The Physical origin of the nuclear symmetry energy is studied within the relativistic mean field (RMF) theory. Based on the nuclear binding energies calculated with and without mean isovector potential for several isobaric chains we conform earlier Skyrme-Hartree-Fock result that the nuclear symmetry energy strength depends on the mean level spacing $epsilon (A)$ and an effective mean isovector potential strength $kappa (A)$. A detaied analysis of isospin dependence of the two components contributing to the nuclear symmetry energy reveals a quadratic dependence due to the mean-isoscalar potential, $simepsilon T^2$, and, completely unexpectedly, the presence of a strong linear component $simkappa T(T+1+epsilon/kappa)$ in the isovector potential. The latter generates a nuclear symmetry energy in RMF theory that is proportional to $E_{sym}sim T(T+1)$ at variance to the non-relativistic calculation. The origin of the linear term in RMF theory needs to be further explored.
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