Sources of tritium
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Sources of tritium



Paper presented at 2nd Intl. Conference on Nuclear Science and Technology in Iran, April 27-30, 2004, Shiraz, Iran

Paper presented at 2nd Intl. Conference on Nuclear Science and Technology in Iran, April 27-30, 2004, Shiraz, Iran



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Sources of tritium Sources of tritium Document Transcript

  • In this paper a short review of sources of tritium is presented. More details can be find in our book „TRITIUM ISOTOPE SEPARATION” published by CRC Press, [1]. I. SOURCES OF TRITIUM Tritium (T), the hydrogen isotope of mass three, decays by emission of a ßparticle with a maximum energy of 18.6 keV and an average energy of 5.7 keV to form 3 He. The half life of tritium is 12.26 years. There is no gamma radiation and the low energy of the ß- particle suggests that there would be little radiation damage from the decay. The others isotopes of hydrogen - protium (H) and deuterium (D) - are stables. The most important chemical combinations in which can be find these isotopes are: - molecular combinations in gaseous phase: H2, HD, D 2, HT, T2 or DT; - molecular combinations in gaseous or liquid phase: H2O (light or ordinary water), D2O or HDO (heavy water or deuterium oxide), T2O, HTO or DTO (tritiated heavy water or tritium oxide). Regardless of origin, tritium is predominantly incorpored in molecules of HT, HTO and sometimes the CH3T type. The existence of tritium was theoretically predicted by Wigner in 1933. The radioactivity of tritium was established by Alvarez and Cornog [2] in 1939. The natural occurrence of the radioactive isotopes of carbon and hydrogen, (14C and T), predicted by Libby [3], was first reported by Anderson et al. [4] in the atmosphere; and then by Faltings and Harteck [5], Grosse et al. [6], and Ostlund and Mason [7] in environmental water samples (atmospheric water and hydrogen) as the HT and HTO forms, respectively. The large differences in tritium concentration of atmospheric water and hydrogen reported by the last two groups of researchers illustrate the fact that hydrogen and water do not easily exchange isotopes. The rapid diffusion of hydrogen isotopes means that tritium is difficult to contain. Once in the environment, it enters in biological material rapidly. In the atmosphere it equilibrates with water at a rate of 0.2 to 3% per day and is most commonly encountered in the form of water vapour. Thus, although tritium is usually classed as one of the least hazardeous radioisotopes, its rapid assimilation by biological systems makes it of special concern to personnel who work with high concentrations. Also, the half life of 12.26 years means that any increased production rate must be carefully evaluated in terms of long-range effects . Unlike the isotopes of other elements, the relatively large mass differences of hydrogen, deuterium and tritium cause appreciable differences in properties of the elements and their compounds. Sources of tritium production are both natural and artificial. A. NATURAL SOURCES Tritium of natural origin is generated in the upper atmosphere of the earth, from atmospheric nitrogen or oxygen by bombardment with cosmic ray neutrons or solar protons. The most important nuclear reactions for natural tritium generation in atmosphere are [8-9]:
  • N + 1n º T + 12C - 4.3 MeV 14 (1) with an activation cross section of 11 ` 2 mb for fission neutrons with energies E > 4.4 MeV [9], N + 1n º T + 3 4He - 11.5 MeV (2) O + 1n º T + 14C (3) 14 and 16 Proton bombardment of nitrogen, oxygen and carbon can also yield tritium. Some discrepancies exist about the value of the production rate of atmospheric tritium. According to Craig and Lal [10], tritium production in the atmosphere is approximately 0.25 T atom/cm2/s Jacobs [11] estimated a rate as high as 2 T atom/cm2/s Later after reviewing the previous data, Nir et al. [12] calculated a rate of about 0.19 T atom/cm2/s corresponding to a steady state value of about 2.6 x 107 Ci for the world inventory. The natural steady-state level evaluated in 1972 appears to be somewhat higher than this (approximately 6.9 x 107 Ci) and corresponds to a production rate of about 0.5 T atom/cm2/s [8]. More recently data evaluations gives for the annual production of natural tritium the value of 4 to 8 x 106 Ci resulting in a steady-state world inventory of 0.7 to 1.4 x 108 Ci [13]. From this, 99% are located in hydrosphere as HTO, the remaining 1% being in atmosphere as HTO vapor or HT gas. The tritium formed is oxidized to water or is exchanged with atmospheric water vapour; the exchange is readily achieved since the mass action equilibrium coefficient for the reaction: HT + H2O º HTO + H 2 (4) is approximately 6 at 25oC [10]. By condensation and evaporation mainly to and from the oceans, tritium in the form of HTO becomes part of the hydrological cycle. For this reason tritium has been used many years as tracer in different studies of meteorologic, glaciologic, oceanographic and hydrologic interest [14]. Tritium also can be generated inside of the earth’s crust by (n,α) reactions from aluminium and lithium silicates; the neutrons necessary for this operation being obtained by (α,n) reactions resulted in the decay processes of natural radioactive elements. This contribution constitutes a small fraction in comparison with the total natural production of tritium [15]. In natural conditions a steady state exists when tritium passes by different global reservoirs of water with different residence times which determine his abundance in each reservoir. In the absence of the artificial causes for tritium pollution, this abundance in the environment, particularly in the atmosphere, is 1 to 6 tritium units (TU) [16-17]. (1 TU unit is equivalent to a concentration of 1 tritium atom in 10 18 hydrogen atoms or at a T:H ratio of 10-18; 1 litre of water of 1 TU contains 3.24 pCi tritium).
