In this study deuteron induced nuclear reaction on ²⁰Ne target was studied to get nuclear information about ¹⁸F and ²¹Na radioisotopes which are widely used in medical and nuclear reactor technologies respectively. This nuclear reaction is important to get nuclear data since the produced radioisotope is widely used in nuclear medicine due to its appropriate short half-life and positron emitter. The main objective of the study was to analyse and interpret the behaviour of the resulting reaction cross section. It also aimed to compare the computed theoretical result with the experimental data retrieved from IAEA EXFOR for its validity. From such nuclear reaction, the reaction cross sections of ²⁰Ne(d, α)¹⁸F, ²⁰Ne(d, x)¹⁸F, and ²⁰Ne(d, n)²¹Na reaction channels were computed using a nuclear computational code called COMPLET. The computed reaction cross sections for each channel were found in good agreement with the experimental data within the specified energy range and show a strong correlation as assessed by Pearson’s correlation coefficient. The analysis of the result shows that compound nucleus reaction is found the dominant reaction mechanism at the lower energies of the projectile.

Reaction cross section, compound nucleus, nuclear medicine, fluorine, EXFOR

The study of nuclear reactions nowadays has become the interest of scientists and researchers. Nuclear physics has now put its crucial importance starting from cosmological studies to the microscopic study of nature. The eagerness of human beings to live in the new world and know deep space, celestial bodies like stars, planets, asteroids, the sun, and so forth calls for the knowledge of nuclear reactions (Agency 2005). A nuclear reaction is an important process to produce new nuclei for different applications (Kebede 2021). A nuclear reaction is the process in which two nuclear particles (a nucleon with a nucleus or a nucleus with a nucleus) get into close contact with one another and produce two or more nuclear particles or γ-rays and a residual nucleus (Agency 2017). In order for a nuclear reaction to occur, the incident projectile particle interacts with the target nucleus for which the projectile should move with enough energy to overcome the electromagnetic repulsion from the protons of the target. The probability for a given nuclear reaction to occur depends on the reaction cross section which is the effective area upon which the event takes place (Heyde 2020). There are different types of nuclear reaction mechanisms based on the time taken for intra-nuclear collisions of nucleons before the statistical equilibrium is reached and based on the energy of the incident projectile particle (Unnati et al. 2005). Direct nuclear reaction is called a fast reaction where the interaction ends with of the order of ~ 10⁻²² seconds which takes place at a high projectile energy of 200 MeV /nucleon (Sabir Ali 2016) whereas in compound reaction, the incident projectile particle is captured by the target nucleus, forming a compound nucleus in a highly excited unstable state and the interaction between the nucleons of the target and the projectile takes relatively long time scales of 10⁻¹⁸ s and the energy and momentum of the projectile is shared and re-shared among the nucleons of the compound nucleus until statistical equilibrium is achieved. This reaction mechanism is called a slow reaction which takes place at a low projectile energy (Heyde 2020). In a pre-equilibrium nuclear reaction, the incident projectile particle is captured by the target nucleus and a composite system is formed, but particles are emitted prior to the establishment of statistical equilibration of the system. Pre-equilibrium reaction is a bridge between the two extremes, which is neither direct nor compound nucleus reaction, and hence the interaction time scale is intermediate between the very fast direct reactions and the relatively slow compound nucleus formation (10⁻²² s < t < 10⁻¹⁸ s) (Stock 2013). This reaction mechanism becomes dominant at the intermediate energy of the projectile of 20–200 MeV/nucleon (Sharma et al. 2004).

Radioisotope production through nuclear reaction by bombardment of the target nucleus using light particles has attracted significant attention, due to the rising applications of nuclear physics in many fields such as in nuclear medicine, environmental science, agricultural science, and industrial application (Yiğit and Tel 2014). In the present study, a deuteron-induced nuclear reaction was studied to produce a radioisotope that is used in medical applications and scientific research. Radionuclides are useful for a variety of applications in nuclear medicine, such as for radiation therapy, diagnosis, prevention of many serious ailments, and for research to evaluate physiologic, pathologic, and metabolic conditions of the human body (Noori et al. 2018). The successful production and usage of radionuclides also extend to areas such as oncology, cardiology, and even psychiatry by producing the detailed image of the internal organs where information about the function of every organ and or tissue of the human body can be clearly generated (Weber et al. 2020). Positron Emission Tomography (PET) is a nuclear medicine imaging technique that requires positron-emitting radioisotope to produce a three-dimensional image of the details of the internal organ. It is used for early diagnosis of cancer and evaluation of the treatment response in patients with cancer and for the evaluation of diseases like heart, brain, thyroid, etc (Noori et al. 2018). The desired radionuclide is injected or swallowed by mouth or inhaled as a gas (with aerosols) or it can also be injected through a vein and accumulates in the target tissue. As it decays, it emits a positron, which combines with a nearby electron through annihilation which results in the emission of gamma rays. The gamma radiation is then detected by a PET detector and further analyzed by software in a computer. Fluorine is the most common radioisotope used in PET (Şentürk et al. 2022). Fluorine has several isotopes; ²¹F, ²⁰F, ¹⁹F, ¹⁸F, and ¹⁷F. Except ¹⁹F, all of its isotopes are radioactive and have very short half-lives which are preferable for scientific applications. Especially ¹⁸F is widely used in PET because of its short half-life (109.8 min) and positron emission (Alauddin 2011). It can emit gamma rays of sufficient energy to escape from the body and have an appropriate half-life which is short enough to decay completely soon after imaging is completed. According to Cancer Statistics 2021, more than 9 million deaths every year worldwide are due to cancer and according to the Global Cancer Observatory; about 15–17 million new cancer cases are recorded every year, out of which 60% are from the developing countries (Chakravarty and Chakraborty 2021) and such statistics calls for the need of scientific treatment.

