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In this work, reaction cross-sections w
ere
calculate
d
and Excitation Functions were evaluated for productions of ^{208}Bi, ^{212,211,210}At, ^{211,210}Po isotopes using EXIFON code in the energy range from 0 MeV to 30 MeV. The code is based on an analytical model for statistical multistep direct and multistep compound reactions (SMD/SMC model)
.
This work also investigate
s
the shell structure effect on the reaction cross-section, the results obtained show that the cross-se
c
tio
ns
of (a, na) reaction for both with shell correction and without shell correction are zeros at energies range considered, this shows that the energy of the incident particle is below the threshold of this reaction due to the present of coulomb repulsive force between the projectile and target nucleus.

Studies of excitation functions of particle-induced reactions are of considerable significance for testing nuclear models as well as for practical applications, especially in cyclotron production of radioisotopes [

A nuclear reaction is a process that occurs when a nuclear particle (nucleon or nucleus) gets into close contact with another [

The first two reactions (1.1) are distinguished by the fact that the projectile re-emerges after the reaction. The first of these represents elastic scattering. The second reaction represents inelastic scattering.

To calculate the reaction cross section, it is necessary to compute the number of particles that disappear from the elastic channel, what is measured by the flux of the current of probability vector through a spherical surface of large radius centered at the target [

A radial wave function inside the nucleus should connect to the external function with a continuous function and its derivative at

The function must have identical values if calculated with the internal or the external function and this condition creates a relationship between

We have an equation that is useful when we study the presence of resonances in the excitation function (cross section as a function of the energy).

Statistical multistep model

Statistical multistep models are very successful in describing nuclear reactions at energies up to about 100 MeV [

In the statistical multistep model, the total emission spectrum of the process

The first term on the right hand side of Equation (1.5) represents the statistical multistep direct (SMD) part which contains from single-step up to five-step contributions. The second term represents the statistical multistep compound (SMC) emission which is based on a master equation. Both terms together (SMD + SMC) represents the first-chance emission process [

The following relations between the optical model (OM) reaction cross section and the energy-integrated partial cross sections should be satisfied (at each incident energy

With

where

For example, the (n,p)-activation cross sections have the form

The SMD cross section is a sum over s-step direct processes given by: [

The SMD cross section has the form

where

and

The multiple particle emission is expressed as:

To keep the model tractable, a simple two-body interaction is assumed: [

The factor

The single-particle state density of particles

Where

The single-particle state density of bound particles (at Fermi energy) is then defined by

Where the factor 4 considers the spin and isospin degeneracy

EXIFON code was used which is computer program package for computational nuclear Data physics which is based on an analytical model for statistical multistep direct and multistep compound reactions (SMD/SMC model). It predicts emission spectra, angular distributions, and activation cross sections for neutrons, protons, alpha particles, and photons. Multiple particle emissions are considered for up to three decays of the compound system. EXIFON is a fast, easy-to-handle code which predicts cross sections from one global parameter set. The only adjustable quantity is the pairing shift. The INPEXI code creates input files for EXIFON2.0 from mass and shell-correction tables. The MAKE6 code transforms EXIFON output into an ENDF-6 format file [

The model is based on random matrix physics with the use of the Green’s function formalism [

The program was run and the input and output directory was defined, and then the target nucleus is specified. The neutron was chooses as incident particle followed by selecting the target nucleus and excitation function in the general option section for this calculation.

The number of incident energy was specified followed by the first incident energy, and then the incident energy step is also specified. The cross section correspond to each particular energy was obtained.

The shell structure effects are considered in SMC processes. Under such a situation, the single-particle state density g, in Equation (1.19) is multiplied by the factors

With

The calculations in this study were performed with

The cross section obtained was tabulated in hot-pot Figures 1-3 and the excita-

tion function was showed in Figures 1-10. The calculations in which the shell correction was taken into consideration are denoted by “With shell correction” on the graph’s legend, while those without the shell correction effects are denoted by “Without shell correction”.

In hot-pot ^{208}Bi(a, na)^{207}Bi and ^{208}Bi(a, an)^{207}Bi reactions are zeros. This shows that these two reactions would not occur at the incident energy of (0 - 30) MeV.

The two reactions are distinguished by the fact that the projectile re-emerges after the reaction. The first of these represents elastic scattering. The second reaction represents inelastic scattering in Equation (2.3).

Figures 5-8 are graphs of cross section against incident energy of the alpha particle, ^{208}Bi(a, g)^{212}At is a compound nucleus formation of Astatine(212) followed by gamma emission. ^{208}Bi(a, ng)^{21}^{1}At is a knock out reaction for the nucleus formation of Astatine (211) followed by gamma emission. ^{208}Bi(a, pg)^{21}^{1}Po is also a knock out reaction for the nucleus formation of Polonium (211) followed by gamma emission. ^{208}Bi(a, 2ng)^{210}At is also a knock out reaction for the nucleus formation of Astatine(210) followed by gamma emission. All the results shows that shell structure correction does not much changes at the range of energies from (0 - 30) MeV.

Figures 10-13 are graphs of cross section against incident energy of the alpha particle, ^{208}Bi(a, n)^{211}At is a knock out reaction for the nucleus formation of Astatine (211). ^{208}Bi(a ,2n) ^{210}At is also a knock out reaction for the nucleus formation of Astatine (210) ^{208}Bi(a, pn)^{210}Po is also a knock out reaction for the nucleus formation of Polonium (210). ^{208}Bi(a, 3n)^{211}At is a knock out reaction for the nucleus formation of Astatine (209) All the results shows that shell structure correction does not much changes at the range of energies from (0 - 30) MeV except for ^{208}Bi(a, 3n) ^{212}At reaction although the cross section value is very small.

Nuclear reaction in the intermediate-energy region is a matter of interest in some fields of technology and science such as reactor technology, radiation therapy in nuclear medicine, medical radionuclide production, diagnostic and therapeutic studies, Accelerator Driven Systems (ADS), fusion and fission reactor. Radioactive isotopes play an important role in the field of medical

science in terms of beneficial applications in both diagnosis and therapy purposes. The reaction cross-sections were calculated and Excitation Functions were evaluated for productions of ^{208}Bi, ^{212,211,210}At, ^{211,210}Po isotopes in the energy range from 0 MeV to 30 MeV. We also investigate the shell structure effect on the reaction cross-section, the results obtained show that the cross-section of (a, na) reaction for both with shell correction and without shell correction are zeros at energies range considered, this shows that the energy of the incident particle is below the threshold of this reaction due to the present of coulomb repulsive force between the projectile and target nucleus. The application in precise evaluation of the Excitation Functions as well as the production of isotopes is necessary to embrace the current and future needs for medical radionuclide.

Ahmad, I., Yola, Y.I. and Koki, F.S. (2017) Evaluation of Excita- tion Functions of Reactions Used in Produc- tion of Some Medical Radioisotopes. Inter- national Journal of Medical Physics, Clinical Engineering and Radiation Oncology, 6, 290-303. https://doi.org/10.4236/ijmpcero.2017.63026