In recent years, the attention of scientists has been drawn to laser accelerators because they have a smaller size and more power than RT accelerators. But to upgrade these laser accelerators for hadron therapy, the theory governing these accelerators needs more investigation. The present paper represents the theory of laser-driven accelerators. Also, for the first time, we calculated the quantum relativistic important parameters such as the effective atomic number, z_eff, β=v⁄c , parameter, the density effect, δ⁄2, the shell effect,〖∆L〗_shell, Barkas effect, L_Barkas , Lynard Sorensen, effect, 〖∆L〗_LS, the standard perturbation function, L_stand, the first order general term of quantum perturbation theory, L_Pert, for proton and carbon beams in different energies versus the depth of penetration in the different human tissues using Maple programming, and our numerical results show that since the physical and chemical properties of carbon and hydrogen ions are not the same and carbon is heavier than hydrogen, carbon and hydrogen ion beams in hadron therapy do not have the same behavior inside the different human tissues. تفاصيل المقالة