Abstract: In this paper we study a given system of two identical nucleons in the presence of an attractive δ interaction. We derive the formulas for energies of identical nucleons with the configuration |j_1 j_2 J \rangle explicitly, and explain all empirical rules of the energy level ordering with spin J and parity, deep understandings of which have been desirable for a few decades. We also proved analytically that the energy interval between the lowest level and the second lowest level is larger than the sum of intervals of all other successive levels, thus present a sound explanation of the large energy gap between the ground state and the first excited state of such system.