UMYU Scientifica

A periodical of the Faculty of Natural and Applied Sciences, UMYU, Katsina

ISSN: 2955 – 1145 (print); 2955 – 1153 (online)

ORIGINAL RESEARCH ARTICLE

Estimation of the Production Cross Sections of Medical ⁶¹Cu Radioisotope Using EXIFON Code

Emmanuel J. Adoyi¹, Olumide O. Ige¹, Sunday A. Jonah², Abel B. Olorunsola³ and Abraham F. Olalowo⁴

¹Department of Physics, Nigerian Defence Academy, Kaduna, Kaduna State, Nigeria

²Centre for Energy Research and Training, Ahmadu Bello University, Zaria, Nigeria

³Department of Physics, Faculty of Science, University of Abuja, FCT Abuja, Nigeria

⁴School of Preliminary Studies, Faculty of Science, Nile University of Nigeria, Abuja, Nigeria

*Corresponding Author: Emmanuel J. Adoyi jeadoyi@nda.edu.ng

ABSTRACT

PET relies on short-lived radionuclides, such as ¹⁸F-FDG, but their limited half-lives limit clinical applications. Copper-61 (⁶¹Cu), a promising non-standard positron emitter with a T_1/2 of 3.33 hours, offers advantages for imaging slower biological processes. This study evaluates the cross-sections for ⁶¹Cu production on enriched nickel targets: ⁶¹Ni(p,n)⁶¹Cu and ⁶²Ni(p,2n)⁶¹Cu, using EXIFON 2.0 code. The calculations incorporated shell structure effects and compared the results with those of other studies. For ⁶¹Ni(p,n)⁶¹Cu, the cross-section, showing reasonable comparison of 3.3% with measured data up to 11 MeV but diverging at higher energies, likely due to pre-equilibrium contributions. Comparative analysis revealed ⁶¹Ni(p,n)⁶¹Cu as the optimal route for ⁶¹Cu production, yielding higher cross sections at lower energies, thereby reducing costs and complexity. This work underscores the viability of ⁶¹Ni(p,n)⁶¹Cu for cyclotron-based ⁶¹Cu production and supports its potential for PET imaging.

Key Word: Copper-61, Shell structure effect, EXIFON 2.0 Code, Positron emission Tomography.

INTRODUCTION

Pharmaceuticals that are always positron emitters are used in Positron Emission Tomography (PET). For example, ¹⁸F-FDG (fluorodeoxyglucose) is used as a radiopharmaceutical in glucose metabolism. In the context of staging and therapeutic monitoring in cancer patients, ¹⁸F-FDG is primarily used for whole-body imaging. It is used in pre-clinical studies (cancer research), mapping normal human brain and heart function, and detecting pairs of gamma rays indirectly released by a positron-emitting radionuclide (tracer) (Aslam and Qaim, 2014). The short half-life of many of the radionuclides used in PET limits its widespread applications worldwide. This is because producing the short-lived radionuclide for PET scanning requires a costly cyclotron co-located with the PET facility.

Since any organic carrier for the radioisotope is destroyed by cyclotron bombardment during preparation, the organic radioisotope cannot be synthesized first and then prepared within it. These short-lived positron emitters of light elements are [¹¹C (T_1/2=20min), ¹³N (T_1/2=10min), ¹⁵O (T_1/2=2min), and ¹⁸F (T_1/2=110min)] and are generally found in organic compounds. This restriction primarily limits clinical PET to tracers tagged with fluorine-18, which has a half-life of 110 minutes and can be manufactured at a decent distance before use, unlike other short-lived positron emitters, which decay quickly due to their short half-lives.

More focus is being placed on the creation of non-standard positron emitters, or those with longer lifetimes. These include copper isotopes with a variety of medicinal applications, such as ⁶⁰Cu (T_1/2 = 23.7min), ⁶²Cu (T_1/2 = 9.7min), ⁶⁴Cu (T_1/2 = 12.7h), and ⁶⁷Cu (T_1/2 = 61.8h) (Blower et al., 1996: Anderson et al., 2003: Rowshanfarazad 2006). ⁶¹Cu (T_1/2= 3.33h) is another copper radionuclide that could be useful in nuclear medicine (Szelecsenyi et al., 1993). It decays predominantly by positron emission (Iβ+ = 62%; Eβ+ = 1.159Mev; EC = 38%) with notable ϒ-rays at 283KeV (12%) and 656KeV (10.8%) as companion particles.

