Calculating the stopping power and neutron yield of 133CS (A,2N) 135LA reaction for the energies between (18.5-47)

In the present work, calculated the cross sections of 133CS (A,2N) 135LA reaction By using interpolated and take the cross-sections published in the international literature for the selection of the appropriate energies ground level interaction in a computer–based program (MATALAB-17.0), in steps of energies (0.5 MeV). The quasi-experimental equation was derived from tabulated results linking a specific cross-section with energies, accounting for the neutron yield in accordance with the Zeigler neutron interactions formula using the program (SRIM 2013), and accounting for the stopping power which was also drawn and tabulated by measuring the yield at two closely spaced energies E1 and E2, one can determine the average value of the integrand over this energy interval and it turns out that the values are directly proportional until the alpha energy values reach 40 million electron volts. We notice that the change in the values is very slight. The neutron yield values begin to increase until the alpha energy reaches 40 million electron volts, after which the neutron yield becomes almost constant.


Introduction
Nuclear Reactions: When two particles collide between the m1 projectile and the m2 target, in general, in the products m3 and m4 they are defined as nuclear reactions and are governed by the conversation [1].A direct nuclear reaction is a set of nuclear processes such as inelastic nuclear collisions, denudation and capture reaction without forming a compound nucleus Products created by the development of a compound nucleus appear fundamentally different from those produced through the interaction between the falling particle and the target nucleus, which takes place in a significantly shorter amount of time than the corresponding compound nucleus' life [2].As a result, it appears that the mechanisms behind nuclear reactions are seen differently by the two processes (compound nucleus and direct reaction).Assuming the possibility of some tens of MeV of depth contact, the target nucleus's lifetime in the falling particle system and the direct reaction process is 10 -22 .. Despite this, a compound nucleus can only hold energy for a small fraction of an electron volt for 10-14 seconds.As a result, the two reaction mechanisms' time scales are entirely different [2].Based on one of the reaction mechanisms, estimating the energy of a nuclear reaction is very challenging.It is qualitatively possible to argue that as incident particle energy increases, so do partial widths and reaction channel counts, leading to a decreasing amount of time the system spends in the compound nucleus.At lower energies, the formation of a compound nucleus is more likely, while at higher energies, the direct reaction mechanism is more prevalent [3].Direct reaction is therefore a one-step procedure.This was discovered experimentally in reactions (d, p) where they were more common than (d, n) interactions.It was initially identified by Oppenheimer and Philip in the analysis of low energy interactions (d, p) [3].. This is wholly unexpected given that the reaction would have continued until the compound nucleus was formed.Additionally, interactions (d, n) will predominate over reactions (d, p) because there is no coulomb barrier.According to Oppenheimer and Phillips, the deuteron is a loosely bound system, which explains the reaction..When the proton approaches the target nucleus, the Coulomb field separates it from the deuteron, while the neutron is captured at low energies [3].In the name of the abstraction process, this process is referred to as the Oppenheimer and Phillips process, or More, at both low and high energies.The reactions of (d, p) and (d, n) are equally likely in high energy regions.However, the angular distribution of the dissociation products peaks in the forward direction with very small intensities in the backward direction, which sets the direct reaction apart from other nuclear reaction mechanisms [3].

Radioisotopes production:
Nuclear reactions in reactors or charged particle bombardment in accelerators produce radioisotopes for use in biomedical applications, such as diagnostic imaging or therapeutic treatments.Protons, deuterons, and helium particles (3He and 4He) are the usual charged particle reactions in accelerators; neutrons are responsible for starting nuclear reactions.In special cases big sized accelerators deliver heavy ions.The radiation beam, especially the gamma beam, is obtained either generated by small accelerators or from decay of some special radionuclide (e.g. 60 Co)... Currently more than 80% of the medical radioisotopes are produced by research reactors, the remaining isotopes are made by particle accelerators, mostly with circular accelerators (cyclotrons) and sometimes with linear accelerators [4].
Since the radionuclide are produced using both cyclotrons and reactors accurate information of the relevant charged-particle as well as neutron induced the importance for choice the radionuclide for diagnostic application or therapeutic, the data of nuclear reaction are of great importance in the optimization of the production processes, i.e. achieving the minimum level of impurities with the maximum yield of desirable radionuclide [4].

