2 are higher in ~5104 times. • However, optimal realization of the considered method with relatively high sensitivity depends on a set of rather complicated aspects. The studies by researchers of the INR (RAS), Lebedev Physical Institute (RAS), Skobeltsyn Institute of Nuclear Physics (MSU), Frank Laboratory of Neutron Physics (JINR, Dubna), et al. were devoted to some of such aspects. The results of these studies are discussed in the presented overview. L.Z. Dzhilavyan 10.10.2018 17/3

4. The nuclear reactions involved in the methodThe (12N; 12B)-producing photonuclear reactions For analysis of the discussed photonuclear method, information is needed on the main involved nuclear reactions (as on the (12N; 12B)-producing photonuclear reactions, as on the background nuclear reactions). In the considered method (12N; 12B)-radioisotopes supposed to be produced in the following main photonuclear reactions :  (is 99.63%) n (Ethr 30.6 MeV); (I)  (is 99.63%) B p (Ethr 25.1 MeV); (II) 3C (is  1.11%) B p (Ethr 17.5 MeV). (III) Data on cross sections and yields of these main (12N; 12B)-producing photonuclear reactions are necessary for analysis of the method first of all. These data were compiled, partly obtained by model calculations, and analyzed [O.I.Achakovskiy, S.S.Belyshev, L.Z.Dzhilavyan, Yu.N.Pokotilovski, Bull. Russ. Acad. Sci.: Phys. 80, 572 (2016)]. 10.10.2018 L.Z. Dzhilavyan 17/4

5. The nuclear reactions involved in the methodThe cross sections of the (12N; 12B)-producing photonuclear reactions It was shown that only for the reaction 13C(, p)12B there are the experimental data for reaction cross sections  in dependence on photon energies E up to 30 MeV with accuracy acceptable for analysis of the method. [B.C,Cook, Phys. Rev. 106, 300 (1957);V.P.Denisov, A.V.Kulikov, L.A.Kul’chitskii, Soviet Physics JETP 19, 1007 (1964); D.Zubanov, et al. Phys. Rev. C 27, 1957 (1983)] Limitations and lack ofexperimental data on the cross sections of the reactions 13C(, p)12Band especially 14N(, 2n)12N with 14N(, 2p)12B force us to consider model calculations of these cross sections. First of all in these calculations the models of nuclear reactions TALYS and EMPIRE were used. 13C(, p)12B 13C(, p)12B 14N(, 2n)12N 14N(, 2p)12B 10.10.2018 L.Z. Dzhilavyan 17/5

6. The nuclear reactions involved in the methodThe yields of the (12N; 12B)-producing photonuclear reactions A spectrum of bremsstrahlung photons at all angles from a radiator with an atomic number Z, a radiation length X0r , and a thickness rdxr is: where: k – a bremsstrahlung photon energy; E and Ne – a total energy for each of incident on a radiator electrons and their number; r и Mr – density and molecular weight of radiator material; NA – Avogadro's number; (db(k,E,Z)/dk) – a differential in photon energy cross section of bremsstrahlung production; (dn(k,E,Z)/dk)  (NArX0r/Mr)(db(k,E,Z)/dk) – number of produced bremsstrahlung photons with energies from k to (k + dk), reduced to one electron incident on a radiator element with its thickness measured in X0r units. Values of k(dn/dk) are shown in Fig. 5 for three representations of (db(k,E,Z)/dk)[S.S.Belyshev, L.Z.Dzhilavyan, K.A.Stopani, Bull. Russ. Acad. Sci.: Phys. (submitted)] Values of k(dn/dk) for tungsten in dependence on photon energies k. 1; 2; 3; 4; 5 – for the electron kinetic energies T  (8; 15; 20; 30; 60) MeV according to [S.M.Seltzer, M.J.Berger] (solid curves); [L. I. Schiff] (dashed curves); assumption (dn / dk)  k1 (dash-dotted curve). 10.10.2018 L.Z. Dzhilavyan 17/6