  • The situation was drastically changed during 1963 when, due the thermonuclear tests in atmosphere, the tritium concentration in rainwater attained a maximum of 4,000 TU [9]. B. ARTIFICIAL SOURCES Tritium of artificial origin is generated both by thermonuclear detonations and by the activities in the field of nuclear power. I. Thermonuclear Detonations Tritium generated by thermonuclear detonation can be released from: - The residues from the testing of thermonuclear weapons, - The fusion reaction [18]: D + D º T + H + 4.03 MeV (5) - The induced reactions by fusion neutrons in lithium contained in thermonuclear weapons [9]: Li + 1n º T + 4He + 4.69 MeV 6 (6) - The reaction of atmospheric nitrogen (Reaction 1), facilitated by the neutrons generated during the explosion, by fusion reaction D-D. On can suppose that the deuterium fusion reaction (Reaction 5) represents the most important source of residual tritium and due to this fact, the produced tritium quantity is practically proportional with the power fraction generated by fusion. In a deuterium-tritium weapon, the tritium release is composed of a residual amount of tritium and a production yield due to the neutron irradiation of nitrogen. The total yield it is not known. It has been reported to range between 7 and 50 MCi/Mt fusion with a suggested average value of 20 MCi/Mt [19]. (1 MCi = 106Ci; 1 g of tritium is equivalent to about 9,700 Ci). Comparison with the 7 kg of natural tritium, the quantity resulted from thermonuclear detonations - at the planet scale - is evaluated at 120 kg. II. Fission Nuclear Reactors In the fission nuclear reactors, tritium may be generated both as a fission product, by ternary fission, and as an activation product from neutrons interacting with different elements of the reactor core.
  • a. Light Water Reactors (LWR) The principal source of tritium in a LWR is the uranium ternary fission: 1 atom of tritium is generated at 1.25 x 104 acts of fission in 235U and at 1.41 x 10 4 acts of fission in 233 U [20]. It is important to mention that from tritium activity measurements useful informations about the burning level of the fuel elements can be obtained. A greater part of the tritium released in this type of reactors remains in the fuel element, being liberated only when the elements are reprocessed. A smaller part (about (1%) gets into the cooling system [21]. The tritium production levels released by ternary fission in LWR are evaluated at 67 Ci/GW(e)/d (24.455 kCi/GW(e)/year) [21]. The IAEA gives a value of 15 to 20 kCi/GW(e)/year [22]. This tritium is partly transferred with the fuel to the reprocessing plant. The amount of tritium that is produced through neutron reactions in the coolant and moderator is small, less than 1 kCi/GW(e)/year, giving tritium concentrations less than 1 mCi/kg in these systems. Because of such low concentrations the tritiated effluents from these systems can be released directly to the environment without additional processing [23]. The most important nuclear reactions used for tritium release in LWR are [9], [24]: - Nuclear reactions with thermal neutrons (in coolant water): D + 1n º T + γ + 6.26 MeV He + 1n º T + H + 0.76 MeV 3 (7) (8) and in the 6Li. reaction (Reaction 6). - Nuclear reactions with fast neutrons in 10B (from control rods) or in residual gas): B + 1n º T + 2 4He 10 14 N (from (9) and in the 14N reaction (Reaction 1). Reaction (7) and, in a smallest measure, the activation reaction of deuterium (natural concentration: 0.015%) and of hydrogen from ordinary water: H + 1n º D + 1n º T + γ + 6.26 MeV (10) permit tritium production levels of 10 Ci/GW(e)/year [19]. In the hypothesis of doubling deuterium content from ordinary water by means of Reaction 10, the tritium production yield by Reactions 9 and 10 in a nuclear reactor of 3,000 MW(t) is evaluated at 0.03 Ci/d (10.95 Ci/year) [8]. The tritium production from the Reactions 8 is negligible, because the concentrations of 3He in the reactor are very low [8]. Reaction 6 takes place in lithium
