The experimental reaction cross-section data and the corresponding projectile energy data were generated from the experimental nuclear reaction data base (EXFOR), which has recently stored experimental measurements of reaction cross sections for alpha particles, protons, neutrons, deuterons, and etc; the reader is referred to these reports for additional experimental details.

EXFOR, the library and format for collecting, exchanging, and preserving experimental nuclear reaction data, is maintained by the IAEA’s Nuclear Data Department (NDS) (Asres et al. 2019b). Data from experimental nuclear processes can be collected, stored, shared, and retrieved using this format and library (Kara 2017). The product nuclei differ in terms of particle energy, half-lives, and other properties.

In this study the COMPLET nuclear reaction code were employed for the calculation of excitation function for the nucleon induced reaction on stable selenoium-80 isotope. Nucleon-cross sections on a range of isotopes have been predicted using theoretical reaction codes such as COMPLET, which are based on various nuclear theories. The computer code COMPLET was developed using the Weisskopf-Ewing model, which describes the equilibrium process before particle emission, and Blann’s Hybrid model, which takes into account the shape and configuration of the interacting nuclei for both equilibrium and pre-equilibrium processes (Yiğit 2020). The COMPLET is computer software, which is developed using FORTRAN programming language, and can calculates nuclear reactions cross-section and also as used by different scholars for the calculation of excitation function for compound and pre-compound nuclear reaction for ain induced reaction mechanisms the (Zegeye et al. 2025; Mekonen and Rao 2025; Degu Belete et al. 2024; Asres et al. 2019a). The method used in this work is an important and typical calculation method and also results were compared with the existing experimental results to verify calculation method. The findings of the model excitation function data were validated against experimental excitation function data, which were retrieved from the EXFOR data centre.

The initial excitation configurations and level density parameters are crucial variables in pre-equilibrium emission calculations. Various input parameters were used in the complete code to estimate reactions (Yiğit 2020). Pre-equilibrium emission calculations heavily rely on the level density parameters and initial excitation configurations. The Complete code estimated reactions using a variety of input parameters. The calculated excitation functions’ shape and height are influenced by the nuclear level density. When the decay rate equation governing nuclear transformation and decay of the activated products is taken into account, the expression for nuclear reaction cross-section can be written (Ditrói et al. 2018). By using the Fermi density distribution function as shown in Equation (1):

ρ(E)=π12e2aE12a14E54 (1)

Where α, is the level density parameter and E is the excitation energy. The level density parameter, which was determined through experiment, exhibits a linear relationship with the mass number of the compound nucleus expressed as in Equation (2):

a=ACNK (2)

Where ACN stands for the compound nucleus’s mass number and K for the free adjustable constant ranging from 7 to 12. Theoretical calculations in this work were done by using the level density parameter with the application of free adjustable constant K from 7 to 12, for all the reactions. However, using free adjustable constants of 11 and 12 in Equation (1) (i.e., a=ACN11, and a=ACN12) are the best fit to experimental results for proton induced and k is equal to 8 and 7 (i.e.a=ACN8, and a=ACN7) are best fit to experimental results for neutron induced reaction. Also exciton number n_o = 1 and n₀ = 3(2p+h) are used but n_o = 2, 3, 4 and 5 are found to give satisfactory reproduction of the experimental data for both reactions.

These excitons interact independently with the particles below the Fermi level, creating new particle-hole configuration in the second stage or getting emitted into the continuum (Barbaro et al. 2021). The input parameters incorporated in the code COMPLET in this work for the given projectile energy for the theoretically calculated pre-equilibrium and equilibrium reaction mechanism are selected and considered based on the recently existed literatures of (Asres et al. 2019b; Degu Belete et al. 2024; Mekonen and Rao 2025; Zegeye et al. 2025).

The uncorrected reaction cross section, (σun), was derived for every forward cone size from, shown in Equation (3):

σun=1nx[(I0−I)I0−(i0−i)i0] (3)

where x is the target thickness and n is the number of nuclei per unit volume in the target. For every target, a set of target-in and target-out measurements were made. The difference between the term (I0−I) and the corresponding quantity (i0−i) derived from target-out measurements was used to calculate the uncorrected reaction cross section (σun).

