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In this paper, we focused on the investigated and studied the cold fusion reaction rate for D-D using the theory of Bose-Einstein condensation and depending on the quantum mechanics consideration. The quantum theory was based on the concept of single conventional of deuterons in Nickel-metal due to Bose-Einstein condensation, it has supplied a consistent description and explained of the experimental data. The analysis theory model has capable of explaining the physical behaviour of deuteron induced nuclear reactions in Nickel metals upon the five-star matter, it‘s the most expected for a quantitative predicted of the physical theory. Based on the Bose-Einstein condensation theorem formulation, we calculation the cold fusion reaction rate for D-D transfer to Nickel-metal using the astrophysical S factors (S = 110KeV — barn) for d(d,p)T, d(d, n)3He reactions and (S = 110 × 106 and S = 110 × 1013KeV — barn) for D + D × 4 He + 23.8MeV reaction. The results of the calculation for three reactions give rise a wide compatible with the other experimental works.

Fusion cross-section of reactions Mg24+C12, Mg24+Mg24,26, Si28+Si28,29,30 have been calculated by employing Skyrme effective interaction. SkIII, Ska and SkM*. A comparison with different theoretical approaches is presented. Good agreement has been found between the current results and the corresponding experimental results.

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