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In this paper, we have studied the electric dipole (E1) transitions in odd-mass 153–159Eu nuclei within Translational+Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM). Within the scope, the Giant and Pygmy Dipole Resonances (GDR and PDR) have been investigated in the energy range of 5–20 MeV. The numerical results show that the contribution of PDR and GDR to the total E1 strength is 2% and 98%, respectively. It has been found that the TGI-QPNM predicts the double hump structure and that the agreement between theoretical results and the existing experimental data is perfect, especially near the neutron binding energy Sn and the first hump of the GDR. Also the comparison of the theoretical results and the existing experimental data shows reasonable agreement for the integrated moments of the cross-sections in the GDR region. We can also deduce from the structure analysis of excited states the studied isotopes, that the GDR states can be considered to be more collective than the PDR states.

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This study presents the descriptive characteristics of the electric dipole (E1) excitations for the first time in the 237Np nucleus, such as the reduced transition probability, the photo-absorption cross-section, the energy-weighted sum rule, and so on, as calculated by the Translational and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM). To accurately determine the dipole properties of the collective pygmy and giant resonances, it was necessary to eliminate the spurious states mixed into the dipole spectrum because the mean-field Hamiltonian breaks the translational invariance symmetry. We therefore also investigated the effect of spurious states on the PDR and GDR spectra using the TGI-QPNM method. In addition, we consulted the available knowledge for the energy-weighted sum rule to test the TGI-QPNM model, and this resulted in 97% accuracy for E1 dipole excitations. Furthermore, the theoretical results were compared with experimental data for the photo-absorption cross-sections in the 5–20 MeV energy range for the 237Np nucleus, with a satisfactory agreement being found.

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The low-lying magnetic (M1) and electric (E1) dipole modes in well-deformed odd-proton 175Lu have been investigated in the framework of the Rotational, Translational, and Galilean Invariant-Quasiparticle Phonon Nuclear Model (RTGI-QPNM) for the first time. In this model, the single-particle basis obtained from an axially symmetric Woods-Saxon potential, E1 and M1 excitations are assumed to be generated by isovector dipole-dipole and spin-spin interactions between nucleons, respectively. It also includes the restoration forces for breaking the Rotational, Translational and Galilean symmetries of the nuclear Hamiltonian. The transition probabilities, radiation widths and the structure for both M1 and E1 transitions in 175Lu have been calculated. The theory has satisfactorily reproduced the observed fragmentation in dipole spectra. However, the individual dipole strength of the states is higher than the experimental ones, which may be attributed to the lack of multiphonon configurations in the model used. Besides, the predicted total dipole radiation width and its reduced value are almost twice the experimental data. This difference is a well-known phenomenon for odd-mass deformed nuclei, called ‘missing strength’, arising in the Nuclear Resonance Flouracanse experiment due to the high-level densities.