































Microsoft Word - Tiguaded_ Theoretical Model Predictions for Production of Medically Used Radionuclides _DOI


East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, Issue. 1, 1-12 
 

 

 

 

 

 

Theoretical Model Predictions for Production of Medically Used Radionuclides on Alpha Induced 

with Cobalt-59 At Energies of 25 - 172 MeV 

 

 

Department of Applied Physics, Hawassa University, P.O.Box 05, Hawassa, Ethiopia 
 

 
KEYWORDS:  

COMPLET code; Excitation 

function; Radionuclide 

production; Reaction cross 

section; TALYS-1.95 code  

 

 

 

 

ABSTRACT 

This study used the theoretical nuclear model codes COMPLET and TALYS-1.95 to make 
theoretical predictions of the medically important production cross-sections for 
Chromium-51, Manganese-54, Iron-59, Cobalt-59 and Cobalt-60 radionuclides produced 
in the interaction of alpha- projectile with Cobalt-59 target ≈ 25 – 172 MeV alpha-
energies. The results were compared with the measured values in the EXFOR data library. 
Pearson's correlation coefficient indicates a strong and positive correlation between the 
predicted and the previously measured medically important production cross-sections for 
Chromium-51, Manganese-54, Iron-59, Cobalt-59, and Cobalt-60 radionuclides. Further, 
the results showed that except for Chromium-51, the COMPLET code predicts more 
successful outcomes than the TALYS-1.95. 

  

 

INTRODUCTION 

Nuclear reaction cross-section data are very 
important to the field of medical radiobiology in 
both diagnostic imaging and targeted therapy 
(Kebede, 2021), which is crucial for the 
optimized production of radionuclides. In 
nuclear medicine, radionuclides are used for 
various useful applications, such as diagnosis, 
therapy, prevention of many serious ailments, 
and research to evaluate metabolic, physiologic, 
and pathologic conditions of the human body 
(Aydin et al., 2007). The successful production 

and usage of these radionuclides extends to 
oncology, cardiology, and even psychiatry 
through imaging procedures where information 
about the function of every major organ and 
tissue of the human body can be generated. 
Many radionuclides used in nuclear medicine 
are produced in cyclotrons, accelerators, or 
nuclear reactors, and production is an important 
and constantly evolving issue. In addition to 
this, different radionuclides play significant 
roles in technological applications of 
importance to our daily lives and scientific 
research (Aydin et al., 2007; Kilinç et al.,2016). 

Journal homepage : https://journals.hu.edu.et/hu-journals/index.php/eajbcs 
  

East African Journal of Biophysical and Computational Sciences 

 
*Corresponding author: 
  Email: a_fessahatsion@yahoo.com  +251911567435 https://dx.doi.org/10.4314/eajbcs.v5i1.1S 
 

Y. Tiguaded, F. K. Amanuel* 

 
Research article



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

2 

The Positron Emission Tomography (PET) 
imaging technique is widely used for planning, 
early diagnosis of cancer, and evaluation of the 
treatment response in patients with cancer. This 
imaging technique is also used to study diseases 
of the heart, brain, thyroid, etc. (Noori et al., 
2017) for example, Cobalt-57(T1/2 =272 d) is 
used as a marker to estimate organ size and for 
in vitro diagnostic kits. Similarly, Chromium-51 
radionuclide (T1/2=28 d) is used to label red 
blood cells and quantify gastro-intestinal protein 
loss (Aydin et al., 2007; Kilinç et al., 2016). 
Production cross sections for charged particles, 
especially nuclear reactions on metals that are 
induced by alpha, are important in medical 
radioisotope production (Mohamed, 2006; 
Demir et al., 2017). Accordingly, reasonable 
comparative theoretical reaction model studies 
with an experiment using light-charged 
projectiles (proton, deuteron, and alpha) are 
beneficial (Qaim et al., 2016; Tárkányi et al., 
2019; Amanuel, 2023) because of the non-
availability of experimental cross-section data 
for the production of medical radionuclides, 
particularly in alpha-induced reactions, which 
are limited and still need further investigations. 
To optimize the production routes, charged 
particle-induced cross-sections are desired. To 
optimize the radioisotope produced, a full 
knowledge of the excitation function is 
necessary, which helps maximize the yield of 
the desired product and minimize the 
radioactive impurities (Qaim et al., 2002). 