  • impurities (for pH maintenance) of the fuel rods, from primary coolant or from graphite rods. The natural concentration of 6Li is 7.42%. This reaction can be used as an important source of tritium, introducing materials with lithium content in the reactor core. For the same purpose the fast neutron reaction can be used: Li + 1n º T + 4He + 1n - 2.5 MeV 7 (11) with the important advantage of the neutron conservation [25]. The tritium production level in a pressurized water reactor (PWR), in which enriched lithium at 99.96% in 7Li is used, is evaluated at 10 Ci/GW(e)/year [26]. In fast breeder reactors (FBR) the tritium release from 10B of the boron used as B4C in control rods (with 90% 10B) [9], takes place both by Reaction 9 and by the reactions: B + 1n º T + 8Be + 0.2 MeV (12) B + 1n º T + 9Be + 9.6 MeV (13) 10 11 the tritium being retained in the crystalline structure of B4C [27]. It can be extracted by destroying this structure by a chemical method. In PWR a very significant tritium source is the boron used as a "chemical shim", i.e., a chemical added to the coolant to level out the reactivity as a function of time. The rate of tritium production varies with the length of time the fuel has been in service and the coolant turnover rate. An average value would place the contribution from this source about equal to that from fission. This tritium becomes a part of the primary coolant. Boron used in control rods produces significants quantities, but the tritium will be largely fixed within the rods [8]. In the case of PWR, the tritium production levels from nuclear reactions 12 and 13 and succesive reactions B + 1n º 7Li + 4He 10 (14) Li + n º T + He + n 7 1 4 1 are 1,000 to 1,500 Ci/GW(e)/year, from which 300 Ci are released in the reactor water, the rest being retained within the command rods [26]. b. Heavy Water Reactors (HWR) In this kind of reactors the production of tritium is assured by neutron reactions with deuterium (Reaction 7), boron (Reactions 9, 12, and 13), and lithium (Reaction 11) and by ternary fission. The deuterium activation is by far the most important mechanism. It is responsible for the production of about 2.4 kCi (89 TBq) of tritium/MW(e)/year, especially in a moderation system, compared with only 20 Ci (0.7 TBq)/MW(e)/year by ternary fission [23]. This input of tritium results in a steady rise of tritium concentration
  • in the heavy water, with a concentration of about 65 Ci/kg predicted after 30 years of operation. A great part of the tritium from HWR is in the form of tritiated heavy water (DTO). The concentration of the tritium (A) increases towards an equilibrium value (Am) which depends on the neutron flux and the fraction of a heavy water system that is in the reactor core. The tritium concentration in the moderator of a CANDU reactor is higher than that in the coolant. If the heavy water does not leak or is not replaced, the concentration ratio in the two systems is about 26 [22]. In October 1978, the average tritium concentrations in the moderator and coolant at Pickering Generating Station "A" (PGS) (Canada) were approximately 16 Ci/kg (0.6 TBq/kg) and 0.5 Ci/kg (0.02 TBq/kg) respectively. The theoretical equilibrium tritium concentrations are 65 Ci/kg (2.4 TBq/kg) in the moderator and 2.5 Ci/kg (0.09 TBq/kg) in the coolant. When the losses and replenishment are considered in the effects of heavy water mixing between the coolant and the moderator, the equilibrium concentrations are about 40 Ci/kg (1.5 TBq/kg) (moderator) and 2 Ci/kg (0.07 TBq/kg) (coolant system) [22]. Current tritium concentrations in the Ontario Hydro reactors at PGS A are 25 to 30 Ci/kg with much smaller concentrations of <1Ci/kg in the coolant. Leakage of water from these systems gives rise to tritium release into reactor building. By careful design and operation most of the heavy water leakage is recovered, so that tritium emissions to the environment by way of airborne and water emissions are kept below 1% of the allowable release limit [23]. The principal component of airborne tritium control is the placement of heavy water systems within the reactor containment wherever possible. The reactor containment is equipped with an effective closed-cycle heavy water recovery system to prevent tritium escape and