The relativistic consistent angular-momentum projected shell model (ReCAPS) is used in the study of the structure and electromagnetic transitions of the low-lying states in the N =Z nucleus 52 Fe. The model calculations show a reasonably good agreement with the data. The backbending at 12 + is reproduced and the energy level structure suggests that neutron-proton interactions play important roles.ReCAPS, relativistic mean field, angular-momentum projection method, 52 Fe, neutron-proton interactionThe nuclear structure under extreme conditions has attracted much attention recently, for instance, high spin states and superdeformation [1−4] , halos [5,6] , isospin effects [7] , nuclear shape phase transition [9] , three-body interaction [5] which is one of the tasks of quantum simulation, superheavy elements [11,12] . During the last decade, comprehensive new experimental information on the N Z nuclei(A 40) has been collected with the development of radioactive ion beam facilities and large detector arrays [13−17] . The N Z nuclei are especially interesting because they contain rich nuclear physics information and different theoretical models can be tested. Firstly, these nuclei provide a sensitive test for the isospin symmetry of nuclear force and isospin excitations. The study of this region can tell information on the neutron-proton correlations, which maybe play important roles in the nuclear structure. The proton-rich nuclei near the N = Z line being involved in the rapidproton capture process, is important to nuclear astrophysics [18] . The properties of these nuclei have become the focus of some theoretical studies in recent years [19−23] . This paper studies the structure of the N = Z nucleus 52 Fe in the relativistic consistent angularmomentum projected shell model (ReCAPS) developed recently asrecaps1, recaps2. ReCAPS is a self-consistent model, which combines relativistic mean field(RMF) and angular-momentum projection method. This model can describe not only nuclear structures of ground state, but also the low-lying excited states. Especially, ReCAPS can predict the properties of nuclei far from stability as a result of the predictability of the RMF theoretical studies of the ground states. Although these