In radionuclide production, accurate reaction 
cross-section data are required for well-
controlled and maximized production routes 
(Mohamed, 2006; Qaim, 2010). Nuclear 
reaction model-based computer codes can be 
essential in predicting production cross-sections, 
particularly for radionuclides whose 

experimental data are either unavailable or have 
significant discrepancies. In addition, theoretical 
model predictions have played a crucial role in 
creating optimized reference cross-section data, 
particularly in producing medically useful 
radionuclides (Koning et al., 2013) that were 
calculated using the Monte Carlo nuclear 
reaction simulation codes TALYS 1.95 and 
COMPLETE.  

Despite all efforts, one of the crucial aspects of 
the reaction mechanisms study is finding 
optimized production routes for radionuclides, 
particularly for medically used radionuclides. 
Moreover, it is evident that the non-availability 
of experimental cross-section data for producing 
medically useful radionuclides, particularly in 
alpha-induced reaction, are very limited and 
need further investigation. Therefore, the 
present work focuses on finding optimized 
production routes for medically useful 
radionuclides produced in the reaction of α-
projectile with 59Co-target, more specifically, to 
evaluate the nuclear data for the production of 
Chromium-51, Manganese-54, Iron-59, Cobalt-
59, and Cobalt-60 on alpha-induced Cobalt-59 
at alpha energy of positron-emitting 
radionuclides. 

MATERIALS AND METHODS  
 

Several theoretical nuclear reaction model-based 
computer codes have been used to predict 
radionuclide production cross-sections (Koning 
et al., 2013; Amanuel, 2023). In this work, 
predictions of production cross sections for 51 
Cr, 54Mn, 59Fe, and 57,60Co radionuclides 
produced in the interaction of alpha-projectile 
with Cobalt-59 target via (a, x) channel were 
carried out using the computer codes TALYS-



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

3 

1.95 and COMPLETE. The results were 
compared with the experimental data (Michel et 
al., 1980).  

These codes were prefered because they have 
been successful and widely used for predicting 
production cross-sections and evaluating 
reaction data (Amanuel, 2023). The present 
work also used the default values of the level 
density nuclear model TALYS-1.95 computer 
codes. 

TALYS-1.95 Code 

TALYS-1.95 code is an advanced version of the 
TALYS code family with additional features. 
TALYS was first developed in 1998, aiming to 
consolidate the understanding of nuclear 
reactions into a single software tool. This 
program integrates various models—including 
pre-equilibrium, direct, optical, statistical, and 
fission nuclear reaction models—enabling 
predictions across all open reaction channels 
within one calculation framework (Qaim et al., 
2016). The Monte Carlo reaction code simulates 
various types of nuclear reactions, operating on 
a Linux system and written in FORTRAN. A 
significant advantage of employing a Monte 
Carlo method for nuclear data evaluation is its 
ability to extract a series of correlations from 
prior results. Consequently, the code was 
developed with the objective of delivering a 
comprehensive and accurate simulation of 
nuclear reactions involving neutrons, photons, 
protons, deuterons, tritons, 3He, and alpha 
particles within the energy range of 1 keV to 
200 MeV, with a few exceptions. The data 
generated or used by the code developed for the 
Monte Carlo method is derived from a reference 
input parameter library, combining reliable 

nuclear models with a focus on resilience and 
user-friendliness (Koning et al., 2013).  

The theory of excitation functions for the 
generation of medical radioisotopes are obtained 
with alpha-induced reactions (a,x) for some 
radioisotopes used in clinical medicine that are 
relevant for the development of better nuclear 
reaction theory and for several medical 
applications were computed by using TALYS 
1.95 code. In general, the reaction cross section 
for entrance channel α and exit channel β of this 
code can be expressed, using Hauser-Feshback 
(Hauser-Feshback, 1952) formalism as follows: 

σαβ =
π

k2 ∑
(2J+1)

(2iα+1)(2Iα+1)J
∑ Tℓs,ℓ (α) ∑ Tℓ

,
s,,ℓ

, (β)

∑ ∑ Tℓs,ℓ (α)α
      (1) 

Where s is the channel spin, Tℓrepresents the 

transmission coefficients, and l is the orbital 
angular momentum. The Hauser-Feshback 
formula is simplest for the energy-average angle 
integrated cross-section of statistical reactions 
(reaction cross-section leading to a single final 
state). 