to recover heavy water for economic reasons. Heavy water systems, which must be located outside containment, are in ventilated areas, with the air flow designed to move air from less contaminated to more contaminated areas. The average weekly airborne tritium emissions from the Pickering Nuclear Generating Station (4 x 500 MW(e), CANDU) for 1981 averaged 1,350 Ci/month. The monthly aqueous emissions were 625 Ci [23]. Old French calculations show that in the case of a HWR, at an average neutron flux of 1013 neutrons/cm2/s., after one year of operation, the tritium activity attains the value of 0.5 x 10-3 Ci/cm3 D2O, which give a saturation activity of 0.01 Ci/cm3 D2O [28]. In the case of the French EL-3 reactor, with the neutrons flux condition previously mentioned, a tritium production of 47 [Ci/cm3 D2O/month, has been evaluated, yet, experimentally, this has been observed at only 25.8 [Ci/cm3 D2O/month [29]. For the high flux reactor from Grenoble, France, (1015 n/cm2/s) it has been specified that without removal of tritium the heavy water would reach a tritium content of about 84 Ci/l, whereas with tritium extraction a value of about 1.7 Ci/l can be maintained. This requires an annual extraction of about 0.16 MCi [30]. In the hypothesis of a fission yield of 1 x 10-4 (one tritium atom is released at each 4 10 fission acts) the contribution of ternary fission with thermal neutrons on 235U in HWR to the tritium production is of 12 to 15 kCi/GW(e)/year [26]. The released tritium by this process migrate in the metals, alloys and oxides of the reactor core structure or in zircalloy tubes, and remains practically integrally incorporated in these components.
  • Tritium extraction from those components is performed during the fuel reprocessing operations. Recently, evaluations shows that in a HWR tritium can also be produced by the the (n,p) reaction on the tritium decay product 3He (Reaction 8). The relative contribution of this reaction depends on the retention time of 3He in the heavy water system. If the retention is at least 10 d, then with an efective neutron flux of 1014 n/cm2/s, the activity of tritium produced by the 3He reaction is at least 4% of that produced by the deuterium reaction (Reaction 6) after operation for 5 years and is at least 22% after 30 years. Complete retention of the 3He would result in similar contributions from both reactions to the concentration of tritium in heavy water after 30 years [31]. From the above-mentioned considerations on LWR and HWR it can be pointed out that there exists a considerable variability in tritium production in nuclear power reactors. For instance, the tritium yield from 239Pu is about twice that from 235U [10]. The tritium production from the ordinary water is less than 0.1% of the fission yield. However, for HWR the yield would be several times that from fission [8]. c. Tritium Emissions from Reactors Tritium in the reactor may escape into the ventilated areas and subsequently be emitted in air effluents or it may be released as tritiated water and emitted in liquid effluents. The limits on emission (the derived emission limit, DEL) are set as doses to members of the general public that will not exceed 0.5 rem/year [23], [32]. Heavy water moderator has become the major source of tritium emissions in recent years. For example, analysis of the 1977 emission data suggests that almost 90% of the airborne tritium originated from the moderator. Simultaneously with the control and the assurance of the reglementar levels, the possibilities of eliminating or reducing these leakages to a minimum are studied both in the design and operation phases. Thus, the tritium emissions are very small and the reglementar levels are rigorously maintained. d. Fuel-Reprocessing Plants The amount of tritium from the fuel passing to the reprocessing plant depends on the type of reactor and on the fuel cladding material. LWR fuel with stainless-steel cladding may lose up to half of the tritium produced in the fuel through diffusion and permeation through the cladding. Zircalloy-clad fuel will retain esentially all the tritium through formation of zirconium tritide. In