7. The nuclear reactions involved in the methodThe yields of the (12N; 12B)-producing photonuclear reactions In works with bremsstrahlung photons, number of acts for a certain photonuclear reaction is determined not directly by reaction cross sections, but by integral values: yield Y(E) or cross sections per equivalent quantum σq(E), which are obtained by convolutions of cross section distributions σ(k) with distributions of bremsstrahlung photons in their energies k at various E (here:  – the rest energy of an electron; (E) T – kinetic energies of electrons). For a target almost completely enclosing a flow of bremsstrahlung photons produced in a radiator element (dxr)/X0r, we have for the reaction yield Y(E): While within the framework of approximation (dn / dk) k1, we have: In a number of photonuclear studies with full-spectrum bremsstrahlung, instead of yields Y(E), cross sections per equivalent quantum σq(E) were used: For the reactions 68Zn(, p); 14N(, 2p); 14N(, 2n) respectively there are shown model calculated values: a – (E); b – Y(T), c – q(T). Data for the reaction 68Zn(, p) (for which presented (E)- shape is rather narrow and compact) are added to others to separate the role of isochromatic shapes for used representations of bremsstrahlung spectra from the role connected with the relatively broad distributions of (E) for the reactions 14N(, 2p) and especially 14N(, 2n). There are only two measurements of the integral characteristics for the reactions 14N(, 2n) at E 120 MeV [W.K.H.Panofsky, D.Reagan, Phys. Rev. 87, 543 (1952)] and 14N(, 2p) at E 90 MeV [A.P.Komar, Ya.Krzhemenek, I.P.Yavor, Nucl. Phys., 34 551 (1962)] but in both cases the achieved accuracies are very poor. 10.10.2018 L.Z. Dzhilavyan 17/7

8. The nuclear reactions involved in the methodThe yields of the (12N; 12B)-producing photonuclear reactions 68Zn(, p) 14N(, 2p) 14N(, 2n) 10.10.2018 L.Z. Dzhilavyan 17/8

9. The nuclear reactions involved in the methodData discussion and drafting new measurements for the (12N; 12B)-producing photonuclear reactions In spite of all attempts to create realistic models for nuclear reactions till now even the most developed of them failure to describe correctly some essential reactions with escape from a nucleus only 1 or 2 nucleons. For example, it was shown that TALYS-predictions underestimate the experimental cross sections and yields of the reaction 68Zn(, p) in about several times, and it was necessary for better agreement to add the large contribution connected with isospin splitting of the electric dipole giant resonance in 68Zn. For the reaction 13C(,p)12B there are even more serious underestimations by models TALYS and EMPIRE (in about one order of magnitude). In this sense, it is particular interesting that a recent paper[P.Žugec, et al. Phys. Rev. C 90, 021601 (2014)]also speaks for the 12C(n, p)12B reaction in a wide range of nuclear excitations about large underestimation of the calculated cross sections, obtained in particular by EMPIRE and TALYS, in comparison with measured ones. The integral measured cross section characteristics of the reactions 14N(, 2n) and 14N(, 2p) in spite of their much worse accuracy also confirm underestimation of a type. New independent measurements for cross sections of the reactions 14N(, 2n)12N and 14N(, 2p)12B are very desirable (even only integral ones!). For this reason, we paid considerable attention to the details of the techniques used in previous experimental studies of the cross sections and yields of these reactions. An analysis of the available data shows that measurements of the pointed out cross sections (and the related yields) at energies from the reaction thresholds and up to at least E ~ 60 MeV are needed. Two variants for these measurements based on detection of (12N and 12B)-activities were considered with registration of: -particles themselves or secondary bremsstrahlung and annihilation -quanta produced by -particles in irradiated targets. Panofsky used the first activation variant with regisntration of +-particles with the energies of ~8 MeV by magnetic spectrometer having rather low registration efficiency. Therefore it is very interesting to consider usage for registration of -particles telescopic detectors which principally may have high efficiency of registration and high ability for suppression of background. 10.10.2018 L.Z. Dzhilavyan 17/9

