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 × 4He + 23.8MeV reaction. The results of the calculation for three reactions give rise a wide compatible with the other experimental works.
