A theoretical study including the effects of the fusion characteristics parameters on the fundamental fusion rate for the BEC state in D-D fusion reaction is deal with varieties physical parameters such as the fuels density, fuel temperature and the astrophysics S-factor are processed to bring an approximately a comparable results to agree with the others previously studies.

         Calculation of the power density of the nuclear fusion reactions plays an important role in the   construction of any power plants. It is clear that the power released by fusion reaction strongly depended on the fusion cross section and fusion reactivity. Our calculation concentrates on the most useful and famous fuels (Deuterium-tritium) since it represents the principle fuels in any large scale system like the so called tokomak.

A standard theoretical neutron energy flux distribution is achieved for the triton-triton nuclear fusion reaction in the range of triton energy about ≤10 MeV. This distribution give raises an evidence to provide the global calculations including the characteristics fusion parameters governing the T-T fusion reaction.

A new results for fusion reactivity and slowing-down energy distribution functions for controlled thermonuclear fusion reactions of the hydrogen isotopes are achieved to reach promising results in calculating the factors that covered the design and construction of a given fusion system or reactor. They are strongly depending upon their operating fuels, the reaction rate, which in turn, reflects the physical behavior of all other parameters characterization of the system design

In this study, light elements Li ,10B for (a,n) and (n,a) reactions
as well as o-particle energy from threshold energy to 10 MeV are
used according to the available data of reaction cross sections. The
more recent cross sections data of (a,n) and (n,a) reactions are
reproduced in fine steps 42 Kev for 10B(n,o) Li in the specified
energy range, as well as cross section (o,n) Values were derived from
the published data of (n,a) as a function of a-energy in the same fine
energy steps by using the principle inverse reactions. This calculation
involves only the ground state of Li OB in the reactions 'Li(a,n) B
B (n,a) Li
Introduction
When two charged nuclei overcome their Coulomb repulsion, a
rearrangement

The challenge in studying fusion reaction when the projectile is neutron or proton rich halo nuclei is the coupling mechanism between the elastic and the breakup channel, therefore the motivation from the present calculations is to estimate the best coupling parameter to introduce the effect of coupled-channels for the calculations of the total cross section of the fusion  , the barrier distribution of the fusion   and the average angular momentum ⟨L⟩ for the systems ⁶He+²⁰⁶Pb, ⁸B+²⁸Si, ¹¹Be+²⁰⁹Bi, ¹⁷F+²⁰⁸Pb, ⁶He+²³⁸U, ⁸He+¹⁹⁷Au and ¹⁵C+²³²Th using quantum mechanical approach.  A

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The cross section evaluation for (α,n) reaction was calculated according to the available International Atomic Energy Agency (IAEA) and other experimental published data . These cross section are the most recent data , while the well known international libraries like ENDF , JENDL , JEFF , etc. We considered an energy range from threshold to 25 M eV in interval (1 MeV). The average weighted cross sections for all available experimental and theoretical(JENDL) data and for all the considered isotopes was calculated . The cross section of the element is then calculated according to the cross sections of the isotopes of that element taking into account their abundance . A mathematical representative equation for each of the element