advanced gas reactors (AGR) and fast breeder reactors (FBR) with stainless-steel clad fuel, only minor amounts of tritium are expected to be passed on to the reprocessing plant. For an LWR fuel reprocessing plant, with a capacity of 1,400 t/year of heavy metal serving 50 GW(e) of electric production capacity, there is estimated to be 0.5 to 1.0 MCi/year of tritium [23]. In the reprocessing plant using the Purex process, the fuel elements are chopped into small pieces and the fuel is dissolved from the cladding with nitric acid. With zircalloy-clad fuel approximately 60% of the total amount of tritium may be retained in the cladding; the bulk of the remainder is in the form of tritiated water and nitric acid, which becomes distributed through the various streams in the process [33]. As fresh
  • water and nitric acid are added to the process, the tritium becomes progressively more diluted, so that large volumes of tritiated aqueous effluents in the order of 100 m3/t of heavy metal are produced. In present reprocessing plants on coastal sites, these large volume effluents are discharged directly to the sea, where there is an enormous dilution effect [34]. Solar evaporation is used in India. In locations where access to the sea is limited or discharge is otherwise prohibited, such as in Germany, concepts for concentrating the tritium into smaller volumes of water have been evaluated [33-35]. Effluent volumes can be reduced to the order of 1 m3/t of heavy metal by means of partial recycling of the water and nitric acid, along with segregation of tritium in the first aqueous head-end cycle. This requires separate acid and water recovery systems, and scrubbing the organic phase of the first contactor with tritium-free acid [23]. Numerous experiences for the determination of "free" tritium in different kinds of fuels has shown that 25-50% of tritium is in a gas form; from this quantity only 0.2% is released. In a fuel constituted from pellets of UO2 in zircalloy cladding, it has been found that 9.27% of the theoretical quantity of tritium is in a gas form. By evaporation in a distillation column of a dissolution acid with a content of 430 Ci tritium per tonne of fuel, the withdrawn solvent will contain 30% of the total tritium; the rectifying section from the top of the column will contain 47%; and the concentrated acid will contain 23%. After some French evaluations [26], the content of tritium in the fuel of a PWR of 1,000 MW(e), after a storage for 5 months in a piscine, is of 7 x 10-2 g tritium per tonne. of uranium with an activity of 310 Ci per fuel cladding, and of about 20 kCi for an annual discharge (64 assemblages). The tritium fraction from gaseous effluents depends entirely on the reprocessing method. For instance, in the case of the La Hague (France) reprocessing plant this fraction is below 5% .In the case mentioned above, the activity of liquid effluents rejected into the sea is 5 kCi (the ejection being performed after a previous dillution). The same source gives the values of the tritium radioactivity in the sea water (0.16 pCi/l) and in the river water (300 pCi/l), (1 pCi = 10 -12Ci). From the previously mentioned consideration, the reprocessing plants will handle an important amount of tritium, probably 50-90% from the amounts produced in fission reactors (about 1 kCi tritium per tonne of processed fuel) [8]. For a mean reprocessing plant of about 103 t./year, 106Ci tritium/year is ejected in a liquid form and 105Ci, in a gas form, respectively [13]. In the future it is possible that bigger plants will be able to reprocess 5 to 10 t burned fuel per day. This will made possible by multiplying the results mentioned above by 3 to 4 times. The rigorous control of tritium leakage, both in power reactors and in reprocessing plants, imposes the selection of avoiding methods and the problem of the waste storage becoming serious. Consequently, there is a necessity of developing simple, effective, and economical detritiation methods, which permit the reduction of tritium concentration in environment below the established levels, and also of finding some storage methods for tritiated water.