⁶¹Cu is considered superior to ⁶⁴Cu for imaging due to its shorter half-life and a more pronounced positron decay branching ratio, which can result in higher image quality. Its rapid optimal uptake within 1-4 hours makes its brief half-life advantageous (McCarthy et al., 1999; Cutler et al., 1999). Moreover, ⁶¹Cu exhibits a similar radiation dosage to ¹⁸FDG (William et al., 2005) and a longer half-life than ⁶⁰Cu and ⁶²Cu, making it suitable for prolonged imaging of slow kinetic processes (Szelecsenyi et al., 2005; Rowshanfarzad et al., 2006). This study investigates nickel targets for ⁶¹Cu production, noting that 61Cu can also be produced on a medical cyclotron from zinc, nickel, or cobalt using proton, deuteron, or alpha particles.

A review of archived cross-sections in the EXFOR database frequently reveals significant discrepancies between different observations, even within the same energy region. While pinpointing the precise causes of these inconsistencies is challenging, they are commonly attributed to uncertainties in factors such as monitor cross-sections, calibration sources, and detector efficiency. To address this, a comprehensive data evaluation process is crucial for generating a reliable, accepted dataset for a specific reaction. Accurate nuclear reaction cross-sections are fundamental for optimizing radionuclide production, evaluating various nuclear models, and deepening understanding of nuclear reaction mechanisms.

The experimental determination of cross-sections for short-lived copper radioisotopes is inherently difficult. Consequently, there has been an increasing focus on production cross-sections calculated using nuclear codes (Uncu and Ozdogan, 2023). However, theoretical model conclusions often lack strong agreement with experimental data. Theoretical calculations are typically adjusted to experimental data using a range of nuclear approximations, including level density, gamma-strength functions, and optical potential models. This reliance on multiple models for calculations leads to variability and uncertainty in cross-section values. Despite the application of various codes and sophisticated statistical analyses to mitigate this issue, the desired outcomes are not consistently achieved (Uncu and Ozdogan, 2023). This investigation will specifically examine the copper-61 production routes via (p,n) and (p,2n) reactions, with EXIFON 2.0 employed for a critical evaluation of their excitation functions.

MATERIAL AND METHODS

H. Kalka developed the EXIFON analytical model from a purely statistical multistep reaction framework. It provides a distinct description of emission spectra, angular distributions, and activation cross sections, encompassing equilibrium, pre-equilibrium, and direct theory processes (both collective and non-collective). The model is grounded in extensive research on Green's function formalism and random matrix physics. The shift from simpler single-step direct models and the basic compound nucleus model to statistical multistep theories was primarily influenced by three significant concepts: the treatment of the chaotic nuclear Hamiltonian as a random matrix (D. Agassi et al., 1975), the differentiation between bound and unbound state configurations (Feshbach et al., 1980), and the classification of nuclear states based on their complexity or exciton numbers (Griffin, 1967).

The EXIFON code computation in this study was based on the Optical Model (OM) formalism for the Statistical Multistep Compound (SMC), Statistical Multistep Direct (SMD), and Multi-Particle Emission (MPE) processes. This technique will forecast angular distributions, activation cross sections, and emission spectra, including equilibrium and pre-equilibrium events. The model permits the induction of reactions using neutrons, protons, alphas, and photons in the outgoing channels, but it prohibits the employment of gamma and heavy charged particles as incident particles (Kalka 1991). For this study, the ⁶¹Ni and ⁶²Ni nickel isotopes were examined using the EXIFON method.

To comprehensively assess all conceivable scenarios regarding the influence of shell structure on interactions, and drawing upon data from the computational code, the reactions (p, n) and (p, 2n) were investigated from 1 – 20 MeV.