10. The nuclear reactions involved in the methodThe involved background nuclear reactions These reactions were considered in [L.Z.Dzhilavyan, Bull. Russ. Acad. Sci.: Phys. 73, 799–805 (2009)]. At the same conditions except for the reactions (I–III) many other photonuclear reactions with production of radioisotopes may occur. In the reactions (IV, V), the radioisotopes are produced with T1/2 close to T1/2 for 12N and 12B. In the reactions (VI, VII) the radioisotopes with T1/2 ~ 0.1 s are produced. 6O (is 99.76%) 3B   3p (Ethr 43.2 MeV; ; T1/2  17.4 ms); (IV) 6O (is 99.76%) 3O  3n (Ethr 52.1 MeV; ; T1/2  8.6 ms); (V) 2C (is 98.9%)  9Li  3p (Ethr 46.8 MeV; ; T1/2 178.3 ms); (VI) 2C (is 98.9%)  9C  3n (Ethr 53.1 MeV; ; T1/2 126.5 ms). (VII) There are only model calculated cross sections for the reactions (IVVII). The neutrons (produced in photonuclear reactions) are subjected to scattering, slowing down, and secondary neutron-nuclear reactions during their travel in a hall of irradiation. Among secondary neutron-nuclear reactions there are reactions under fast neutrons and particularly the reaction giving 12B: n 2C (is 98.9%)  12B  p (Ethr 12.6 MeV; ; T1/2  20.2 ms). (VIII) But mostly secondary neutron-nuclear reactions are reactions of radiation capture which happen under slow if not thermal neutrons and give background of secondary '-quanta which falls in time t after beam pulse. And particularly there may be the reaction which produces 12B: n11B(is 80.1%) B' (Ereleased3.4 MeV; ; T1/2 20.2 ms) (IX) The small fraction of boron in typical tested objects permits to believe the background from the reaction (IX) not very much obstruct the method usage. The background from the reaction (VIII) should be small because (i) the fraction of primary photoneutrons with EnEn thresh for this reaction is small and (ii) such neutrons with overwhelming probability first undergo scattering, and after only a few scattering, their energy En decreases to values below En thresh. 10.10.2018 L.Z. Dzhilavyan 17/10

11. Emission of g-quanta, electrons, and positrons from irradiated objects at decays of 12N and 12B produced in these objects The calculations[S.S.Belyshev, L.Z.Dzhilavyan, Yu.N.Pokotilovski, Bull. Russ. Acad. Sci.: Phys. 80, 566 (2016);S.S.Belyshev, L.Z.Dzhilavyan, A.M.Lapik, Yu.N.Pokotilovski, A.V.Rusakov, Bull. Russ. Acad. Sci.: Phys. (submitted)]were performed to determine fluxes and shapes of spectra for these particles in dependence on energies E (energies of -quanta or here kinetic energies of e and e+ ). The spectra in kinetic energy Eof the primary -particles (e and e+ emitted in the decays of 12B and 12N, respectively) are shown in Fig. per one emitted -particle. Based on these primary spectra, there were calculated with GEANT-4 and MCNPX-5 energy spectra of e, e+ and -quanta (from bremsstrahlung and annihilation), emitted from these objects. Verification of these calculations, carried out by comparing the results obtained with both programs, revealed good agreement. There were used the simplified objectsfor the convenience of calculations. We suppose that with them it is possible to identify some characteristic features of the task. These objects consist of a homogeneous equiatomic mixture of H, C, N, and O and have the form of a sphere with a radius r10 cm and densities  = (0.05; 0.10; 0.25; 0.50; 0.69; 1.00; 1.50; 2.00; 3.00) gcm3. These spectra were calculated for decays of 12B or 12N in the sphere centers. Evolution of these spectra in dependence on r may be seen in Figures on the right.  10.10.2018 L.Z. Dzhilavyan 17/11