The data for this work was properly organized by tabulating and presenting the results using a spread sheet. Theoretical and experimental response profiles plotted against projectile energy using Origin-2018 software. The Pearson correlation coefficient (R-value) was used to assess the relationship between the experimental and theoretical total cross-section values and it tells the relationship between the theoretical and experimental results (Asres et al. 2018; Mekonen and Rao 2025).

R=∑iN((XTi−⟨XT⟩)(XEi−⟨XE⟩))N−1(SXT)(SXE) (4)

where R- stands for the correlation coefficient having the values lies between 1 and -1 and unit less, S_XT and S_XE for the standard deviations of the theoretical and experimental cross-sections, and N for the quantity of theoretical and experimental data. These are the mean theoretical and experimental cross-sections of the i^th values, respectively (Asres et al. 2018). According to (Mekonen and Rao 2025), the values of person correlation coefficient have five range values to show the relationship between experimental results with theoretical results. When the values of R>0.9 indicates an excellent correlation; the values 0.7<R≤0.9 indicates a strong correlation; 0.5<R≤0.7 indicates a moderate correlation; 0.3<R≤0.5 indicates a weak correlation; R≤0.3 indicates a very weak or no correlation.

The percentage (%) error can be obtained using this formula as shown in Equation (5):

Percent error =" experimental value − theoretical value theoretical value "% (5)

In research, significant numbers are important, and even if the question is posed correctly, presenting an answer that is either excessively or insufficiently expenditure may be considered erroneous (Helmenstine 2020).

In this work, the excitation functions for an induced reaction of proton ⁸⁰Se(p, 4n)⁷⁷Br, ⁸⁰Se(p, 5n)⁷⁶Br, and ⁸⁰Se(p, α)⁷⁶As and an induced reaction of neutron ⁸⁰Se(n, α)⁷⁷Ge and ⁸⁰Se(n, p)⁸⁰As were calculated using computer code COMPLET with possible input parameters.

The table summarizes Q-values and decay data for several product radioisotopes produced from reactions on a selenium-80 target. For the (p, 4n) channel producing ⁷⁷Br, the product has a half-life of 57.0 hours and decays purely by electron capture (EC), with a Q-value of 1.4 MeV. The (p, 5n) channel yields ⁷⁶Br, which has a 16.2 hour half-life and decays by a mixture of electron capture (57%) and positron emission (β+, 43%), and its Q-value is 5.0 MeV. Proton-induced alpha emission (p, α) produces ⁷⁶As, a nuclide with a 1.0 day half-life that decays exclusively by beta-minus emission (β−) and has a Q-value of 3.0 MeV. Neutron-induced alpha emission (n, α) leads to ⁷⁷Ge, which has an 11 hour half-life, decays 100% by beta-minus, and has a Q-value of 2.7 MeV. Finally, the (n, p) reaction produces ⁸⁰As with a short half-life of 9.0 minutes, decaying entirely by beta-minus and having a Q-value of 2.3 MeV.

In this study, the excitation functions for protons induced for ⁸⁰Se(p, 4n)⁷⁷Br, ⁸⁰Se(p, 5n)⁷⁶Br, and ⁸⁰Se(p, α)⁷⁶As reactions were obtained using COMPLET computer code and the results are plotted in Fig. 1, Fig. 2 and Fig. 3 at proton energies up to 70.5 MeV. The calculations results are compared with experimental values from EXFOR library.

In general, the nuclear reactions ⁸⁰Se(p, 4n)⁷⁷Br, ⁸⁰Se(p, 5n)⁷⁶Br, and ⁸⁰Se(p, α)⁷⁶As are employed to produced ⁷⁷Br, ⁷⁶Br and ⁷⁶As respectively. The theoretical calculations are in agreement with the experimental data, as shown in Fig. 1, with the expectation of one experimental value in the peaked region, which is approximately 30% higher. As seen in Fig. 3 the experimental data the peaked region is approximately 25% lower. As noted for proton induced ⁸⁰Se(p, 4n)⁷⁷Br, ⁸⁰Se(p, 5n)⁷⁶Br, and ⁸⁰Se(p, α)⁷⁶As reactions, the best energy range for production is from 34.5 to 43.4 MeV, 53.9 to 61.4 MeV and from 24.8 to 28.5 MeV, respectively.