COMPLETE code 

Computer code COMPLETE is a revised and 
improved version of the Alice code family with 
additional physics, corrections, and 
competencies and has been used to predict 
production cross-sections (Asres et al., 2018). 
This code has successfully predicted several 
nuclear data sets, particularly for the production 
of radionuclides used in nuclear medicine 
medical (Yiğit and Tel, 2013; Asres et al., 
2019). This code utilizes the Weisskopf-Ewing 
(Weisskopf and Ewing, 1940) formulation for 
compound nucleus (CN) emission, along with 
Blann’s hybrid and geometry-dependent hybrid 
models for particle emission (PE) (Blann and 



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

4 

Vonach, 1983). In the complete code, level 
densities of residual nuclei play a crucial role in 
deciding the shapes and absolute values of 
excitation functions (Akkoyun et al., 2015). 
This code uses the Weisskopf-Ewing 
formulation to predict reaction cross-sections as 
follows: 
 

σ dε = σ (α)
( ) ( ) ( )

∑ ∫ ( ) ( ) ( )
    (2) 

Where u  is the reduced mass of the ejectile α, 
and σ (α) is the cross-section for the 
production of the CN. 

Comparison between experimental and 
Theoretical results 

As shown in figures 1–5, the theoretical and 
experimental reaction cross-sections are 
represented in relation to the projectile energies. 
Pearson's correlation coefficient quantifies the 
level of mutual statistical dependence between 
two variables (Baak et al., 2020). Typically, 
their values range from -1 to +1 or 0 to +1, 
where 0 means no statistical association, +1 
means the strongest possible association, and −1 
means the strongest negative relation. 

In general, the data of this study have been 
analyzed after the theoretical data have been 
generated using the computer codes TALYS-
1.95 and COMPLETE. The theoretical and 
experimental total cross-section results are 
compared using Pearson's correlation 
coefficient. Correlation is a measure of 
association between two variables. The 
mathematical description is given by Tárkányi 
et al. (2019). 

     

R=
∑ (XTi

−<XT>)(XEi
−<XE>)N

i=1

(N−1)(SXT)(SXE)
   (3) 

 Where ; 

  < X >= ∑ X                      (4) 

   S =

∑ (X −< X >)            (5)   <

X >= ∑ X                    (6) 

 S = ∑ (X −< X >)            (7) 

Where R is the correlation coefficient and unit 
less, 〈XT〉 and 〈XE〉 are the mean theoretical and 
experimental reaction cross-sections, 
respectively, X and X  are the theoretical and 

experimental total cross-sections of the i  
value, respectively, whereas N is the number of 
the theoretical and experimental data, and SXE 
and SXT are the standard deviations of the 
experimental and theoretical total cross-
sections, respectively. If 0 ≤ R ≤ 0.3, the 
correlation is weak and positive, 0.3≤R ≤ 0.7 
describes a moderate correlation, and 0.7 ≤ R 
≤1, the correlation is strong (Baak et al., 2020).  

RESULTS AND DISCUSSION 

The current work investigated the excitation 
functions of medically important Chromium-51, 
Mangenes-54, Iron-59, Cobalt-59, and Cobalt-
60 radionuclides produced in the interaction of 
alpha-projectile with Cobalt-59 target at 25–172 
MeV alpha-energies. In addition, the 
experimentally measured excitation functions 
available in the literature (Michel et al., 1980) 
were compared using the nuclear reaction-
model codes TALYS-1.95 and COMPLET.  



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

5 

In COMPLETE code, the level density 
parameter a, which predominantly influence the 
equilibrium state components of a cross-section, 
is computed from the expression: 

         𝑎 =                                           (8) 

Where A is the nucleon number of a compound 
system, and K is an adjustable constant, which 
may be varied to match the experimental data. 
For the present system, a representative 59Co (α, 
x) 60Co reaction, the value of K was varied (K = 
values of 8, 10, and 12 were used) to match the 
experimental data. A value of K = 10 in general 
reproduced satisfactorily experimentally 
measured EFs for Cobalt-60 residue. This value 
is consistently used for other residues populated 
in the interaction of the alpha-projectile with the 
target Cobalt-59. For the same representative 
Cobelt-60 residue, the initial exciton numbers no 
= 4 (2,2,0), 5 (2,2,1) were varied, and it was 
found that a value of no = 4 (2,2,0) better 
reproduced the measured excitation function 
(Michel and Brinkmann, 1980). For 
COMPLETE code prediction, K = 10 and no = 4 
are consistently used for all residues populated 
in the interaction of the alpha-projectile with the 
target Cobalt-59. 

