Phonon operators in deformed nuclei

For the description of excited states of deformed nuclei, the mathematical formalism with phonon operators that do not depend on the sign of the angular momentum projection has proved inadequate. New phonon operators are introduced that depend on the sign of the projection of the angular momentum onto the symmetry axis of the deformed nucleus. It is shown that calculations with the new phonons take into account the Pauli principle correctly in the two-phonon components of the wave functions. There is a difference from calculations with phonons that do not depend on the sign of the angular momentum projection. The new phonons must be used in deformed nuclei if the Pauli principle is to be taken into account properly and in calculations with wave functions of excited states having components with more than one phonon operator.