East East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, Issue. 1, 18-27 *Corresponding author: Email: rabirhanu@gmail.com, https://dx.doi.org/10.4314/eajbcs.v4i1.2S Study of Reaction Mechanisms in α + 69Ga reaction at ≈10 – 50 MeV F. K. Amanuel 1Department of Applied Physics, Hawassa University, Hawassa, Ethiopia KEYWORDS: Reaction cross-section; COMPLETE code; Reaction channel; Excitation function ABSTRACT The excitation functions of 69Ga(α, n)72As, 69Ga(α, 2n)71As, 69Ga(α, 3n)70As, 69Ga(α, x)69Ge, 69Ga(α, x)68Ga and 69Ga(α, x)67Ga reactions formed in the interaction of α- projectile with 69Ga-target were studied at ≈ 10-50 MeV. The produced nuclei were different isotopes of As, Ge, and Ga, some of which have important medical applications. The theoretical model predictions were based on the statistical code COMPLETE, and the predicted results were compared and discussed with existing experimental data. Good agreement between the theoretical predictions and experimental results were obtained. Pearson's relational statistics revealed moderate to strong positive associations between the theoretically predicted and experimentally measured reaction cross-sections. Furthermore, the present investigation revealed significant pre-compound contributions in the studied energy range. Therefore, it is important to consider the admixture of pre- equilibrium and equilibrium modes of reactions when predicting the reaction cross- sections. INTRODUCTION Advances in accelerator technology and cyclotrons have enabled the use of light- and heavy-charged nuclei as projectiles in nuclear reactions. This development has improved our understanding of the reaction mechanism and nuclear structure at various energies near and above the Coulomb barriers (Cavinato et al., 1995; Amorini et al., 1998; Gadioli et al., 1998). For example, at moderate excitation energies, reactions induced by nucleons and light-charged projectiles are found to proceed through the equilibrium (EQ) and pre- equilibrium (PE) mode reactions (Baure et al., 1995;Agrawal et al., 2001; Patronis et al., 2007; Johari and Saxena, 2015). To understand these reaction mechanisms, reaction cross-section data evaluation is essential. Accordingly, comparative studies based on experimental data and theoretical predictions are demanding. In this regard, nuclear reaction model-based computer codes can swiftly help to predict unknown reaction cross-sections and thus improve computer code predictions. Studies of light-charged induced nuclear reactions help better understand the reaction mechanisms and test the validity of various available and newly evolving computer codes. Furthermore, in light-charged induced nuclear reactions, the processes of PE and EQ particle(s) emissions are vital in comprehending and characterizing the reaction mechanisms, attributable to the strong competition between East African Journal of Biophysical and Computational Sciences Journal homepage : https://journals.hu.edu.et/hu-journals/index.php/eajbcs Hawassa University College of Natural & Computational Sciences Year 2021 Volume xx No xx Research article https://dx.doi.org/10.4314/eajbcs.v4i1.2S East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 19 PE and EQ mode of reactions at moderate excitation energies. Numerous studies have compared theoretically predicted and experimentally measured reaction cross sections for light-charged particle induced reactions, aiming to elucidate the underlying reaction mechanisms (Agarwal et al., 2002; Abhishek et al., 2008; Amanuel et al., 2011; Yigit and Tel, 2014; Asres et al., 2018; Asres et al., 2019; Amanuel, 2021). However, reasonable comparative reaction mechanisms studies between theory and experiment of 72As, 71As, 70As, 69Ge, 68Ga, and 67Ga reaction products produced in α-projectile induced reactions on 69Ga-target at ≈10 – 60 MeV, have not been investigated efficiently; therefore, further investigations and scientific evidence are required (Ismail 1990; Rezvi et al., 1989; Didik et al., 1994). Furthermore, understanding the reaction mechanisms induced by a light-charged projectile, such as in α + 69Ga reaction helps to investigate new works on producing pure and optimized 72As and 68, 67Ga radionuclides that are useful in medical applications embracing the present and possible future needs. The present