An Investigation about The Deuterium-Deuterium Nuclear Fusion differential cross section .

Differential cross section for the D-D fusion reaction represents an important parameter in calculating the neutron or proton yield and this calculation need to study the changes of the differential cross section with both deuteron energy and reaction angle .We see that the differential cross section are strongly effected with a range of reaction angle between [0-100] degree , and it seems that it has a maximum value when the reaction angle equal to zero because the present of the parameter cos θ in there calculated equation .From the figures we notice a good agreement between our calculated results and the experimentally results. This lead to the ability for using this model in the future for different calculations and the ability for modifying it's to construction a like formulas for another fusion reactions by depending on their physical characteristics.


Introduction
The D(d,n)3He and D(d,p)3H reaction is of interest for nuclear processes in the early solar system and early universe and for fusion energy applications.This reaction belongs to the network of processes which will be used to fuel the first inertial-confinement fusion reactors [1].The knowledge of D(d,n)3He and D(d,p)3H fusion cross sections at low energies is of interest in pure and applied physics.Both reactions are crucial for the Standard Big Bang Nucleosynthesis (SBBN) network calculations, as they are involved in the synthesis of D, 3He, 4He and 7Li in the early universe.[2].

Theory
For nuclear reactions in which the reactant must penetrate a barrier, which is the case with thermonuclear reactions, the cross section can be expressed in the form [3]. σDD = 288/Ed (-45.8/Ed)……………(1) Where Ed is the deuteron bombarding energy in KeV, and σDD is the total cross section in barns.
Also there is another relation to compute total cross sections for D-D reactions as follows [4].σDD = exp(4.727-0.03154Ed)………………(2) Where Ed is the deuteron bombarding energy in MeV, and σDD is the total cross section in mille barns.

Calculation of differential cross section
The differential cross sections dσ/dΩ are calculated as a function of reaction angle θ for deuteron energies Ed for wide range from (18-26) MeV by using the relation

Discussion and conclusion
Firstly, we have made a theoretical study about the differential cross section for the D-D reaction From the calculations deals with the differential cross section in the centre of mass system that represented in Figure ( 2)and(3) and Tables (2)and(3) we conclude that there are a good agreement between our results and the published results in ref. [7].For wide range of incident deuteron energy that represented in keV unites and Mev unites, we concentrate on the energy range from [18-26 MeV] since there is an published result present which explained in below.Through the study the change of the total cross sections for D-D reaction with deuteron velocities we see that the probability of interaction increased when deuteron velocities increasing in the range of velocities between (1.E+6-1.E+8).From figure (1) We see that our calculated results about the total reaction cross section are more compatible with the published results ref. [5].we concentrate on the velocity range from(1.E+6-1.E+8) since there is published result present From the comparison between our calculated results and the experimentally published result we have obtained the same behavior .From the comparison between our calculated results and the experimentally result we have obtained the same behavior but it is necessary to note that there are a different values for the differential cross section and this case can be explained by the fact that we use an empirical formulas for calculation the total cross section given by eq.( 1)which is especially deals with energy given in KeV and another empirical formulas for calculation the total cross section given in eq.( 2)which is especially deals with energy given in MeV .