In the majority of the cases, radionuclides can be artificially produced using reactor and particle accelerators (Bekele 2022). These two methods of preparation of a radioisotope require very expensive technologies and research facilities, and they are not easily accessible. It is practically and economically difficult to determine the necessary nuclear information, such as reaction cross section and nuclear reaction mechanism for all isotopes in the periodic table for different ranges of energies. Therefore, theoretical nuclear reaction models play a crucial role in the determination of reaction cross-sections when there is a shortage of experimental facilities (Zinabe Kebede 2021). For the maximization of the yield of the desired radioisotope and to minimize the radioactive impurities, it is important to handle the necessary nuclear data, such as reaction cross-section and the possible nuclear reaction mechanisms upon which the reaction can take place for all elements in the entire periodic table for different ranges of energies for the selection of appropriate radionuclides for various applications (Gandhi et al. 2019; Tsega Alemu and Asradew 2021). In the present study, the calculations of the reaction cross-section were performed for a deuteron induced reaction on ²⁰Ne as a target to produce a medically important nuclide called ¹⁸F using a nuclear simulation code called COMPLET (Cherie Sisay and Teshagre Aklie 2023). The reaction mechanisms can be determined from the plot of excitation function (Bekele 2022). The results of the theoretical excitation function of the reactions were compared with the experimentally obtained results from the IAEA EXFOR database for accuracy and validation (Ejerso et al. 2023).

The theoretical nuclear reaction cross-section of deuteron-induced reaction on ²⁰Ne was calculated using a nuclear computational computer code called COMPLET. The resulting excitation function is used to reveal the nuclear reaction mechanisms. The resulting data has been arranged in proper order and organized in figures. Origin and spreadsheet were used for graphical and analytical purposes. The COMPLET code is a nuclear reaction computer program that is written in the FORTRAN programming language and which is important to studying reaction cross-section and reaction mechanisms (Escher et al. 2012) when it is impossible to measure the reaction cross-sections due to the experimental difficulties. COMPLET code is an improved version of ALICE-91 (Cherie Sisay and Teshagre Aklie 2023). This code is capable of calculating Compound (equilibrium) and pre-equilibrium reaction cross-sections that are induced by neutrons, protons, deuterons, tritons, ³He, and alpha particles in the energy range from up to 300 MeV (Asres et al. 2018). The projectile energy is measured in Mega Electronvolt (MeV) and the reaction cross-section is measured in millibarn (mb) (Mekonen and Rao 2023).

The code is based on different models; the geometry dependent hybrid model is used in the calculation pre-equilibrium emission of course it is a version of the earlier Hybrid model whereas Weisskopf-Ewing model is used for compound nucleus emission (Yiğit, Tel, and Sarpün 2016) and those models are based on different adjustable nuclear parameters. The various parameters are used for calculations of excitation functions that influence the shape and the height of the calculated excitation functions. The nuclear level density parameter affects the reaction cross section of the compound nucleus reaction. The level density parameter ‘a’ is calculated using the relation a = ACN/K, where ACN is the mass of the compound nucleus and K is the free constant which varies to get the best fit to experimental results (Cherie Sisay and Teshagre Aklie 2023). The K value was varied from 8 to 12 and a best fitted level density parameter is chosen for each reaction channel.

The other main parameter is exciton number n which plays an important role in the calculation of pre-equilibrium reactions which accounts for the particles above and holes below the Fermi level (sea) (Bekele 2022). The value of n was varied from 2 to 5 and a best fitted one was selected. Even though the above parameters were varied like this to match the experimental data, in the present work, all calculations and analysis were performed consistently using level density (K = 10) and initial exciton number (n = 2) as shown in Figs 1–3 from which the best fitted excitation functions were generated. In addition to the above mentioned input parameters, during the calculation of the theoretical reaction cross section, the simulation takes different input parameters like a projectile mass number and atomic number, target mass number and atomic number, the energy range of the projectile, and their values were given to the code accurately (Ejerso et al. 2023).

Figure 1. 

Parameters for ²⁰Ne(d, α)¹⁸F reaction channel.

Figure 2. 

Parameters for ²⁰Ne(d, x)¹⁸F reaction channel.

Figure 3. 

Parameters for ²⁰Ne(d, n)²¹Na reaction channel.