work investigates the reaction mechanisms involved in the interactin of α- prjectile with 69Ga-target at ≈10 - 50 MeV. Excitation functions of 69Ga(α, n)72As, 69Ga(α, 2n)71As, 69Ga(α, 3n)70As, 69Ga(α, x)69Ge, 69Ga(α, x)68Ga and 69Ga(α, x)67Ga reactions were predicted using the statistical model code COMPLETE. The corresponding experimental data were collected from the EXFOR database (Levkovski, 1991). The COMPLETE computer code has proven effective in reaction mechanism studies, particularly for light- and medium-nuclei induced reactions (Agarwal et al., 2002; Asres et al., 2018; Asres et al., 2019). THEORETICAL BACKGROUND Several theoretical nuclear reaction model-based computer codes have been used to predict reaction cross-sections (Abhishek et al., 2008; Yigit and Tel, 2014; Amanuel, 2021). The nuclear reaction mechanisms change with light- charged projectile energies near and above the Coulomb barrier. The reaction mechanism is considered to proceed through EQ as well as PE emission of particles at moderate excitation energies (≈10- 60 MeV) (Baure et al., 1995; Agrawal et al., 2001; Pal et al., 2005; Johari et al. 2015; Asres et al., 2019). The EQ mode of reaction mechanism dminates in the low energy regin (in general, below 20 MeV). Furthermore, this reaction mechanism occurs in a nuclear reaction time scale of abut 10-16 to 10-18 s. In the EQ mode of reactions, the projectile is captured by the target nucleus, and its energy is shared and re-shared amongst the nucleons, losing their identity and forming a single excited cmplex system that eventually leads to a fully equilibrated cmpound nucleus (CN). The EQ emissions of nuclear reactions are usually treated using statistical models. For example, the Hauser-Feshbach (Hauser and Feshbach, 1952) formalism considers the angular momentum and the nuclear level structure to define the EQ emission spectrum. On the other hand, in the Weisskopf-Ewing (Weisskopf and Ewing, 1940) EQ emission formalism, angular momentum, and parity are not considered. The PE mode of reaction mechanism becomes increasingly crucial at a relatively high energy region (above ≈20 MeV). Therefore, the PE emissions of nuclear reactions occur before the thermalization of a composite system and are usually treated using non-statistical models; and the popular models used for the description and calculations of the PE mode of the reaction mechanism are the exciton model (Griffin, 1966; Blann, 1975; Agassi et al., 1975), hybrid model (Blann, 1971), and geometry-dependent hybrid model (Blann and Vonach, 1983). Various computer codes were developed for years based on different nuclear reaction models East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 20 that helped study nuclear structure and reaction mechanisms (Young et al., 1992; Uhl and Strohmaier, 1976; Strohmaier and Uhl, 1980). The ALICE-91 (Blann, 1991) analytic code developed by Blann was also vastly used over the years to predict reaction cross-sections in the intermediate energy regions. The computer code COMPLETE (Ernst, 1997) is an advanced modified version of the ALICE-91 code family and has been successfully applied to the calculation of EQ and PE reaction cross-sections (Aydin et al., 2010; Asres et al., 2018; Asres et al., 2019; Amanuel, 2021). COMPLETE code The computer code COMPLETE with new corrections and capabilities has successfully predicted nuclear reaction cross-sections, especially for reaction mechanisms studies (Asres et al., 2018; Asres et al., 2019; Amanuel et al., 2011). This code employs the Weisskopf- Ewing formalism (Weisskopf and Ewing, 1940) for the EQ reaction component and Hybrid (H) model (Blann, 1971) as well as the Geometric Dependent Hybrid (GDH) model of Blann (Blann and Vonach, 1983) for the PE reaction component. According to the Weisskopf-Ewing model, and based on Bohr's independence hypothesis, the nuclear reaction cross-section for a reaction with entrance channel α and exit channel β can be expressed as (1) Where is the crss-sectin for the frmation of the CN and , , respectively, represent the energy average width for the decay of the CN in channel β, and the energy averaged total width. In Eq. (1) can be given as: Where and represent the ejectile's reduced mass and spin, respectively, the quantity represents the inverse reactin crss-sectin, and U