Symmetrized Vibrational-Rotational Basis for Collective Nuclear Models

The generalized projection operators for the intrinsic group acting in the space L2(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 D̅4y 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.