Several isotopes of bromine have long been proposed for use in nuclear medicine. Bromine-77 has a half-life of 57 hours and decays almost completely (99.3%) by capturing electrons. Its half-life is suitable for long-term physiological studies using single-photon emission computed tomography (SPECT) (Mohamed and Shehata 2011). In addition, the Auger electrons emitted during the decay of Bromine-77 have certain therapeutic implications. Several methods have been proposed for obtaining the radionuclides under consideration. However, the proton-mediated reaction on selenium appears to be the most important (Mohamed and Shehata 2011). Bromine-77 occurs when a projectile (proton particle) hits the target element selenium-80 and emits four neutrons (4n). By comparing the calculated values with the experimental results, the pre-equilibrated and the equilibrated reactions can be seen in the reaction excitation function ⁸⁰Se(p, 4n)⁷⁷Br. The experimental data for this reaction are taken from the author (Spahn et al. 2019).

As shown in Fig. 1, the excitation function for the reaction ⁸⁰Se(p, 4n)⁷⁷Br was experimentally measured and theoretically calculated using different sets of input parameters. The pre-equilibrium reaction cross-sections reach its maximum peak at 155.5 mb while equilibrium reaction cross-section attains its maximum peak value at 494.3 mb. At high energies, the theoretical pre-equilibrium cross-section agrees with the experimental results reported by (Spahn et al. 2019) in EXFOR. The compound nucleus theory is not valid for a larger number of neutron emissions, as its value is much larger than the experimental value.

So, the equilibrium reaction gives the best results up to 46.2 MeV with a cross-section value of 430.3 mb. The theoretical pre-equilibrium and equilibrium cross-sections are in good agreement with the experimental data between the energy 34.5 MeV and 43.4 MeV. However, after an incident energy of 43.4 MeV and above, the pre-equilibrium reaction cross-section gives better agreement with the experimental data reported by (Spahn et al. 2019) in EXFOR. At higher energies, the equilibrated reaction showed no nuclear emission recombination, and the pre-equilibrated emission gave better results up to 62.4 MeV with the cross-section value 155.5 mb. However, at higher energies above 62.4 MeV, both the pre-equilibrium and equilibrium nuclear reaction mechanisms are far from the experimental values. This confirms that pre-equilibrium and equilibrium nuclear reaction mechanisms are not formed. But it could be a direct reaction mechanism.

Based on the correlation values (R =0.945) between experimentally obtained and theoretically calculated pre-equilibrium reaction cross-section results both have excellent correlations and significant large positive relationship between them. The highest value of person correlation value indicates the predictive capabilities of the model COMPLET for this reaction channel. Whereas, the correlation coefficient between the experimental and the compound nuclear reactions cross section is to be (R=0.892) and we said that there is strong positive correlation between them.

It is clear that the theoretical results obtained using the computer code COMPLET are in good agreement with the experimental results obtained from the EXFOR data for energy values up to 66 MeV. Basically, theoretical result has been calculated by using different sets of input parameters, exciton number no = 5, level density parameter a=ACN12 and mean free path multiplier MFP = 2. This plays a key role in the theoretical calculation for the code COMPLET.

The radioisotope ⁷⁶Br and ⁷⁷Br were produced in high radionuclides purity via the proton and neutron irradiation of novel isotopically-enriched, ⁸⁰Se intermetallic target. Radionuclide Bromine-76 can be used for functional studies with positron emission tomography (PET), the former for fast metabolic processes and the latter for slower processes. Bromine-76 decays by positron emission (58%) and electron capture (42%) (Ellison et al. 2019).

The half-life (16.2 hours) allows the use of radiotracers with an accumulation time of one or two days. The high energy of the emitted positrons can affect the positron emission picture to some extent. Recently, bromine isotopes have received increased attention in the development of PET and high-energy gamma-ray cameras (Mohamed and Shehata 2011). Bromine-76 is produced when a projectile (proton particle) strikes a target element selenium-80 and emits five neutrons (5n). The calculated excitation functions of the reaction ⁸⁰Se(p, 5n)⁷⁶Br, is compared with the experimental result taken from the author (Spahn et al. 2019).

As we can see from Table 3 and Fig. 2, both equilibrium and pre-equilibrium nuclear reactions are possible in the incident energy range of 46.2 MeV to 53.9 MeV. In the reaction channel of ⁸⁰Se(p, 5n)⁷⁶Br for the incident energy greater than 53.9 MeV, calculated values of equilibrium reaction are much larger than the experimental value. Radioisotope, bromine-76 is not produced by equilibrium reactions followed by evaporation of five neutrons due to high neutron emission.