the excitatin energy of the residual nucleus. corresponds to the total single-particle level density at excitation energy, E. The H model formulation of Blann and Vonach (Blann and Vonach, 1983) for PE reaction differential cross-section is given by: (2) , (3) Here, represents the reaction cross-section, and represents the number of particles of the type ν emitted into the unbounded continuum with channel energy between ε and ε+dε. The quantity in the first set of the square bracket of Eq. (3) represents the number of particles to be found (per MeV) at a given energy "ε" with respect to the cntinuum for all scattering processes leading to an "n" excition configuration. The nucleon-nucleon scattering energy partition function, represents the number of combinations with which n exciton may share the excitation energy, Eex and represent the excitn number of ν type nucleon for a given total excitn state n. corresponds to the single-particle level density for nuclen of the “ν" type. The secnd set of a square bracket in Eq. (3) represents the fraction of the ν type particles at energy ε, which should underg emission int a cntinuum rather than making an inter-nuclear transition. The represents the average fractin f the initial East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 21 ppulation surviving the treated excitn number. The quantity represents the cntinuum emissin rate fr particles with "ε" channel energy, and represents the intranuclear transitin rate. The quantities U and E represent the residual nucleus and composite system excitation energies, respectively. The GDH hybrid model has successfully reproduced a wide range of nuclear reaction data (Blann, 1972; Blann and Vonach, 1983; Harp et al., 1966). The GDH mdel is a modified versin of the H mdel in which the nuclear gemetry effects are cnsidered. In addition, the GDH mdel onsiders the reduced matter density, hence the shallow potential. Accordingly, the PE decay formalism incorporated the diffused surface prperties sampled by higher impact parameters. The differential crss-section for PE emissin in the GDH model is frmulated as follows: (4) The quantity represents the transmissin cefficient fr the lth partial wave, and represents decay prbability at channel energy “ε” and rbital angular mmentum “l”. is the reduced de-Brglie wavelength. Pearson’s correlation coefficient The prediction quality of our optimization in fitting COMPLETE code using essential input parameters for the experimental reaction cross sections available in the literature was evaluated using the statistical Pearson’s coefficient, R(Sedgwick, 2012; Wang, 2012; Patrick, 2018). In addition, the present wrk used Pearsn's crrelation cefficient to provide information on the linear relational strength between the COMPLETE projected and experimentally measured reaction crss-sections. Pearson's crrelation cefficient, R, is given by: (5) Where N is the number of the theretical and experimental data pints, and are the theretical and experimental crss-sectin of the ith value, respectively. Eq. (5) returns unitless values for R between -l and +l, where +l represents a strong positive relatinship, -l indicates a strng negative relatinship; and 0 indicates n relatinship. If 0 < R < 0.3, the crrelation is weak and psitive, if 0.3 ≤ R < 0.7 the crrelation is mderate and psitive; and if 0.7 ≤ R < l the crrelation is strng and psitive. RESULTS AND DISCUSSION Excitation functions of 69Ga(α, n)72As, 69Ga(α, 2n)71As, 69Ga(α, 3n)70As, 69Ga(α, x)69Ge, 69Ga(α, x)68Ga and 69Ga(α, x)67Ga reactions produced via EQ and PE processes were considered at ≈ 10-50 MeV. The experimentally quantified excitatin functins were cmpared with the theretical model code COMPLETE predictins, which account for both EQ and PE processes. In this cde, the level density parameter a, which predominantly affects the EQ compnents of a crss-sectin, is calculated frm the expressin a = A/K MeV-1, where A is the nuclen number of a CN and K is an adjustable constant. K may vary t match the experimenta1 data. The initial exciton number no (no= n+p+h, which is described by the number f neutrns (n), the number of prtons (p) in excited states, and the number of hles (h) after the first cllision) that governs the PE component, represents the initial cnfiguration East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 22 f the number of particles in the excited states and the number of hles after the first cllision. In the present work, to match the experimental data, the values of important input parameters K(K=8, 10, 12) and no (no=4, 5, 6) were varied for a representative 69Ga(α, n)72As Reaction. Figure 1 displays the experimentally measured excitation functions and theoretical predictions using different K and no values for 69Ga(α, n)72As Reaction. 