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Proton irradiation of both n-type and semi-insulating bulk samples of β-Ga2O3 leads to the formation of two paramagnetic defects with spin S = 1/2 and monoclinic point symmetry. Their high introduction rates indicate them to be primary irradiation induced defects. The first electron spin resonance (EPR1) has a g-tensor with principal values of gb = 2.0313, gc = 2.0079, and ga* = 2.0025 and quasi-isotropic superhyperfine interaction of 13G with two equivalent Ga neighbors. Under low temperature photoexcitation, this defect is quenched and replaced by a different metastable spin S = 1/2 center of comparable intensity. This second defect (EPR2) has similar principal g-values of gb = 2.0064, gc = 2.0464, and ga* = 2.0024 and shows equally superhyperfine interaction with two equivalent Ga atoms. This EPR2 defect is stable up to T = 100 K, whereas for T > 100 K the initial defect is recovered. Density functional theory calculations of the spin Hamiltonian parameters of various intrinsic defects are carried out using the gauge including projector augmented wave method in order to determine the microscopic structure of these defects. The intuitive models of undistorted gallium monovacancies or self-trapped hole centers are not compatible with neither of these two defects.