Production of Chromium-51 radionuclide 

Figure 1 illustrates the excitation functions for 
the Chromium-51 radionuclide, which were 
predicted theoretically and measured 
experimentally, as produced through the (α, x) 
channel during the interaction of the alpha 
projectile with the Cobalt-59 target. By using 
the TALYS-1.95 code, predicted cross-section 
values, except at alpha energies of 90–120 
MeV, are in very good agreement with the 
measurements of Michel and Brinkmann (1980). 
It may further be seen that COMPLETE code 
predicted cross-section values that were 
generally in satisfactory agreement with the 
measured values of Michel and Brinkmann 
(1980). 

Table 1 reveals that the Pearson's correlation 
coefficient values for the cross-section 
predictions from TALYS-1.95 and the 
COMPLETE code indicate a strong positive 
correlation between the theoretically predicted 
and experimentally measured production cross-
sections (Michel and Brinkmann, 1980). 

 

 



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

6 

 

Figure 1. The experimentally measured and theoretically predicted excitation functions for 
medically used Crominum-51. 

Production of Manganese-54 Radionuclide 

The experimentally quantified production cross-
sections for Manganese-54 radionuclide from 
the existing literature are compared with the 
theoretical predictions obtained using the 
COMPLET and TALYS-1.95 codes. Figure 2 
shows the quantified excitation functions along 
with theoretical predictions for Manganese-54 
radionuclide produced through the (𝛼, x) 
channel in the interaction of alpha-projectile 

with a Cobalt-59 target at 25 MeV–172 MeV. 
Using COMPLETE code, predicted cross-
section values except for 60 MeV–90 MeV are 
in very good agreement with the cross-section 
values measured by Michel and Brinkmann 
(1980). Figure 2 shows that the predicted cross-
section values using the TALYS-1.95 code 
generally minimize the measured values of 
Michel and Brinkmann (1980). The 
COMPLETE code predicted production cross 
sections for Manigenes-54 radionuclide to have 
a peak value of 111 mb at ≈170 MeV. 

60 80 100 120 140 160 180
0.1

1

10

100

1000 59Co(,x)51Cr

  
(m

b
)

E
Lab

(MeV)

 Michele & Brinkmann,1980
 COMPLETE
 TALYS-1.95



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

7 

Furthermore, it may be observed from Table 1 
that, for Manganese-54 radionuclide, Pearson's 
correlation coefficient values between 
theoretically anticipated on COMPLETE and 
experimentally quantified production cross 
sections confirmed moderately positive 

correlations. In contrast, Pearson's correlation 
coefficient values between theoretically 
predicted using TALYS-1.95 and 
experimentally quantified production cross-
sections confirmed strong positive correlations. 

 

 

 
Figure 2. The experimentally measured and theoretically predicted excitation functions for 
medically used Manganese-54. 

Production of Iron-59 radionuclide 

Figure 3 shows the experimentally quantified 
excitation functions along with theoretical 
predictions obtained using TALYS-1.95 and 
COMPLETE codes for Iron-59 radionuclide 
produced via (α, x) channel in the interaction of 

alpha-projectile with the Cobalt-59 target. Using 
COMPLETE code, the predicted cross-section 
values in the energy range 55–172 MeV usually 
agree with the experimental measurements of 
Michel and Brinkmann (1980). However, the 
prediction of COMPLETE code below 55 MeV 

30 60 90 120 150 180
0.1

10

1000 59Co(, x)54Mn

  
(m

b
)

E
Lab

(MeV)

 Michel & Brinkmann,1980
 COMPLETE
 TALYS-1.95



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

8 

underestimates the cross-section values 
measured by Michel and Brinkmann (1980). It 
may further be observed from Figure 3 that the 
predicted cross-section values at low energy 
using the TALYS-1.95 code are in satisfactory 
agreement with the measured cross-section 
values of Michel and Brinkmann (1980). On the 
contrary, the predicted cross-section values at a 
high energy range using the TALYS-1.95 code 

underestimate the measured cross-section values 
of Michel and Brinkmann (1980). 

Moreover, Table 1 further reveals that the 
Pearson's correlation coefficient values for the 
Iron-59 radionuclide indicate strong positive 
correlations between the cross-section values 
predicted by the COMPLETE code and those 
measured by Michel and Brinkmann (1980).

 

 
Figure 3. The experimentally measured and theoretically predicted excitation functions for 
medically used Iron-59.  

