Symmetrized Vibrational-Rotational Basis for Collective Nuclear Models

The generalized projection operators for the intrinsic group acting in the space L ₂(SO(3)) and in the space spanned by the eigenfunctions of a multidimensional harmonic oscillator are constructed. New symbolic-numerical algorithm implemented in computer algebra system for generating irreducible representations of the point symmetry groups in the rotor + shape vibrational space of a nuclear collective model in the intrinsic frame is presented. The efficiency of the algoritm is investigated by calculating the bases of irreducible representations subgroup D̅_4y of octahedral group in the intrinsic frame of a quadrupole-octupole collective nuclear model. The discrete variable representation algorithm proposed for solving eigenvalue problem, describing vibrational-rotational motion of collective nuclear model in intrinsic frame.