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Gallium nitride co-doped with magnesium and europium shows great potential for active layers in red light emitting diode structures due to strong and sharp luminescence emission around 620 nm. In this work, sharp and intense Eu3+ luminescence lines from the excited states of the 5D J (J = 0, 1) multiplets to the ground states of the 7F J (J = 0, 1, 2) multiplets have been analyzed using a C 2 v crystal-field equivalent operator Hamiltonian. A model of Eu centers with the C 2 v symmetry has been proposed to be an Eu3+ complex accompanied by either a pair of nitrogen and gallium vacancies (V N - V Ga) or a pair consisting of a nitrogen vacancy and magnesium impurity (V N - Mg Ga) in the vicinity of the Eu ion based on the crystal-field analysis, the selection rules and the observed polarization of the Eu3+ luminescence lines. Energy transfer from the host to the Eu ions under band-to-band excitation occurs through electron-hole recombination between V N with the electron-like state and V Ga or Mg Ga with the hole-like state; these may be associated with the shallow-trapped or deep-trapped states, respectively, proposed as the energy transfer mechanism in previous literature. • Polarized photoluminescence/cascade-luminescence from ex situ Eu-doped GaN(Mg). • Energy levels/states of 7F 0 ,7F 1 and 7F 2 multiplets of Eu3+ experimentally estimated. • Model of Eu centers in GaN(Mg) with C 2 v (orthorhombic) symmetry proposed. • Eu complex with N/Ga vacancy pair, or a pair consisting of N vacancy and Mg impurity. • Energy transfer GaN.→Eu via recombination between these electron-like/hole-like states [ABSTRACT FROM AUTHOR]