Production of Cobalt-57 radionuclide 

In Figure 4, the measured excitation functions 
for the medically used Cobalt-57 radionuclide 
produced via the complex (α, x) channel in the 

interaction of alpha-projectile with Cobalt-59 
target are clearly presented along with the 
theoretically predicted excitation functions by 
using the TALYS-1.95 and COMPLETE codes. 
Using COMPLETE code, predicted production 

30 60 90 120 150 180
1E-3

0.1

10

1000 59Co(, x)59Fe

 
(m

b
)

E
Lab

(MeV)

 Michel & Brinkmann, 1980
 COMPLETE
 TALYS-1.95



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

9 

cross-sections are in very good agreement with 
the measured values of Michel and Brinkmann 
(1980). Using the TALYS-1.95 code, predicted 
production cross sections in the energy range 30 
MeV–90 MeV are in very good agreement with 
the measured values (Michel and Brinkmann, 
1980). However, predicted production cross 
sections using the TALYS-1.95 code at energies 
above 90 MeV are in satisfactory agreement 
with the measured values of Michel and 

Brinkmann (1980). The COMPLETE predicted 
production cross sections for Cobalt-57 
radionuclide have a maximum value of ≈207 mb 
at ≈39 MeV. Furthermore, Table 1 clearly 
shows and confirmed that Pearson's correlation 
coefficient values for Cobalt-57 radionuclide 
has strong and positive correlations between the 
cross-section values predicted and the values 
measured by Michel and Brinkmann (1980). 

 

  

Figure 4. The experimentally measured and theoretically predicted excitation functions for 
medically used Cobalt-57  

Production of Cobalt-60 Radionuclide 

Figure 5 displays the experimentally quantified 
and theoretically predicted excitation functions 
for the medically used Cobalt-60 radionuclide 

produced in alpha-projectile interaction with the 
Cobalt-59 target via complex (α, x) channel. 
The cross-section values predicted using 
COMPLETE codes usually exaggerate the 
cross-section values measured by Michel and 

30 60 90 120 150 180
0.1

1

10

100

1000 59Co(, x)57Co

  
(m

b
)

E
Lab

(MeV)

 Michel & Brinkmann,1980
 COMPLETE
 TALYS-1.95



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

10 

Brinkmann (1980). However, predicted 
production cross sections in the energy range 30 
MeV – 45 MeV are in very good agreement 
with the measured values of Michel and 
Brinkmann (1980). The prediction of the 
TALYS-1.95 code underestimates the cross-
section values of the measurement of Michel 
and Brinkmann (1980). Moreover, the attainable 

value of the production cross section for Cobalt-
60 radionuclide obtained using the COMPLETE 
code is about ≈343 mb at ≈39 MeV. The result 
on Table 1 further revealed that Pearson's 
correlation coefficient values between 
theoretically predicted, and experimentally 
quantified production cross-sections confirmed 
strong and positive associations. 

 

 

Figure 5. The experimentally measured and theoretically predicted excitation functions for 

medically used Cobalt-60. 

 
 
  

30 60 90 120 150 180
0.1

1

10

100

1000 59Co(, x)60Co

(
m

b
)

E
Lab

(MeV)

 Michel& Brinkmann,1980
 COMPLETE
 TALYS-1.95



East Afr. J. Biophys. Comput. Sci. (2024), Vol. 5, No. 1, 1-12 
 

11 

 
Table 1. Pearson's correlation coefficient, R, between experimental measurements by Michel and 
Brinkmann (1980) and theoretical predictions 
 

Radionuclide TALYS-1.95 [COMPLETE] 
51Cr 0.921  [0.86] 
54Mn 0.65 [0.92] 
59Fe -     [0.84] 
57Co 0.5  [0.76] 
60Co 0.4 [0.96] 

 

CONCLUSION 

Excitation functions for the production of 
radionuclides from the alpha-bombardment of 
Cobalt-59 were studied for alpha-energies from 
25 to 172.5 MeV. The theoretical nuclear 
reaction model codes COMPLET and TALYS-
1.95 were used to logically predict the medically 
important production cross-sections for 
Chromium-51, Mangenes-54, Iron-59, Cobalt-
59, and Cobalt-60 radionuclides produced in the 
interaction of alpha-projectile with Cobalt-59 
target ≈ 25 - 172 MeV alpha-energies. The 
results were compared with the measured values 
in the EXFOR data library. Pearson's correlation 
coefficient shows a robust positive relationship 
between the predicted and previously observed 
production cross-sections for the medically 
relevant radionuclides Chromium-51, Iron-59, 
Manganese-54, Cobalt-59, and Cobalt-60. 
Further, the results show that except for 
Chromium-51, the COMPLETE code predicts 
more successful outcomes than the TALYS-
1.95. 

Acknowledgment 

The authors thank Dr Zelalem A. for his helpful 
scientific discussions on the present work. 

However, all opinions and any errors are the 
author's responsibility alone.   

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