[en] Electronic and positron band structures and charge densities of GaN, AlN, and their alloy Ga_0.5Al_0.5N in zinc-blende structure using the empirical pseudopotential method are investigated. For the ternary alloy Ga_1-xAl_xN, the virtual crystal approximation is coupled with the pseudopotential method. The energies along Γ, X, and L of Ga_1-xAl_xN alloy as a function of the alloy concentration are calculated. Angular correlation of positron annihilation radiation along different crystallographic directions in GaN, AlN, and Ga_0.5Al_0.5N is calculated. Other quantities such as ionicity character and bulk modulus by means of recent models with respect to the alloy concentration are discussed