Nuclear Reaction Cross Sections:
The probability that a specific nuclear reaction will occur is known as the cross section, and it is commonly used to determine the effective nucleus size [3].An essential and fundamental requirement for studying nuclear systems is having cross-section data for the reaction [5]: where I is the number of incident particles per unit time per unit area, R is the number of reactions per unit time per nucleus, and  is the cross sections [6].. The cross section is a unit of area and is within the square of the nuclear radius.A commonly used unit is the barn [7][8] : 1 b a r n = 1 0 -24 cm 2

Stopping Power
Is a measure of the effect of a substance on the kinetic energy of a charged particle passing through it.Stopping power is often quoted relative to that of a standard substance, usually air or aluminum [9].Particle Stopping Power :the stopping power of alpha particles is mainly due to the ionization of the target electrons, the excitation of lower levels, the exchange of charge between the projectile and the target, and the nuclear stopping ability [10] [11] , that is: Neutron Yield For a perfect , thin, and uniform target for MONO-ENERGETIC particles incident energy E b , the neutron yield detection per incident particles , [12].Y = nt σ (Eb) ϵ (Eb) --------(3) Where n = number of target atoms/ volume , t = thickness.σ = cross sections., ϵ = efficiency of neutron .and [11].
( E thr = Eb -ΔE) E thr = Threshold Energy [12] , ΔE = In the target energy loss of the beam.f = In each targetmolecule the number of target atoms.

  E dx dE
= The beam energy as a function OF the stopping power of the [12] [13] medium .

Result
In this study, the researcher relied on the values of the cross sections (N.P.M.Sathik, M.Afzal Ansari, B.P.Singh, R.Prasad) [16] for the energy range from 18.5 to 47 million electron volts.Using simulation programs, the values of the cross sections were obtained with energy steps of 0.5 million electron volts, as shown in Table (1) .Figure (1 ) shows the values of the cross sections and their relationship to the alpha energy.Also, a semi-empirical equation was obtained from figure (2)

4e+07 where y=cross section and x=Alpha Energy
The relationship is direct for the values ranging from 18.5 MeV to 26.5 MeV.The higher the alpha energy, the greater the probability of the reaction occurring until it reaches 1146.9 mbarn times 26.5 MeV .In Table No. 2, based on the SRIM program and the Zeckler equations, the nuclear stopping power, the electronic stopping power, and the total stopping power were calculated, and according to Equation No. 2, the results were plotted in Figure 3.It was found that the relationship between the stopping power and the alpha energy falling on the cesium isotope decreases smoothly.In Table No. ( 3) , the neutron yield of the reaction was calculated of 133 CS (A,2N) 135 LA reaction in units ( (n/10 6 alpha) ) based on equations ( 5) and ( 6) and using the average cross section and s. Figure 3 shows that the highest neutron yield that can be obtained from the reaction is at values ranging from 40 million electron volts to 4 million electron volts.

Conclusions
It turns out that the values of the cross sections are directly proportional to the alpha energy for values from 188.5 million electron volts to 26.5 million electron volts, after which they begin to decline exponentially.The stopping power values are inversely proportional to the alpha power, where as the alpha power increases, the stopping power decreases smoothly .The neutron yield values begin to increase until the alpha energy reaches 40 million electron volts, after which the neutron yield becomes almost constant.

1 ,
and it turns out that the values are directly proportional until the alpha energy values reach 40 million electron volts.We notice that the change in the values is very slight, as shown in Figure ( 4).

Table 1 .
The Energy of Alpha particle a function of the cross section for 55-CS-133(A,2N)57-LA-135 reaction( p.work) .

Table 2 .
The

Table 3 .
The neutron yield as a function of Alpha Energy for the 55-CS-133(A,2N)57-LA-135 reaction p.work .