The spectra of the luminescence and magnetic circular polarization of luminescence (MCPL) in the praseodymium yttrium garnet aluminate Pr3+:YAG (PrYAG) have been studied within the visible spectral range at temperature T = 300 K. Analysis of the spectral dependences of the magnetooptical and optical spectra has made it possible to identify the optical 4f → 4f transitions occurring between the Stark sublevels of the 3P0, 3P1 and 3H5, 3H6 multiplets in PrYAG. It has been shown that for this paramagnetic garnet in the MCPL degree spectrum for the “green” luminescence band associated with forbidden 4f→ 4f transitions 3P0 → 3H5 within the visible spectral range, a significant role is being played by the effect of quantum mechanical J - J “mixing” of the energy states of Stark singlets of the 3H5 and 3H6 multiplets of the non-Kramers rare-earth (RE) Pr3+ ion. A parameterized Hamiltonian defined to operate within the entire 4 f(2) ground electronic configuration of Pr3+ was used to model the experimental Stark levels, their irreducible representations (irreps.) and wavefunctions. Nine independent CF parameters, Bqk" role="presentation">, were optimized using standard least-squares fitting between calculated and experimental levels. The final fitting standard deviation between 61 calculated-to-experimental levels is 17.86 cm–1.