The correlation coefficient of the reaction cross-section of experimental and the equilibrium nuclear reactions is calculated to be (R =0.81) this indicate a strong correlation between them. Therefore, in the incident energy greater than 53.9 MeV of the ⁸⁰Se(p, 5n)⁷⁶Br reaction there is a great difference between the excitation functions of the experimental result and the equilibrium nuclear reaction. The correlation coefficient of the reaction cross-section of experimental and pre- equilibrium nuclear reactions is calculated to be (R= 0.93) for the higher energy region and the result indicated that there is significant large positive and excellent correlation between them. Also, the highest R value confirms the predictive power of the code COMPLET as confirmed by other studies (Mekonen and Rao 2025). Above the incident energy of 56.5 MeV, the pre-equilibrium reaction mechanism better agrees with the experimental data reported by (Spahn et al. 2019) in EXFOR than the pure equilibrium reaction mechanism above 56.5 MeV energy range and there is no signatures of equilibrium reaction. It is clearly observed that for larger numbers of neutron emission the reaction is taking place by pre-equilibrium decay even at the low energy end side.

As a result, the theoretical pre-equilibrium result obtained by using a computer code COMPLET best agrees with the experimental result obtained from the EXFOR data. Basically, theoretical result has been calculated by using different set of input parameters, exciton number no = 4, level density parameter a=ACN11 and mean free path multiplier MFP=2. This plays a key role in the theoretical calculation.

Arsenic has numerous radionuclides of interest for scientific (medical) or environmental applications. Its chemical properties are similar to those of nitrogen and phosphorus, both of which are common biologically active molecules (Mohamed and Shehata 2011). Arsenic-76, is produced when a projectile (proton particle) strikes a target element selenium-80 and emits (α) particles. Arsenic-76 -decays by negatron emission or undergoes beta mines decay with a 24 hour half-life (Ali et al. 2020). The calculated excitation functions of the reaction, ⁸⁰Se(p, α)⁷⁶As is compared with the experimental result taken from the author (Levkovski 2019).

As can be seen from Fig. 3, the experimental values at energy values around 26.6 MeV are very similar to those calculated for both equilibrium and pre-equilibrium reactions but are closer to pre-equilibrium nuclear emission. In the incident energy range greater than 26.6 MeV, the value calculated by the equilibrium reaction theory is much larger than the experimental value and decreases rapidly, while the experimental value increases slightly.

The correlation coefficient of the reaction cross-section of experimental and equilibrium nuclear reactions is calculated to be (R=0.91) this is an excellent positive correlation between them, which means that high experimental value scores go with high equilibrium value scores. They show that there is less evidence of an equilibrium reaction than pre-equilibrium reaction in this energy range. At the higher energies from 26 to 28.5 MeV, the experimental values are very close to nuclear calculations confirming to the formation of a pre-equilibrium reaction.

The pre-equilibrium reaction cross-sections reach its maximum peak at 19.65 mb while equilibrium reaction cross-section attains its maximum peak value at 35.18 mb. It is evident that both the equilibrium and pre-equilibrium nuclear reaction cross-section are in good agreement with the experimental values up to the incident energies of 26 MeV. After incident energy of 26 MeV and above, the pre-equilibrium reaction cross-section gives better agreement with the experimental data reported by (Levkovski 2019) in EXFOR. The correlation coefficient (R = 0.98) between experimental and pre-equilibrium reaction cross section has positive and excellent correlation. Furthermore, it is clear to deduce that from the highest values of R given above for the two cases shows the predicted capability of the model COMPLET what we have been used for this reaction channel.

In general, pre-equilibrium reaction formation theory satisfies the results. Above this energy range, no signatures of equilibrium formation are obtained. The compound nucleus theory is not valid for a larger number of neutron emissions, as its value is much larger than the experimental value.

The production of ⁸⁰Se in neutron irradiation of ⁷⁷Ge and ⁸⁰As occurs in various reactions such as ⁸⁰Se(n, α)⁷⁷Ge, and ⁸⁰Se(n, p)⁸⁰As. The results of computer code COMPLET calculations excitation functions for neutron induced reaction were shown in Fig. 4 and Fig. 5.The obtained results were compared with the existing experiment in the EXFOR, and a good agreement was obtained. As can be seen in Fig. 4, there are no experimental results for ⁸⁰Se beyond the energy of 20 MeV. However, it is clarity seen that the COMPLET computer code can be reliably used to obtained data. For Neutron induced, the best energy range for production is from 13.5 to 14.8 MeV and from 15.1 to 15.5 and 16.5 to 17.9 MeV for ⁸⁰Se(n, α) ⁷⁷Ge, and ⁸⁰Se(n, p) ⁸⁰As reactions, respectively.