12. Emission of g-quanta, electrons, and positrons from irradiated objects at decays of 12N and 12B produced in these objects The calculated values (N / N) for -quanta with energies E Emin obtained in these cases in dependence on r are shown in the Figures a; b; c; d; e; on the right for the values of Emin(0; 0.25; 1.00; 2.00; 2.50) MeV, respectively, in comparison with fitting functions f = A  [1  exp(a1r)]  exp(a2r). In the next Figure on the right there are shown the parameters A, a1, a2 of these functions f found by the method of least squares in dependence on Emin. In the functions f, the factor in the square brackets has the saturation value equal to 1 at r ∞ and approximates the dependence of quantities of -quanta produced by -particles along their path in the matter of these spherical objects, whereas the factor exp(a2r) approximately describes absorption of such -quanta . 10.10.2018 L.Z. Dzhilavyan 17/12

13. Radiation safety problems in the method An important aspect of the considered method is its radiation safety, since the cross section distributions of the used in it photonuclear reactions force to choice incident electron energies ~(50-60) MeV, at which different radioisotopes are efficiently produced. This is especially important at baggage checking in airports. As an example, there was considered[L.Z.Dzhilavyan, A.I.Karev. Bull. Russ. Acad. Sci.: Phys. 75, 1557 (2011)]irradiation of abaggage unit, having the surface density X3.7 gcm2, a molecular weight M, chemical chem and isotopic is abundances, for Ne 1012 electrons in each pulse of an accelerator and the total number of such pulses nimp150, when they incident on the radiator with a thickness in radiation length units (Xr / X0r)  0.1. Within the framework of approximation (3) (see above for σ1(T)constσ1 satur along radiator thickness), for a total induced activity a(t0) under bremsstrahlung from the radiator resulting from a certain photonuclear reaction in a irradiated baggage unit for some radioisotope with its half-life T1/2 at the end (at t0) of short irradiation procedure at neglecting of flow weakening for bremsstrahlung photons in radiator and baggage thicknesses we obtain: (5) If in the case: a(t  0)is in [s1]; σ1 saturis in [mb];  M is in [gmol 1]; T1/2 is in [s],  then we have: a(t  0) 2.31010 [(chem is σ1 satur) / (MT1/2)]. Results of such estimates should be compared with[Radiation Safety Standards (RSS-99). M.: Minzdrav]: annual limits on intakes (in human body, ALI); minimum significant activities (MSA); minimum significant specific activities (MSSA). Estimated a(t  0) do not exceed the ALI for all radioisotopes which have T1/2  1.01 d). For some radioisotopes with T1/2  1.01 d there are data on MSA and MSSA, and we may try to use them for comparing, and, for example, for 15O from reaction 16O(, n) estimates of accumulated activities present quite satisfactory levels in such a sense. A more complicated situation exists for radioisotopes, for which there are no data on MSA and MSSA. It is so, for example, for 11C from reaction 12C(, n). We tried to use in this case data on ALI for 14C also for 11C, if the baggage unit there is 20 kg of 12C estimated a(t  0) is higher than this ALI in ~5 times, but a(t  48 min) will suit pointed out ALI. The results of our subsequent experimental studies [A.I.Karev, et al. Bull. Russ. Acad. Sci.: Phys. 78, 452 (2014)] are consistent with the estimates described above. . 10.10.2018 L.Z. Dzhilavyan 17/13

