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 10.1515/ract-2013-2234
Received December 4, 2013; accepted July 14, 2014
1 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,
e-mail: [email protected]
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
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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 (LEXFOR [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 𝐸0 , number
of beam particles irradiating the sample per unit irradiation time 𝐼0 ¹ ) to produce an isotope of interest. If the cross
section to produce the isotope at depth 𝑥 in the sample is
𝜎(𝑥), the total number of the produced nuclei 𝑌(𝑡) during
an irradiation time 𝑡 (𝑡 = 0 at the beginning of irradiation)
is
𝐿
𝑌(𝑡) = 𝑡 ∫d𝑥 𝐼(𝑥)𝜎(𝑥)(𝜌/𝑍𝑒)
(1)
0
𝐸0
≃ 𝑡𝐼0 ∫d𝐸 (−
𝐸𝐿
≡ 𝑡𝐼0 𝑦,
1 d𝐸 −1
) 𝜎(𝐸)/(𝑍𝑒)
𝜌 d𝑥
(2)
(3)
If the product is radioactive with decay constant 𝜆, the
number of the produced nuclei present in the sample 𝑁(𝑡)
satisfies
d𝑁(𝑡) d𝑌(𝑡)
=
− 𝜆𝑁(𝑡) = 𝐼0 𝑦 − 𝜆𝑁(𝑡),
d𝑡
d𝑡
(4)
and its solution is
𝑁(𝑡) = 𝐼0 𝑦
1 − 𝑒−𝜆𝑡
.
𝜆
(5)
The activity of the sample material per unit current at 𝑡 is
therefore
𝜆𝑁(𝑡)
= 𝑦 (1 − 𝑒−𝜆𝑡 ) ≡ 𝑎(𝑡),
𝐼0
(6)
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 ≡ 𝑎sat ,
(7)
which is defined as the saturation thick target yield in
LEXFOR.
Equation (7) shows that the thick target product yield
𝑦 and the saturation thick target yield 𝑎sat 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 𝑎sat 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
where 𝐸𝐿 is the beam energy at the exit of the sample (or
𝐸𝐿 = 0 if 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.
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.
3 “yield” and “activity” of a radioactive product are hereafter related
by yield = activity/current [26].
2 An exception is [28] where thick target product yields of radioactive
products are tabulated.
4 Because 𝛼phys is time derivative of 𝑎(𝑡), use of MBq/μA/h is also possible. But this is not commonly used and not recommendable.
d𝑎(𝑡)
= 𝜆𝑦𝑒−𝜆𝑡 ≡ 𝛼(𝑡).
d𝑡
(8)
In particular, the rate at the beginning of the irradiation
(𝑡 = 0) per unit current
𝛼(𝑡 = 0) = 𝜆𝑦 ≡ 𝛼phys
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N. Otuka and S. Takács, Definition of radioisotope thick target yields
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Table 1: Thick target yield quantities defined in EXFOR (𝑡 = 0 at the beginning of irradiation).
Name
(in EXFOR) [24]
This paper
Symbol
[26]
thick target product yield§
𝑦
–
–
–
,PY„TT/CH
nuclei/μC,
nuclei/μA⋅h
end-of-bombardment thick target yield
𝑎(𝑡)
𝐴/𝐼
𝐻EOB
∗
,TTY„EOB
MBq/μA
saturation thick target yield
𝑎sat = 𝑎(𝑡 → ∞)
–
–
𝐴2
,TTY„SAT
MBq/μA
physical thick target yield
𝛼phys = 𝛼(𝑡 = 0)
𝐵
𝑌EOIB†
𝑌
,TTY„PHY‡
MBq/C¶ ,
MBq/μA⋅h
[25]
Typical unit
[27]
EXFOR
§
Usually used for stable products.
𝑎(𝑡 = 1 h) is defined as 𝐴 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 = 0.0036 MBq/μA⋅h.
∗
25
TTY (GBq/μA)
20
αphys⋅t
15
10
asat=a(t→∞)
dTTY/dt (GBq/μA⋅h)
5
a(t)
0
2.5
αphys
2
1.5
α(t)=da(t)/dt
1
0.5
0
0
1
2
3
4
5
Irradiation time t (hour)
6
7
8
Fig. 1: Time dependence of the production thick target yield 𝑎(𝑡) and its rate 𝛼(𝑡) for 18 O(p,n)18 F(𝑇1/2 = 110 min) at 𝐸0 = 10.0 MeV based on
𝑎sat = 6.630 GBq/μA, 𝛼phys = 697.5 GBq/C≃2.5 GBq/μA⋅h [27]. TTY = thick target yield.
