Cross Sections Calculations of 33 S ( n , α ) 30 Si reaction by using the inverse reaction for the first exited state

In this study light elements Si , S for Si(α,n)S reaction as well as α-particle energy from (5.001) MeV to (6.284) MeV are used according to the available data of reaction cross sections with threshold energy (3.959MeV). The more recent cross sections data of Si(α,n)S reaction is reproduced in fine steps in the specified energy range , as well as cross section (α,n) values were derived from the published data of (n,α) as a function of energy in the same fine energy steps by using the principle of inverse reaction . This calculations involves the first exited state of Si , S in the reactions Si(α,n)S and S(n,α)Si . These data are listing , plotted and dissection .


Introduction
The interaction of particles with matter is described in terms of quantities known as cross sections which is defined in the following way [1].Consider a thin target of area (a) and thickness (X) containing (N) atoms per unit volume, placed in a uniform mono-directional beam of incident particles (neutrons for example of intensity I o ) , which strikes the entire target normal to its surface as shown in fig.(1).It is found that the rate at which interactions occur within the target is proportional to the beam intensity and to the atom density, area and thickness of the target.Summarizing this experimental result by an equation, we define the interaction rate (interaction rate)=σINaX ---(1) Where the proportionality constant σ is known as the cross section , Thus σ = interaction rate / INaX ---- (2) As NaX is equal to the total number of atoms in the target, it follow that σ is the interaction rate per atom in the target per unit intensity of the incident beam [2] .

Reciprocity Theory
If the cross-sections of the reaction A(α,n)B is measured as a functions of Tα (Tα = Kinetic energy of α-particle) the cross-sections of the inverse reaction B(n,α)A can be calculated as a function of Tn (Tn = Kinetic energy of neutron) using the reciprocity theorem [3] which states that : Where σ (α,n) and σ (n,α) represent cross-sections of (α,n) and (n,α) reactions respectively , g is a statistical factor and  is the De-Broglie Wave Length divided by 2π and is given by Where ħ is Dirac constant (h /2π ) , h is plank constant , M and V are mass and velocity of α or n particle .
From eq.( 4),we have Where T is kinetic energy The statistical g-factors are givens by [3] The conservation law of the momentum implies that: ) ℓn ----(9) J c and π c are total angular momentum and parity of the compound nucleus .

J. of university of
Where I α is the total angular momentum of alpha particle.s α is spin of α-particle = 0 l α is the orbital angular momentum of α-particle.And I n is the total angular momentum of the neutron s n is spin of neutron = 1/2 l n is the orbital angular momentum of neutron .From eq.( 8),we have: The reactions A(α,n)B and B(n,α)A can be represented with the compound nucleus C as in the following schematic diagram.It is clear that there are some important and useful relations between the kinetic energies of the neutron and alpha particle.
One can calculate the separation energies of αparticle (S α ) and neutron (S n ) using the following relations: S α and S n are separation energies of α and n from C. Then 17) Combining (15a) , (15b) , ( 16) and ( 17 The threshold energy E th is given by : Thus eq.( 3) can be written as follows : It is clear from this equation that the cross sections of reverse reaction are related by a variable parameters which can be calculated if the nuclear characteristics of the reactions are known.

Results and Discussion
The atomic mass of elements and isotopes mentioned in this study have been taken from the latest (1995) nuclear wallet cards released by the National Nuclear Data Center(NNDC) [4] and abundances are given for stable isotopes from reference International Atomic Energy Agency (IAEA) [5].The energy level, parity and spin scheme of isotopes used in the present work is given in table (1) [6].1):Energy level, spin and parity of isotopes( 33 S and 30 Si) [6] The cross sections of 30 Si(α,n) 33 S reaction have been, calculated in fine steps from (5.001) MeV to (6.284) MeV of α-particle energy by Flynn D.S. , Sekharan K.K. , Hiller B.A., Laumer H. and Weil J.L. [7] these data are plotted in Fig. (2).
By using the compound theory we derive the mathematical formula for 33 S(n,α) 30 Si reaction by first exited state : The evaluated cross sections as a function of neutron energy from (0.9468 ) MeV to (2.1133) MeV of present work are listed in tables (2).These data are plotted in Fig. (3) and we do not get equation for distribution because there are resonance and we get the maximum cross section to produce the 30 Si by neutron energy (1.4123) MeV is (1508.0)mbarn. 30Si is very important in technology field.In Fig. (3) we observed that the high probability to produce 30 Si in fast neutron which (1.6878) MeV and (2.0860) MeV are (1116.4)mbarn and (1192.4)mbarn respectively.
In figure (4) the cross sections as a function of neutron energy by Wagemans C. , Weigmann H. , Barthelemy R. [8] , we observed that the high probability to produce 30 Si by bombard 33 S by (0.9489MeV) is (66.55mbarn) .

Detector I o I
x )I n and π n are total angular momentum and parity of neutron .the reactions and as the Q-value of the reaction A(α,n)B is given by :

Figure ( 1 )
Figure (1): A schematic diagram illustrating the definition of total cross section in terms of the reduction of intensity[1].

Table ( 2
):The cross sections of 33 S(n,α)30Si reaction as a function of neutron energy present work