14. Detectors for registration of (12N; 12B)-activities atpulsed electron accelerators In [L.Z.Dzhilavyan, A.M.Lapik, A.V.Rusakov,Bull. Russ. Acad. Sci.: Phys. (submitted)],there were considered the registration problems for -quanta, electrons, positrons emitted from irradiated objects at decays of 12N and 12B produced in these objects due to the reactions (I) (III) at pulsed electron accelerators. Earlier there were attempts of usage for these purposes scintillation detectors and water Cherenkov detectors. In all these cases, photomultiplier tubes (PMT) were used. Here there was chosen NaI-monocrystal (100 mm 150 mm) and the PMT FEU-49B, and the role of some changes in time for operation modes of this detector was studied. The consideration was carried out for closed irradiation halls at pulsed electron accelerators, supposed, for example, for checking baggage of air passengers. Electrons in their pulses at accelerators produce big numbers of bremsstrahlung photons and fast photoneutrons (if the kinetic energies of electrons exceed the corresponding thresholds). A “quasi-instantaneous” background of these particles may "dazzle" PMT in used detectors of (12N; 12B)-activities. Background photoneutrons are also troublesome because they "walk" in an irradiation hall, slow down and experience radiation captures, giving (n& )-background stretched in t after an electron beam pulse. It is supposed that we have: duration of a beam pulse ~(106105) s; a time between such pulses ~40 ms. To provide correct registration of (12N; 12B)- activities in such conditions we used for PMT controllable voltage dividers.We took in these studies signals with usage of: the radioactive -sources; the light emission diodes (LED); background at the electron linac LUE-8-5 with 3.5 s, E8 MeV, and different values of electron current in beam pulses up to I30 mA. Beam measurements at the linac showed two types of PMT-response to background loading. The first type is the "linear illumination", which takes place for small I, when the shape of the pulse from the anode of the PMT repeats the shape of I, close to the rectangular one with 3.5 μs. But higher some Imax, with a further increase in I, the response function "looses" its final part until it transforms to the second type - "non-linear illumination" with short pulses near the leading edge of the beam pulse. Further measurements were carried out with LEDs simulating a beam, and with the -sources. It turned out that the upper limit of the "linear illumination" Imax corresponds to the energy release in the scintillator of ~100 MeV. Oscillograms of pulses from the anode of FEU-49B in the mode of “infinite afterglow” are shown in Fig. (rays 3) on the right for "non-linear illuminations". At a high intensity of an electron beam, the control circuit significantly improves the PMT-operation and reduces the recovery time of the operation mode down to 120 s. . 10.10.2018 L.Z. Dzhilavyan 17/14

15. Model descriptions for attempts to realize the method The possibility to realize the considered method is determined by a set of relatively complicated processes depending on a number of various factors (for some of which experimental modifications may be difficult and/or expensive). Therefore, adequate model descriptions of attempts to realize the method seem to be very useful. In [L.Z.Dzhilavyan, Yu.N.Pokotilovski.Phys. Particles Nuclei Lett. 14, 726 (2017)] Monte-Carlo model description for the attempt with the graphite target ( 2.3 gcm3, the height 5cm, 6 cm, at 1m from the floor) was given, based on MCNPX-5. For verification of built model at the same conditions, there were also given independent estimations of its two essentialcharacteristics. . There were used in the model: Ne1.251011; no radiator; the irradiation hall dimensions (the height 4m6m6m); the “needle-like” electron beam fallen vertically along target axis; walls, a floor and a ceiling of the hall with the same thicknesses of 1m made of concrete with the known composition; 4 plastic scintillators (the thickness h6cm 12cm at R0.5m from the center of the target) immersed in lead “glasses” with wall and bottom thicknesses of 10cm; the bremsstrahlung photon spectra, calculated by MCNPX-5 itself; the cross sections of the reaction 13C(, p)12B see in Fig.1. We have per one incident electron with E50MeV number of 12B-nuclei produced in the target NB121.39106, which corresponds to 1.74105 per accelerator pulse. The independent estimation gave with even too good agreement value NB-121.4106, and total number of 12B-decays per one incident electron in the first ms after a beam pulse nB-124.8108мс1. Calculated for a case the expected counting rate in the detector at registration of -quanta and electrons from 12B-decays at a threshold of 10mV is N(t)3.9exp(t/29) where t is in ms. The t-dependence of the expected n-background in the hall and its ratio to the measured effect from 12B-decays are important. The calculation results are shown in upper Fig. A good correlation is seen between the t-dependences of the flux densities of -quanta 1 and n 3 in the irradiation hall, as well as the apparent dominance of the effect of 12B-decays 2 over the background 1. The lower Fig. shows a comparison of the experimental result with the calculation. The points correspond to the experimental data, curve 1 gives a fit of these data: (6) Curve 2 is the result of calculation (see red expression above), which is in a good agreement with the main component of the time dependence of the detector counting rate measured in experiment. (7) This rough estimated value is in reasonable agreement with the model value  0.81012 cm2ms1. . 10.10.2018 L.Z. Dzhilavyan 17/15