During the execution of each computational analysis, the input and output directories are initially delineated, followed by the specification of the target nuclei as ⁶¹Ni and ⁶²Ni. The incident particle pertinent to this investigation is the proton, which is subsequently selected, while the Excitation Function is designated as the overarching option for the calculations. In the following step, the number of incident energy levels is defined as 20 MeV, thereby indicating the maximum incident energy considered for the analysis, which is succeeded by the specification of the initial incident energy set at 1 MeV, denoting the minimum energy for which the cross-section is to be computed; thereafter, the incident energy increment is established at 1 MeV to delineate the energy scale for the cross-section calculations. Moreover, in the modification section, this study exclusively examines the effects of shell structure, applying its two shell-correction options to each reaction channel. The OUTEXI file for each current computation is meticulously saved either in the working directory or in an alternative location.

The phenomenon of shell structure is manifested in Statistical Multistep Compound (SMC) processes, wherein the single-particle state density g, as delineated in equation (1) (Ignatius et al., 1975), is augmented by the resulting outcomes.

\(g = (1 + \frac{\delta W}{E_{X}}\ \lbrack\ 1 - exp\ \left( - \gamma E_{X} \right)\rbrack\)) (1)

The shell correction energy is represented by \(\gamma\) = 0.05 Me\(V^{- 1}\) and the excitation energy of the residual systems is indicated by the amount \(E_{X}\)= E or U, respectively. Both shell corrections (δW = 0) and (δW ≠ 0) were used in the computations. Cross-sectional findings were obtained by conducting the methods WITH and WITHOUT shell correction multiple times. This forecasts the activation of neutrons, protons, alpha particles, and photons as well as their angular distributions, emission spectra, and cross sections. It is also possible to arrange the EXIFON output into ENDF/B-6 format.

RESULTS AND DISCUSSION

Evaluation of the production data of ⁶¹Cu

⁶¹Ni(p,n)⁶¹Cu

Several writers have examined the proton-induced reaction on ⁶¹Ni as a potential method for producing ⁶¹Cu, while accounting for various model parameters. According to Aslam and Qaim (2014), this reaction is an effective way to produce ⁶¹Cu, even though it requires the use of costly enriched ⁶¹Ni as the target material. Several tests were conducted using enriched ⁶¹Ni target, with Szelecsenyi et al. (1993) performing the most comprehensive measurement. None of the targets, nevertheless, was completely enriched. The remaining measurements, as described by Blaser et al. (1951), were carried out using ^natNi target foils.

The ⁶¹Ni(p,n)⁶¹Cu reaction's excitation curve is shown in Figure 1, and equation (2) (wong, 1998) indicates that the reaction's threshold energy is between 3 and 4 MeV.

\(T_{p} \geq - Q(\frac{M_{T} + m_{p}}{M_{T}})\) (2)

This compares well with the calculated threshold energy for reaction obtained as 3.07MeV using the well-known formalism and using Q from Blaser et al. (1951).

Figure 1: Plot of ⁶¹Ni(p,n) ⁶¹Cu reaction.

The calculated cross sections with shell correction (WSC) and without shell correction (WoSC) appear to agree fairly well up to 20 MeV, with percentage differences mostly less than 1%. The two values compare very closely and are consistent throughout the entire energy range. Furthermore, both show a 3.3% difference compared with the predicted result by TENDL (2023) and the measured data from Szelecsenyi et al. (1993) up to about 11 MeV. Our work differs significantly from the TENDL (2023) evaluation, which has a lower cross-section at 11 MeV.

The deviation of our calculation and TENDL (2023) may be attributed to the pre-equilibrium model used at higher energy. The direct energy dependence of the cross section from the threshold energy of 4 MeV to 11 MeV for cross sections with wsc, wosc, ENDF, and measurements appears consistent with known compound-nucleus theory. (Borh, 1936) Excitation function curves, whose cross section rises sharply beyond the reaction threshold and falls as a result of competitive reaction and the increase of the quantum mechanical pre-equilibrium contribution with proton energy, are a common feature of compound nucleus production (Feshbach et al. 1980)

Our calculations, when compared with other studies (Figure 1), show a significant deviation, suggesting the need for the optical model in the calculation of proton-induced reactions on light-size nuclei, which start at about 5 MeV and become significantly important at about 11 MeV. Thus, a pre-equilibrium description of the (p,n) reaction channel of ⁶¹Ni, as done in EXIFON require accounting for the optical model contribution. This was achieved by calculating Aslam using the EMPIRE code, which compared well with the measured data from Szelecsenyi.