15 20 25 30 35 40 45 50 55 -400 -200 0 200 400 600 800 1000 1200 a) 69 Ga(, 2n) 71 As (Levkovski, 1991) COMPLETE (K=8) COMPLETE (K=10) COMPLETE (K=12)  ( m b ) E lab (MeV) 15 20 25 30 35 40 45 50 55 -400 -200 0 200 400 600 800 1000 1200 b) 69 Ga(, 2n) 71 As (Levkovski, 1991) COMPLETE (n o =4) COMPLETE (n o =5) COMPLETE (n o =6)  ( m b ) E lab (MeV) Figure 1: Experimentally measured and theoretically calculated excitation functions for 71As residue. The curves represent the theoretical predictions (admixture PE and EQ) for different values of K (K = 8, l0, and l2) in panel (a) and no (no = 4, 5, and 6) in panel (b). The open circles represent the experimental cross-sections. As this figure indicates, the measured excitation function is well reproduced by COMPLETE code for values of K=8 and no=5. It may be bserved frm Fig 1(a) that the predicted excitation functions fr different K values are related; if they differ, the alterations are minimal. For other reactin channels ppulated in the interaction of α-prjectile with 69Ga- target, a combination of K=8 and no=5 has been consistently used t predict the reaction crss- sectins. A) 6 9Ga(α, n)72As Reaction When α-projectile bombarded 69Ga-target, a composite [73As]* nucleus is produced in excited states. The excited [73As]* nucleus then emits a neutron leaving the 72As nucleus as a residue, i.e., α + 69Ga [73As]* n + 72As Figure 2(a) displays the experimentally measured excitation function and the COMPLETE code predictions for 69Ga (α, n)72As reaction. As shown in Figure 2(b), the experimentally quantified excitation function is comparatively higher than the theoretically predicted excitation functions (with and without PE contribution), thugh the shapes f the tw excitatin functins showed a similar trend. The observed enhancement on the measured crss- section may be attributable to impurity contributions from the heavier residue(s). In addition, Pearsn's crrelation cefficient East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 23 between theretically predicted and experimentally measured prduction cross- sections has a value of R=0.96. Hence, the theoretical results indicated a strong and positive correlation with the experimental. B) 69Ga(α, 2n)71As Reaction In the case f 69Ga(α, 2n)71As reactin, the residue 71As may be produced following the emission of two neutrons from an excited composite nucleus, [73As]*, i.e., Fig. 2(b) shows the theoretically predicted excitation functions (with and without the contribution of PE reaction) along with the experimentally measured excitatin functin for 69Ga(α, 2n)71As Reaction. As shown in this figure, the predictions of the COMPLETE code, after incorporating the PE reaction, agree with the measured excitation function. Furthermore, Pearson's correlation coefficient value (R ≈ 0.94) indicated a strong and positive correlation between theretically predicted and experimentally measured productin crss- sectins. C) 69Ga(α, 3n)70As reaction The measured excitation function and theoretical predictions obtained from COMPLETE code for 70As residue populated via (α, 3n) channel are shown in Figure 2(c). Note that in the 69Ga(α, 3n)70As reaction, the residue 70As may be formed through the reaction: It may be observed from Figure 2(c) that up to 40 MeV (up to the peak portion), the predicted excitation function after incorporating PE contribution, in general, reproduced the measured excitation function satisfactorily. However, above 40 MeV (in the tail prtion of the excitatin functin), the predicted values are higher than the experimental data. Moreover, Pearson's correlation coefficient between theoretically predicted and experimentally measured reaction crss-sectins has a value of R=0.86. Hence, the theoretical results indicated a strong and positive correlation with the experimental. D) 6 9Ga(α, x)69Ge reaction In 69Ga(α, x)69Ge reaction, 69Ge residue may be formed through the emissions of unidentified particles, x from the composite nucleus, [73As]* via (α, x) complex channel. As seen in Figure 2(d), the predicted excitation functions with the inclusion of PE contribution is in good agreement with the measured excitation function. 