From Eqs. (6), (7) and (9) the three quantities 𝑎(𝑡), 𝑎sat
and 𝛼phys are related by
𝑎(𝑡) = 𝑎sat (1 − 𝑒−𝜆𝑡 ) = 𝛼phys (1 − 𝑒−𝜆𝑡 ) /𝜆.
(10)
Note that 𝛼phys is the time derivative of 𝑎(𝑡) at 𝑡 = 0,
and its dimension is different from 𝑎(𝑡) and 𝑎sat although they all are named “yields”⁵. Table 1 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 𝛼phys
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(𝑇1/2 = 110 min)
reaction at 𝐸0 = 10.0 MeV (𝑎sat = 6.630 GBq/μA, 𝛼phys =
697.5 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
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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) = 𝑎sat (1 − 𝑒−𝜆𝑡 ) = 𝛼phys (1 − 𝑒−𝜆𝑡 )/𝜆.
𝑎(𝑡)
𝑎(𝑡)
𝑎sat = 𝑦
𝛼phys
1
1/(1 − 𝑒−𝜆𝑡 )
𝜆/(1 − 𝑒−𝜆𝑡 )
𝑎sat = 𝑦
(1 − 𝑒
1
𝜆
−𝜆𝑡
𝛼phys
)
(1 − 𝑒−𝜆𝑡 )/𝜆
1/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
𝛼phys gives the slope of the growing curve 𝑎(𝑡) at the beginning of irradiation [26]. If the half-life of the product
𝑇1/2 = ln 2/𝜆 is long compared to the irradiation time (i. e.,
𝜆𝑡 ≪ 1), the EOB thick target yield 𝑎(𝑡) in Eq. (10) can be
approximated by a linear function of the irradiation time 𝑡:
𝜆𝑡≪1
𝑎(𝑡) = 𝛼phys (1 − 𝑒−𝜆𝑡 ) /𝜆 ≃ 𝛼phys 𝑡,
(11)
which gives a formula for derivation of the physical thick
target yield,
𝜆𝑡≪1
𝛼phys = 𝑎(𝑡)𝜆/ (1 − 𝑒−𝜆𝑡 ) ≃ 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 𝑇1/2 , irradiation time 𝑡, their ratio as well as
correction factors for conversion of the thick target yields in [29, 30]
to the corresponding physical thick target yields (𝐶1 ) and 1-hour
end-of-bombardment (EOB) thick target yield (𝐶2 ).
Products
97
Ru
Tc
95
Tc
93
Mo
149
Tb
150
Tb
151
Tb
149
Gd
96
𝑇1/2 (h)
𝑡 (h)
𝑇1/2 /𝑡
𝐶1
𝐶2
67.9
102.7
20.0
6.9
4.1
3.5
17.6
9.3
6
6
6
6
9.3
9.3
9.3
9.3
11.3
17.1
3.3
1.2
0.4
0.4
1.9
1.0
1.03
1.02
1.11
1.33
1.98
2.19
1.19
1.39
1.03
1.02
1.09
1.27
1.83
1.99
1.17
1.34
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 𝐶1 = 𝑡𝜆/(1−𝑒−𝜆𝑡 ) and 𝐶2 = 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
thick target 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⋅h interpreting 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., “1hour 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 are convenient for
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 existUnauthenticated
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N. Otuka and S. Takács, Definition of radioisotope thick target yields
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., beam energy 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. M. Qaim (Forschungszentrum Jülich, Germany)
and Dr. G. F. Steyn (iThemba LABS, South Africa) as well
as the reviewers for careful reading of our manuscript
and for the detailed comments on it. We are indebted
to Dr. R. A. Forrest (IAEA NDS) for a careful reading of
the manuscript and also for Dr. M. Maiti (Saha Institute
of Nuclear Physics, India) for clarifying the definition
of the yields published in [29, 30]. We are also grateful
for contributions from IAEA Member States to organize
the international collaboration on the EXFOR library
development.
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