Definitions of radioisotope thick target yields

Transcription

1 Radiochim. Acta 2015; 103(1): 1 6 Naohiko Otuka* and Sandor Takács Definitions of radioisotope thick target yields Abstract: Definitions of thick target yields are reviewed in relation to their documentation for the experimental nuclear reaction data library (database). Researchers reporting experimental thick target yields are urged to define their yields clearly with an appropriate unit in order to compile them in the experimental data library (EXFOR) in a consistent manner, and also to properly utilise them for comparison with other experimental and evaluated yields. Keywords: Thick target yield, Excitation function, Cross section, Radioisotope production, Nuclear data, EXFOR. DOI /ract Received December 4, 2013; accepted July 14, Introduction Experimental thick target yields and excitation functions (i. e., energy dependent isotope production cross sections) are essential for development of large scale high-current medical systems that can produce enhanced yields of radioisotopes [1]. The thick target yields obtained in routine production (practical yields) are usually lower than those measured under well-defined conditions (nominal yields) due to various possible reasons such as loss of the beam particles, variation of the beam intensity, loss of the reaction product (e. g., evaporation, sublimation, recoil effect), or density reduction and radiation damage effects of the target material [1 7]. Nevertheless the measurements of the nominal yields are useful to validate the excitation functions [8]. Measurement of the reaction rates in broad neutron spectra has been recognized as useful validation of the excitation functions of neutron-induced reactions for dosimetry applications, and the excitation function averaged over the well-known 252 Cf spontaneous fission neutron spectrum has been the most standard observable to *Corresponding author: Naohiko Otuka, Nuclear Data Section, Division of Physical and Chemical Sciences, Department of Nuclear Sciences and Applications, International Atomic Energy Agency, Wagramerstraße 5, A-1400 Wien, Austria, n.otsuka@iaea.org Sandor Takács: Institute of Nuclear Research, Hungarian Academy of Science, Bem tér 18/c, H-4026 Debrecen, Hungary validate the excitation functions of neutron dosimetry reactions [9, 10]. Similar benchmarking can be performed for charged-particle induced reactions by comparison of the experimental thick target yields and excitation functions. Newly measured excitation functions for charged-particle induced reactions are often reported with the thick target yields obtained by integration of the excitation functions, and compared with directly measured ones in the literature (e. g., [2, 3]). There are also a few experimental works where the thick target yields and excitation functions were measured in parallel (e. g.,[8, 11 14]). Experimental excitation functions and thick target yields for charged-particle induced radioisotope production have been compiled in the experimental nuclear reaction data library (EXFOR) [15 22] from more than 800 experimental works by the International Network of Nuclear Reaction Data Centres (NRDC) under the auspices of the International Atomic Energy Agency (IAEA). In order to improve the completeness of EXFOR, the IAEA Nuclear Data Section (NDS) and Hokkaido University Nuclear Reaction Data Centre (JCPRG) have compared experimental works in EXFOR with those in the Landolt-Börnstein compilation [23] for proton, deuteron, triton, helium-3 and alpha induced reactions, and the Data Centres are compiling the articles still missing in EXFOR [15]. In order to retrieve and analyse experimental thick target yields of a specific type from EXFOR efficiently and appropriately, each experimental data set must be properly tagged not only by the reaction (i. e., target, beam particle, product) but also by the definition of the thick target yield. However, the large variety of nomenclature in the literature makes compilation work difficult. There are fewer problems in compilation of the thick target yields of stable reaction products, which are always expressed in terms of the number of the produced nuclei per unit induced electric charge (or per beam particle) irradiating the target. Since the product is stable, the number of produced nuclei is a linear function of the irradiation time, and consequently the thick target yield per unit irradiation time is irradiation time independent. Although the thick target yields of radioactive reaction products can be expressed in the same manner, usually other expressions (e. g., activity instead of number of produced nuclei) have been used for practical reasons, and this has become a major source of confusion. Furthermore, the definition of experimental thick target yields is often insufficient or