The calculated data of Aslam and Qaim (2014) using the EMPIRE and TALYS codes accounted for the optical model, compound-nucleus, and pre-equilibrium models comprehensively up to 20 MeV.

⁶²Ni(p,2n)⁶¹Cu

Figure 2: Plot of ⁶²Ni(p,2n)⁶¹Cu reaction

The ⁶²Ni(p,2n)⁶¹Cu reaction's excitation function is shown in Figure 2. The computation shows that the reaction cross section's threshold energy lies between 14 and 15 MeV. The threshold energy for the reaction, determined to be 13.87 MeV using a Q-value of -13.6 from Piel et al. (1992), compares favourably with this value. The (p,2n) reaction cross section for ⁶²Ni at 15 MeV is 37.5 mb for calculations with a shell structure correction and 37.1 mb for calculations without a correction up to 20 MeV; the two computations compare closely, with a percentage difference of 1-3%. This indicates strong consistency between the two sets of cross-section values.

Figure 2 plots the results of the ⁶²Ni(p,2n)⁶¹Cu excitation calculations along with the experimental data file that was obtained from the EXFOR data library and the evaluated data file that was obtained, ENDF (ENDF/B. VII.1. TENDL, MENDL). The graph shows that the calculations match well with both the ENDF data file (ENDF/B. VII.1. TENDL, MENDL) and the experimental data (EXFOR). Nevertheless, there are differences between the data collected for this study and the data retrieved from the EXFOR trial, as well as the analyzed data from MENDL and TENDL, due to differences in the models of the codes.

Comparative Analysis of (P, N) and (P, 2N) Reactions

Table 1: Calculated cross-section data of (p,n) and (p,2n)

In comparing the (p,n) reaction channel of ⁶¹Ni both for wsc and wosc is more probable as it can be observed from Table 1. at 4 MeV, the shell effect without correction produced a cross section of 63mb as compare to 60.9mb for wsc at the same energy level and the reaction channel (p,n) for ⁶²Ni is more probable for with shell effect correction from the Table as at 6 Mev it generate a cross section of 319.9mb which is higher than without shell effect correction with cross section of 316.8mb at the same energy level. However, this reaction channel for ⁶²Ni is not preferred, as we are interested in producing ⁶¹Cu rather than ⁶²Cu.

In comparing the (p,2n) reaction channel of ⁶²Ni for wsc and wosc, the shell effect with correction is more probable, as shown in Table 1. At 15 MeV, the reaction channel (p,2n) with shell effect correction generate a cross section of 37.5mb while without shell effect correction at the same energy level it is 37.1mb which means to produce ⁶¹Cu from calculation using the EXIFON 2.0 computational code with shell structure being the only adjustable parameter, with production channel (p,n) without shell effect correction is more probable while with production channel (p,2n) with shell effect correction is more probable. Also, the more probable reaction channel for ⁶¹Cu production is ⁶¹Ni(p,n)⁶¹Cu, as it generates a cross section at a low proton energy of 4 MeV, unlike the ⁶²Ni(p,2n)⁶¹Cu channel, which requires an energy of 15 MeV to generate an output. At 15 MeV, the production channel ⁶¹Ni(p,n)⁶¹Cu can have a cross section of 551.7, which is larger than that of the production channel ⁶²Ni(p,2n)⁶¹Cu, which is 37.5 mb at the same proton energy. From this analysis, it can be deduced that the reaction channel ⁶¹Ni(p,n)⁶¹Cu is a more probable channel for the production of ⁶¹Cu for medical applications in PET.

CONCLUSION

The EXIFON 2.0 Code was used to estimate the cross-section of the ⁶¹Ni(p,n)⁶¹Cu and ⁶²Ni(p,2n)⁶¹Cu reactions from threshold to 20 MeV. Reaction cross-section calculations were compared with the evaluated data from ENDF data files (ENDF/B-VII.1, MENDL, TENDL) and experimental data from EXFOR. The results showed a considerable deviation for ⁶²Ni(p,n)⁶¹Cu at a projectile energy of 11 MeV, but they are 3.3% compared with measurements and are in excellent agreement with the ⁶²Ni(p,2n)⁶¹Cu reaction. To optimize different approaches for generating ⁶¹Cu at a cyclotron for PET use, the study recommends the ⁶¹Ni(p,n)⁶¹Cu reaction channel.

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