The study of how a nuclear particles interaction cross-sections change with varying energies is becoming more important, because of their use in targeted radionuclide therapy (TRT) and nuclear imaging. The need for detailed study of interaction data for nuclear particles, particularly within the low energy range (0–25 MeV) is apparently overlooked. This paper employed GEANT4, a C++-based Monte Carlo simulation toolkit, to investigate the energy-dependent behaviour of alpha particles, deuterons, and protons in natural Nickel and to model nuclear reactions involved in the production of theranostic radionuclides, specifically Cu-67 via Ni-66(a,t) and Ni-62(d,n), and Cu-64 through Ni-64(p,n) reactions. The result show the shortest mean free path (MFP) of 2.697 cm at 7.5 MeV, 3.87 cm at 17.5 MeV and 4.012 cm at 17.5 MeV for alpha deuteron and proton respectively. The maximum cross section per atom (CPA) of 4.565 b at 7.5 MeV for α, 3.356 b at 17.5 MeV for d and 2.73 b at 17.5 MeV for p. The maximum total cross section (TCS) for α is 1.4175 b at 25 MeV, 1.773 b at 17.5 MeV for d and 1.17 b at 25 MeV for p, all for the reactions Ni-67(a,t)Cu-67, Ni-62(d,n)Cu-67, and Ni-64(p,n)Cu-64. Theranostic applications utilise Cu-64 and Cu-67 as important pair radionuclides.