  • III. Fusion Nuclear Reactors Estimation of the effect of the development based on controlled thermal fusion reactor (CTR) for the production of tritium is a difficult task, given the fact that tritium serves both as combustible and as a product. In this case, the problems connected with confinement are of a greater complexity than those corresponding to tritium storage, because of the greater amounts and general increased danger. Taking into consideration different energetic scenarios, it has been estimated that the tritium production rate can be of about 10 5 times greater than in the case of fission [10] and that a single reactor of 3000 MW(t) can "burn" about 107 Ci/day, which represents an important fraction of the present world inventory of tritium [8]. For instance, in the case of the reference reactor of 1 GW(e) (CTR UWMAK-1 Tokamak - a study project for a tokamak at the University of Wisconsin, U.S.) [36], the estimated tritium inventory is ~10 kg/GW(t) = 25 kg/GW(e). These considerations are based on the supposition of utilization of the fusion reaction: D + T º 4He (3.5 MeV) + 1n (14.1 MeV) (17) considered as the reaction almost certain to serve as the principal energy source in the first-generation fusion reactors [37]. The energy released amounts to 94,000 thermal kilowatt-hours (kWh[t]/g of reacting nuclei; this is roughly 1,800 times the energy that must be supplied to the reactants in order to initiate fusion. Because tritium is nearly nonexistent in nature, it must be bred (reproduced); this task is possible with Reactions 6 and 11. The fuel flow system from a CTR involving a D-T mixture will include components such as the tritium source, the exhaust gas purification system and the separation of hydrogen isotopes (mainly to eliminate 1H). The assessment of the tritium safety system will deal with: containment techniques; monitoring (both internal and environmental); safety measures to be taken for shipping of tritium supplies when required; and disposal of tritiated wastes. It is also anticipated that an accountability of tritium will be required to prevent diverted use. The development of tritium technology will be supported by extended research on the physical, chemical and radiological properties of tritium and its compounds, to obtain e.g. permeation data, exchange reactions, thermodynamic data at cryogenic temperatures, radiotoxicity, etc. C. THE EVOLUTION OF THE WORLD TRITIUM INVENTORY Prediction of the evolution of the world tritium production is subject to considerable uncertainty, being directly connected with the uncertainty in the evolution of nuclear power, the different scenarios being submitted to continuously modifications. Hovewer, it is certain that in the future a continuous increase in tritium activity in the environment will take place. Table 1 presents rough approximations of tritium yields associated with different nuclear reactors [8].
  • Table 1. Tritium yields for a 3000 MWt reactor (Ci/day). - Thermal fission, 235U: 50 - Reactivity control (chemical shims), PWR: 10-60 - Reactivity control (chemical shims), BWR: 2-15 - 1 ppm Li impurity in primary system: 25 - Deuterium in light water (assumes doubling of natural D content by n reactions with light water): 0.03 - Heavy water moderated reactor, HWR: 80-150 - Fast breeder reactor, FBR: 50-100 - Controlled thermal fusion reactor, CTR: 106-10 7 Jacobs [11] lists annual production rates of 2 x 10 6 in 1980, 6 x 106 in 1990 and 15 x 10 6 in the year 2000, leading to accumulated values of 6 x 106 , 32 x 10 6 and 96 x 10 6 Ci, respectively. A review by Peterson et al., [38] includes contributions from all these sources and leads to production rates of about a factor of three greater. It would seem that Peterson's estimates of 2 x 107 Ci in 1980, 10 8 in 1990 and 3 x 10 8 in the year 2000 might be within a factor of two of the real values, assuming power reactors as the major source and no further H-weapon testing. The evaluation of the Scientific Committee of the United Nations on the effects of ionizing radiations, starting from the hypothesis of a world installed nuclear power of 2000 GW(e) in the year 2000, leads to an annual tritium production of 40 MCi and a cumulative production of 250 MCi [25]. According to the European Communities calculations based on the development of nuclear power at the foreseen rate, gives for tritium activity in the environment at the end of XX-century, a value of 108 Ci. This represents about 6% from the level attained in 1963, when the most intensive thermonuclear testing was performmed [12]. After the year 2000 the nuclear power industry will constitute the most important source of tritium in the biosphere, in the absence of thermonuclear testing. Thanks to the radioactive waste products from weapons testing, the present world tritium inventory is greater with about one order of magnitude, and is supposed that in the absence of others tritium sources, will be necessary about 30 years of radioactive decay to reduce this level to the natural level. . REFERENCES 1. Vasaru G., Tritium Isotope Separation, CRC Press, Boca Raton, 1993 2. Alvarez, L. W. and Cornog, R., Helium and hydrogen of mass 3, Phys. Rev. 2, 56, 613, 1939. 3. Libby, W.F., Atmospheric helium three and radiocarbon from cosmic radiation, Phys. Rev. 69, 671, 1946. 4. Anderson, E. C., Libby, W. F., Weinhouse, S., Reid, A. F., Kirshenbaum, A. D. and 5. 5. Grosse, A. V., Natural radiocarbon from cosmic radiation, Phys. Rev. 72, 931, 1947.
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