The calculated theoretical reaction cross sections for each channel are shown in Figs 4–6. The obtained results were then compared with the experimental data obtained from the EXFOR database. EXFOR which stands for ExchangeFormat was designed by IAEA for the collection, exchange, and dissemination of neutron or charged particle induced experimental nuclear reaction data (Zerkin and Pritychenko 2018) under the aim of making these data available to global researchers in support of nuclear-related applications. It is freely accessible for research, innovation, development, and dissemination (Ahmad and Koki 2017).

Figure 4. 

Comparison of theoretical and experimental cross section for ²⁰Ne(d, α)¹⁸F reaction.

Figure 5. 

Comparison of theoretical and experimental cross section for ²⁰Ne(d, x)¹⁸F reaction.

Figure 6. 

Comparison of theoretical and experimental cross section for ²⁰Ne(d, n)²¹Na reaction.

To compare the theoretical and experimental cross-section results, the researchers apply the Pearson’s correlation coefficient (R) (Asres et al. 2018).

$\text{R}=\frac{{\sum }_i^N(X_{ti}-X_t)(X_{ei}-X_e)}{N-1\left(S_{xt}\right)\left(S_{xe}\right)}$

Where R is unitless in which its value lies between -1 and 1 to show that the results of the study are either positively or negatively correlated with the experimental data or not correlated if R = 0. X_t and X_e are the mean theoretical and experimental reaction cross-sections respectively, X_ti and X_ei are the theoretical and experimental reaction cross-sections of the i^th value respectively, N is the number of the theoretical and experimental data, S_xt and S_xe are the standard deviation of the theoretical and experimental total cross-sections respectively. If 0 < R < 0.3, the correlation is weak and positive, 0.3 ≤ R < 0.7 represents moderate correlation and 0.7 ≤ R < 1 represents strong and positive correlation and the same is true on the negative values of R (Cherie Sisay and Teshagre Aklie 2023).

In this study, the excitation functions of deuteron induced nuclear reaction on ²⁰Ne were calculated using COMPLET simulation code. Such nuclear reaction may result in the following reaction channels; ²⁰Ne(d, α)¹⁸F, ²⁰Ne(d, x)¹⁸F, and ²⁰Ne(d, n)²¹Na. The experimental data of the reaction cross-section of these reaction channels was taken from (Fenyvesi et al. 1997), (Backhausen, Stöcklin, and Weinreich 1981), and (Helus et al. 1986) respectively from IAEA EXFOR data library. The projectile energy range for the calculation of the theoretical reaction cross-section of all of these channels was the same as the energy range used for experimental reaction cross-section determination available from IAEA EXFOR data center. The excitation function which is the plot of reaction cross-section versus projectile energy of these three reaction channels for Compound Nucleus (CN) and Pre-equilibrium (PE) reactions together with their experimental data from EXFOR are shown in Figs 4–6. As shown from the plots, both of the theoretically calculated reaction cross-sections of compound nucleus and pre-equilibrium using COMPLET code and the experimental reaction cross-section taken from IAEA, EXFOR data library shows similar patterns for the same energy range of the projectile. In addition, the correlation coefficient (R) was calculated for both compound nucleus and pre-equilibrium reaction cross-sections and the result shows the correlation is strong and positive. Therefore, our measured values are in good agreement with the experimental result.

Furthermore, because the adjustable parameters are very important in Fermi gas model, the parameters were varied to get the best fitted reaction cross-sections. For this reason, the reaction cross-sections were recorded by varying the input parameters repeatedly, and a plot was made for each to compare with the experimental data. Therefore, as shown in Figs 1–3, n = 2 and K = 10 result a good fit with the experimental results.

The reaction cross sections of the deuteron-induced reactions on ²⁰Ne were calculated for interpreting the contributions of the compound and pre-equilibrium processes on the reaction mechanisms. Thus, the excitation functions of ²⁰Ne(d, α)¹⁸F, ²⁰Ne(d, x)¹⁸F, and ²⁰Ne(d, n)²¹Na nuclear reactions were calculated using the nuclear computer code called COMPLET code for the production of ¹⁸F and ²¹Na radioisotopes which are crucial for medical applications and as a coolant in fast breeder nuclear reactors respectively. For all these reaction channels, the theoretical cross sections of the compound nucleus and pre-equilibrium reaction were compared with the experimental values that were retrieved from IAEA EXFOR library. The input parameters such as the level density parameter and initial excitation number were properly chosen to get best fit reaction cross section with the experimental results. The results of the study show that the theoretically calculated excitation functions for the reaction channels are in good agreement with the corresponding experimental excitation functions within the same energy range. This indicates that COMPLET code can fill the gap of generating nuclear data when there is a lack of experimental equipment. The results of the study are also show that the compound nucleus reaction mechanism is dominant in the lower energies of the projectile as compared to the pre-equilibrium reaction, as it has been observed in the graphs of all reaction channels it has a better fit to the experimental data.

The authors would like to express their sincere gratitude to Department of Physics, Debre Markos University, Ethiopia for giving a chance to join, attend, and providing facilities for carrying out this research. The authors wish to express their gratitude to all those who contributed in various ways to make this work a reality.