Translational and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM) for electric dipole (E1) transitions in odd-mass deformed nuclei

The method of Pyatov, proposed for the exclusion of the spurious states associated with the spontaneous symmetry breaking due to the mean field approximation, is applied to restore broken translation and Galilean invariance of the Quasiparticle Phonon Nuclear Model (QPNM) Hamiltonian of deformed odd-mass nuclei for the first time. The point of the formulated translation and Galilean invariant (TGI-) QPNM is to study electric dipole (E1) response of odd-mass deformed nuclei. The proposed TGI-QPNM is tested by the calculations for fine and gross features of E1 resonance in ¹⁶⁵Ho, ¹⁶⁹Tm, and ²³⁵U in a wide range of excitation energy from 2 to 20 MeV. Predictions of the TGI-QPNM are shown to be in good agreement with the corresponding experimental data.