The nuclear reaction, ⁸⁰Se(n, α)⁷⁷Ge produces ⁷⁷Ge, which decays by emission of β^-- particles into ⁷⁷Ge with the half-life of 11 hour (Ali et al. 2020). Germanium-77, is produced when a projectile (neutron particle) strikes a target element selenium-80 and emits alpha particles. Germanium-77 is used in medical, industrial and research applications. The calculated excitation functions of the reaction, ⁸⁰Se(n, α)⁷⁷Ge, is compared with the experimental result taken from the author (Filatenkov 2021).

As we observed the excitation function for the reaction channel, ⁸⁰Se(n, α)⁷⁷Ge in Fig. 4, the predicted pre-equilibrium and equilibrium nuclear reaction cross-section starts from the bottom of the designated projectile energy of 13.49 MeV up to projectile energy of 14.81 MeV. The pre-equilibrium and the equilibrium reaction cross-section have similar shape to experimental values reported by (Filatenkov 2021) in EXFOR. But, the pre-equilibrium reaction is closer than the equilibrium reaction cross-section. This demonstrates how response mechanisms change as projectile energy rises.

In cases, the experimental and theoretical equilibrium and pre-equilibrium reaction cross-section can have maximum values at the projectile energy of 14.81 MeV with values of 3.1 mb, 4.2 mb, and 3.00 mb, respectively. Also, at the projectile energy of 13.5 MeV, the cross-section values for the experimental and theoretical equilibrium and pre-equilibrium are minimum with the values of 2.1 mb, 3.1 mb, and 2.3 mb, respectively. Both, the pre-equilibrium and equilibrium nuclear reaction mechanisms are closer to the experimental values between the energy range 13.5 MeV and 14.8 MeV.

This confirms that there is formation of both pre-equilibrium and equilibrium nuclear reaction mechanisms with equilibrium cross-section values. It is evident that both the equilibrium and pre-equilibrium nuclear reaction cross-section are good agreement with the experimental values up to incident energy of 14.8 MeV. The correlation coefficient of the cross section of experimental and pre-equilibrium nuclear reactions is calculated to be (R = 0.99) and the correlation coefficient between the experimental and the equilibrium cross section nuclear reactions is calculated to be (R = 0.99) results of the Pearson correlation in both cases indicated that there is significant large positive excellent correlation between the theoretical and experimental cross-section values. Also, the code COMPLET model, which we have been used for this reaction channel has highest predictive power since due the highest values of (R = 0.99). It is clear that the theoretical result obtained by using a computer code COMPLET agree with the experimental result obtained from the EXFOR data.

Arsenic-80 is produced when a projectile (neutron particle) strikes a target element selenium-80 and emits one proton particle. Arsenic-80 decays by negatron emission or undergoes beta minus decay with a 9 minute half-life (Ali et al. 2020). The calculated excitation functions of the reaction, ⁸⁰Se(n, p)⁸⁰As is compared with the experimental result the experimental data taken from the author (Decowski et al. 2021).

From Fig. 5, the theoretical pre-compound nuclear reaction cross-section starts from the bottom of the assigned projectile energy of 13.36 MeV with 1.197 mb, reached its maximum peak at (15.06 MeV, 20.01 mb) and then it begins to increasing with the value of the projectile energy by making long tail.

The equilibrium reaction mechanisms have very small similarity with the experimental values in the given energy ranges. At the lower energies around 15.06 MeV experimental values are good agreement to the compound nucleus reaction with the correlation coefficient of the cross section of experimental and equilibrium nuclear reactions is calculated to be (r = 0.86), which describes a strong and positive correlation between the theoretical and experimental reaction cross-sections. Therefore, from the above result, it clearly understood that the result of pre-equilibrium reaction cross-section calculated using computer code COMPLET, are in good agreement with the experimental result generated from the EXFOR data for energy value up to 17.9 MeV as reported by (Decowski et al. 2021) in EXFOR.