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The interaction of nucleon-nucleon (NN) has certain physical characteristics, indicated by nucleon, and meson degrees of freedom. The main purpose of this work is calculating the ground-state energies of 12H and 24He through the two-body system with the exchange of mesons (π, σ, and ω) that mediated between two nucleons. This paper investigates the NN interaction based on the quasirelativistic decoupled Dirac equation and self-consistent Hartree-Fock formulation. We construct a one-boson exchange potential (OBEP) model, where each nucleon is treated as a Dirac particle and acts as a source of pseudoscalar, scalar, and vector fields. The potential in the present work is analytically derived with two static functions of meson, the single-particle energy-dependent (SPED) and generalized Yukawa (GY) functions; the parameters used in meson functions are just published ones (mass, coupling constant, and cutoff parameters). The theoretical results are compared to other theoretical models and their corresponding experimental data; one can see that the SPED function gives more satisfied agreement than the GY function in the case of the considered nuclei.