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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.  

Furthermore, Pearsn's correlation cefficients r 

mderate to strng psitive crrelatins 

between the theretically predicted and 

experimentally measured excitation functions 

for investigated reaction channels. The present 

results also disclosed a significant contribution 

from a pre-equilibrium reaction, particularly in 

the tail sections of the excitatin functions. 

Thus, the admixtures of pre-equilibrium and 

equilibrium modes of reactions must be 

considered when predicting total reaction cross-

sections. 

Acknowledgment  

The author gratefully acknowledges Webshet 

Beharu and Anabel T. Abosse for their valuable 

scientific discussions that contributed to this 

work. The author remains solely responsible for 

all opinions and any errors.  

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