16. Conclusions and acknowledgements Modeling of the attempt to realize for the C-disk the considered method and the independent estimations for this case permit to obtain the good agreement in their results. This is a strong argument for adequacy of quantitative descriptions of the processes involved in this method. The relationships between the effect and the background of the produced photoneutrons and the background of the photons from captures of these neutrons by atomic nuclei are obtained, as well as the important characteristic for detecting 12B-activity E eff. Unfortunately, the counting rate achieved in this case is rather low. However, there are the significant reserves to achieve greater sensitivity in detection of hidden C-concentrations. There are necessary for it: for each electron pulse the bigger values of Ne (in 11.5 orders of magnitude, as at known pulsed linear electron accelerators); usage of proper radiators; more efficient detectors “capturing” a large total solid angle. The contributions to the background from photoneutrons may be weakened approximately in two orders of magnitude with use of the “beam trap”. It is possible to make significantly faster t-decreasing of the background from photoneutrons by covering all surfaces in the irradiation hall with a layer of materials with large neutron-capture cross sections. A 6Li-shielding for organic scintillators as well as usage of deuterated organic scintillators may also help. Further development of the method for detecting N-concentrations needs measurements of cross sections and yields of the reactions 14N(, 2p) and 14N(, 2n). Monitors of electrons and -quanta in their pulses need further development too. It is clear that the possibilities of these improvements in the method require their further careful modeling and experimental studies. The author is grateful to the co-authors of some cited papers A.I.Karev, V.G.Raevsky, Yu.N.Pokotilovski, B.S.Ishkhanov, V.I.Shvedunov, S.S.Belyshev, A.M.Lapik, A.V.Rusakov, and others. . 10.10.2018 L.Z. Dzhilavyan 17/16

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18. L.Z. Dzhilavyan 17/18 10.10.2018

19. L.Z. Dzhilavyan 17/19 10.10.2018

20. It is assumed that at 12B-decays in targets, production of -quanta and their absorption is described (when thicknesses r are in [gcm2]) by fitting functions f with their parameters A, a1, a2 as for indicated in the section 2 (H, C, N, O)-targets, as for the graphite targets and plastic scintillators indicated in this section. In this case, for example, for E min 0 and r 6.9 gсм2, the value of a2 0.345 cm2g1 for describing absorbed -quanta allows to determine the “effective” energy in their spectrum E eff 25 keV. Let us also estimate approximately  – the flux density of -quanta registered by these plastic scintillation detectors in the first ms after the pulse of the beam per one electron incident on the target at -decays of produced in the target 12B-nuclei for the considered carbon detection: , (7) where: nB-12 4.8108 ms1; (N/N)  0.38; R 50 cm; the factor in the square brackets describes integral part of -quanta at Emin 0 (when a2 0.345 g1cm2), which are absorbed by plastic scintillator with thickness h 6 cm and density pl 1.05 gcm3). This rough estimated value is in reasonable agreement with the model value  0.81012 cm2ms1. L.Z. Dzhilavyan 17/20 10.10.2018

21. It is assumed that at 12B-decays in targets, production of -quanta and their absorption is described (when thicknesses r are in [gcm2]) by fitting functions f with their parameters A, a1, a2 as for indicated in the section 2 (H, C, N, O)-targets, as for the graphite targets and plastic scintillators indicated in this section. In this case, for example, for E min 0 and r 6.9 gcm2, the value of a2 0.345 cm2g 1 for describing absorbed -quanta allows, according to, for example, [36] to determine the “effective” energy in their spectrum E eff 25 keV. Let us also estimate approximately  – the flux density of -quanta registered by these plastic scintillation detectors in the first ms after the pulse of the beam per one electron incident on the target at -decays of produced in the target 12B-nuclei for the considered carbon detection: , (7) where: nB-12 4.8108 ms1; (N/N)  0.38; R 50 cm; the factor in the square brackets describes integral part of -quanta at Emin 0 (when a2 0.345 g1cm2 (see Fig. 13)), which are absorbed by plastic scintillator with thickness h 6 cm and density pl 1.05 gcm3). This rough estimated value is in reasonable agreement with the model value  0.81012 cm2ms1. L.Z. Dzhilavyan 17/21 10.10.2018