15 20 25 30 35 40 45 50 55 -400 -200 0 200 400 600 800 1000 1200 b) 69 Ga(, 2n) 71 As (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 10 15 20 25 30 -400 -200 0 200 400 600 800 1000 1200 a) 69 Ga(, n) 72 As (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 30 35 40 45 -400 -200 0 200 400 600 800 1000 1200 c) 69 Ga(, 3n) 70 As (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 36 38 40 42 44 46 48 -200 0 200 400 d) 69 Ga(, x) 68 Ge (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) α + 69Ga [73As]* 2n + 71As α + 69Ga [73As]* 3n + 70As East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 24 15 20 25 30 35 40 45 50 55 -400 -200 0 200 400 600 800 1000 1200 b) 69 Ga(, 2n) 71 As (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 10 15 20 25 30 -400 -200 0 200 400 600 800 1000 1200 a) 69 Ga(, n) 72 As (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 30 35 40 45 -400 -200 0 200 400 600 800 1000 1200 c) 69 Ga(, 3n) 70 As (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 36 38 40 42 44 46 48 -200 0 200 400 d) 69 Ga(, x) 68 Ge (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) Figure 2. Experimentally quantified and theoretically predicted excitation functions for 72As, 71As, 70As, and 69Ge residues. The curve represents the theretical prediction, and the symbls represent the experimental crss-sectins. Pearsn's crrelation cefficient between theretically predicted and experimentally measured production cross-sections is R ≈ 0.99. This result indicated a strong positive association between the predicted and measured production cross-sections. A) 6 9Ga(α, x)68Ga reaction 68Ga residue is produced when unidentified particles (x) are emitted from an excited composite nucleus [73As]* via 69Ga(α, x)68Ga complex reaction channel. Figure 3(a) shows the theoretically predicted excitation and experimentally measured excitation functions. It may be bserved frm Figure 3(a) that the predicted (pure EQ) excitation function is in good agreement with the measured one. Furthermore, Pearsn's crrelation cefficient between the predicted (pure EQ) and measured crss-sections have a value of R ≈ 0.5, indicating a moderate and positive correlation between the measured and the predicted excitation functions. B) 69Ga(α, x)67Ga reaction The measured excitation functins, alng with the theretical predictins (with and without the contribution of PE reaction) for 69Ga(α, x)67Ga complex reaction channel, are shown in Figure 3(b). Note that 67Ga residue is produced when unidentified particles (x) are emitted from an excited composite nucleus [73As]* via 69Ga(α, x)67Ga complex reaction channel. East Afr. J. Biophys. Comput. Sci. (2023), Vol. 4, No. 1, 18-27 25 25 30 35 40 -200 0 200 a) 69 Ga(, x) 68 Ga (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ)  ( m b ) E lab (MeV) 30 35 40 45 50 -200 0 200 (Levkovski, 1991) COMPLETE (Pure EQ) COMPLETE (PE and EQ) b) 69 Ga(, x) 67 Ga  ( m b ) E lab (MeV) Figure 3. Experimentally measured and theoretically calculated excitation functions for 68Ga and 69Ga residues. The curve represents the theretical prediction, and the symbls represent the experimental crss-sectins. Figure 3(b) shows that the pure EQ-predicted excitation function agrees with the experimentally measured excitation function. Furthermore, Pearson's correlation coefficient value (R≈0.98) indicated a strng and psitive crrelation between theretically predicted and experimentally measured reaction crss- sectins. CONCLUSION Excitation functions of 69Ga(α, n)72As, 69Ga(α, 2n)71As, 69Ga(α, 3n)70As, 69Ga(α, x)69Ge, 69Ga(α, x)68Ga and 69Ga(α, x)67Ga reactions populated in the interactin of α-prjectile with 69Ga-target were studied at ≈10 -50 MeV. Except for 69Ga(α, x)68Ga reaction, the theoretically predicted (admixture of PE and EQ reactions) reaction crss-sections using the statistical mdel code COMPLETE with the K=8 and no=5, in general, were fund to be in gd agreement with the experimentally measured excitation functions. 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