2 2 N. Otuka and S. Takács, Definition of radioisotope thick target yields even missing in the literature. The amount of a radioactive product is determined by measurement of its activity. The problem arises from the fact that the activity is time dependent, and several time dependent corrections should be applied to the measured activity to determine the proper number of the produced nuclei. The purpose of this paper is to review various thick target yields defined in the EXFOR Compiler s Manual (LEX- FOR [24] under revision), compare with definitions given in earlier reports [25 27], and encourage experimentalists to report their thick target yields in a well-defined manner. 2 Definitions Suppose a sample material having the target isotope number density ρ and thickness L is irradiated by beam particles (charge number Z, initial beam energy E 0,number of beam particles irradiating the sample per unit irradiation time I 0 ¹ ) to produce an isotope of interest. If the cross section to produce the isotope at depth x inthesampleis σ(x), the total number of the produced nuclei Y(t) during an irradiation time t (t =0at the beginning of irradiation) is L Y(t) = t dx I(x)σ(x)(ρ/Ze) (1) 0 E de ti 0 de ( ρ dx ) σ(e)/(ze) (2) E L ti 0 y, (3) where E L is the beam energy at the exit of the sample (or E L =0if the sample is thicker than the stopping length), (1/ρ)(dE/dx) is the stopping power, and y is the number of the produced nuclei following deposition of unit induced electric charge. The quantity y is defined as the thick target product yield in LEXFOR. It is sometimes also given as the number of the produced nuclei per beam particle instead of per unit induced electric charge. The thick target product yield can be defined for both stable and radioactive products, but is mostly used for stable ones². If the product is radioactive with decay constant λ,the number of the produced nuclei present in the sample N(t) satisfies dn(t) dt and its solution is = dy(t) dt λn(t)=i 0 y λn(t), (4) N(t) = I 0 y 1 e λt. (5) λ The activity of the sample material per unit current at t is therefore λn(t) =y(1 e λt ) a(t), (6) I 0 which is defined as the end-of-bombardment (EOB) thick target yield in LEXFOR³. For a very long irradiation λt 1 (e. g., irradiation is much longer than the half-life of the product), the production rate and decay rate of the product are in equilibrium, and the EOB thick target yield becomes a(t ) = y a sat, (7) whichisdefinedasthesaturation thick target yield in LEXFOR. Equation (7) shows that the thick target product yield y and the saturation thick target yield a sat are essentially the same except for their interpretation: y is the number of the produced nuclei per unit induced electric charge (e. g., nuclei/μc), while a(t) and a sat are the decay rates of the product per unit current (e. g., MBq/μA). Note that 1[nuclei/μC]= 1[MBq/μA]. The curve of the growing yield a(t) versus irradiation time is not a straight line (See Figure 1 (top)). From Eq. (6), the time evolution (rate) of the activity per unit current is da(t) =λye λt α(t). (8) dt In particular, the rate at the beginning of the irradiation (t =0) per unit current α(t = 0) = λy α phys (9) is defined as the physical thick target yield in LEXFOR. The unit of the physical thick target yield could be MBq/C or MBq/μA h⁴, and this choice will be discussed later. 1 We limit our discussion to irradiation with a constant beam current. 2 An exception is [28] where thick target product yields of radioactive products are tabulated. 3 yield and activity of a radioactive product are hereafter related by yield = activity/current [26]. 4 Because α phys is time derivative of a(t),useofmbq/μa/hisalsopossible. But this is not commonly used and not recommendable.

3 N. Otuka and S. Takács, Definition of radioisotope thick target yields 3 Table 1: Thick targetyield quantities definedin EXFOR (t =0at the beginning of irradiation). Name Symbol Typical unit (in EXFOR) [24] Thispaper [25] [26] [27] EXFOR thick target product yield y,py TT/CH nuclei/μc, nuclei/μa h end-of-bombardment thick target yield a(t) A/I H EOB,TTY EOB MBq/μA saturation thick target yield a sat =a(t ) A 2,TTY SAT MBq/μA physical thick target yield α phys =α(t=0) B Y EOIB Y,TTY PHY MBq/C, MBq/μA h Usually used for stable products. a(t = 1 h)isdefinedasa 1 in [27]. EOIB = End of an instantaneous bombardment. (PHY) is used instead of PHY when the compiler is uncertain if the physical thick target yield is given. Recommended. 1 MBq/C = MBq/μA h TTY (GBq/μA) a sat =a(t ) a(t) α phys t dtty/dt (GBq/μA h) α phys α(t)=da(t)/dt Irradiation time t (hour) Fig. 1: Time dependence of the production thick target yield a(t) and its rate α(t) for 18 O(p,n) 18 F(T 1/2 = 110 min) at E 0 = 10.0 MeV based on a sat = GBq/μA, α phys = GBq/C 2.5 GBq/μA h[27]. TTY = thick target yield. From Eqs. (6), (7)and(9) the three quantities a(t), a sat and α phys are related by a(t) = a sat (1 e λt )=α phys (1 e λt )/λ. (10) Note that α phys is the time derivative of a(t) at t=0, and its dimension is different from a(t) and a sat although they all are named yields ⁵. Table1 lists the four yields defined above with their notations in [25 5 An alternative term thick target production rate used by G. F. Steyn, S. J. Mills et al. [11] clearly indicates that the quantity α phys is time derivative (rate) of the time dependent yield. 27] as well as typical units. A numerical example is also shown in Figure 1 for the 18 O(p,n) 18 F(T 1/2 = 110 min) reaction at E 0 = 10.0 MeV (a sat = GBq/μA, α phys = GBq/C 2.5 GBq/μA h [27]). Table 2 summarizes the conversion coefficients (multipliers) connecting these yields. This table shows that one may convert from one expression to another very easily. As long as the definition chosen by the experimentalists is clearly described, they have freedom to report their experimental yields by any of these expressions. Note that the physical thick target yield is most suitable for comparison of the directly measured yields with yields derived from excitation functions. In addition to the definition of the reported yields, some key parameters for irradiation conditions (e. g.,beam

4 4 N. Otuka and S. Takács, Definition of radioisotope thick target yields Table 2: Conversion coefficient (multiplier) between different types of yields. The first column and first row give the input and output, e. g., a(t) = a sat (1 e λt )=α phys (1 e λt )/λ. a(t) a sat =y α phys a(t) 1 (1 e λt ) (1 e λt )/λ a sat =y 1/(1 e λt ) 1 1/λ α phys λ/(1 e λt ) λ 1 energy range, beam intensity, irradiation time, target thickness and composition) must be described. For example, the EOB thick target yield is not well-defined if the irradiation time (e. g., 1-hour irradiation ) is not specified. 3 Linear approximation for irradiation time The activity for 1 hour-1μa irradiation(a 1 in [27]) is often extrapolated to higher beam intensity or longer irradiation time. Since the activity is exactly proportional to the beam intensity, linear extrapolation to higher beam intensity does not introduce any error. On the other hand one should be more careful in extrapolation of the activity to longer irradiation time since the activity in general is not a linear function of the irradiation time. Figure 1 (top) shows that the physical thick target yield α phys gives the slope of the growing curve a(t) at the beginning of irradiation [26]. If the half-life of the product T 1/2 =ln2/λis long compared to the irradiation time (i. e., λt 1), the EOB thick target yield a(t) in Eq. (10) canbe approximated by a linear function of the irradiation time t: a(t) = α phys (1 e λt )/λ λt 1 α phys t, (11) which gives a formula for derivation of the physical thick target yield, α phys = a(t)λ/ (1 e λt ) λt 1 a(t)/t. (12) This approximation (linear approximation) has been often applied incorrectly for short-lived isotopes not satisfying λt 1. A similar inappropriate approximation is also seen for derivation of the 1-hour EOB yield from the t-hour EOB yield by a(t = 1 h) a(t)/t. Table 3 shows such an example seen in two articles published in 2011 [29, 30]. The corresponding author of these articles later explained that the reported yields were obtained by a(t)/t with t in hour. Fortunately the irradia- Table 3: Half-life T 1/2, irradiation time t,theirratioaswellas correction factors for conversion of the thick target yields in [29, 30] to the corresponding physical thick target yields (C 1 ) and 1-hour end-of-bombardment (EOB) thick target yield (C 2 ). Products T 1/2 (h) t (h) T 1/2 /t C 1 C 2 97 Ru Tc Tc Mo Tb Tb Tb Gd tion time is well documented in the articles, and therefore we can convert their yields to the corresponding physical and 1-hour EOB thick target yields by applying the correction factors C 1 =tλ/(1 e λt ) and C 2 =t(1 e λ )/(1 e λt ), respectively, which are not close to unity for short-lived products. 4 Units of thick target yields Not only experimentalists who extrapolate the 1-hour EOB thicktarget yield a(t = 1 h) from the measured t-hour EOB thick target yield a(t) by a(t)/t, but also those who properly extrapolate the 1-hour EOB thick target yield by applying the factor a(t = 1 h)/a(t) = (1 e λ )/(1 e λt ) often report their 1-hour EOB thick target yield in MBq/μA hinterpreting that h means 1-hour irradiation. On the other hand, people who understand the usage of various units as summarized in Table 1 are confused when they find a yield in MBq/μA h is reported with timing information (e. g., 1- hour irradiation ). The best way to avoid all such confusions is to use MBq/μA for the EOB and saturation thick target yields while to use MBq/C(not MBq/μA h) for the physical thick target yields. When the experimentalists feel that the physical thick target yields in MBq/μA h areconvenientfor a practical reason, the physical thick target yields in this unit can be additionally reported. 5 Conclusion The final goal of compilation of experimental thick target yields is to provide access to all available measured yields to researchers, and help to improve radioisotope production technology based on an intercomparison of the exist-

5 N. Otuka and S. Takács, Definition of radioisotope thick target yields 5 ing experimental and evaluated data. In order to achieve this goal, experimentalists reporting thick target yields are strongly recommended to provide the definition of the reported thick target yield very clearly; report physical thick target yield in MBq/C (and additionally in MBq/μA h if necessary), while EOB and saturation thick target yields in MBq/μA; report EOB thick target yield always with the irradiation time because the quantity is irradiation time dependent; provide the key irradiation parameters (e. g.,beamenergy range, beam intensity, irradiation time, target thickness and composition); provide the decay data (e. g., gamma intensity) and uncertainties adopted in the derivation of the reported yields with their references; do not apply the linear approximation to derive the physical and 1-hour EOB thick target yields from the EOB thick target yield. Acknowledgement: We would like to thank Prof. S. 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