Theoretical investigations of the electric dipole excitations of the odd-A deformed nuclei in the rare-earth region

One of the most effective methods that can be used to investigate a multi-particle quantum system with a complex structure such as an atomic nucleus is to excite it with an externally applied electromagnetic field. Thus, collective excitation states with different multipolarities emerge, providing important information about the individual and collective movements of the nucleons (neutrons and protons) that comprise the nucleus. Collective excitations can be classified depending on the order of multipolarity (λ). For example, λ=0 is called monopole mode, λ=1 is called dipole mode, λ=2 is called quadrupole mode, λ=3 is called octupolar mode. As it is known, as the degree of multipolarity increases, the effect of the corresponding modes weakens. The smallest order λ=0 mode in the nucleus occurs when nucleons expand and contract the nuclear boundaries without disturbing the spherical shape of the nucleus. Therefore, it is generally called breathing mode. Although this mode is fundamental in investigating the compressibility of the nucleus, its volume and surface properties, and the Coulomb effects on them, it does not provide detailed information that will shed light on the complex nature of the nucleus. However, due to the large amount of energy required to compress nuclear matter, this mode occurs at energies too high to be significant for the energy spectra discussed here. The second largest order dipole mode (λ = 1) is of critical importance in understanding the structure of the nucleus, as it emerges due to the collective vibrations of nucleons against each other. For this reason, dipole modes have been at the center of nuclear structure research since their first discovery until today. The dipole mode has two types, depending on whether the parity (π) changes in the transitions that create it. If the parity does not change during transitions (π=+), the excitations are magnetic dipole (M1), and if the parity changes during transitions (π=-), the excitations are electric dipole (E1). Today, as a result of studies carried out, especially with nuclei with even-even nuclei: -It is known that M1 excitations consist of the scissor mode located in the low energy (2-4 MeV) region, the Gamow-Teller transitions occurring in the 6-8 MeV energy range, and the spin-flip resonance in the 8-12 MeV energy range. -E1 excitations consist of low-energy transitions, pygmy dipole resonances (PDR), and giant dipole resonances (GDR). Low-energy transitions are located in the 2-4 MeV energy region, whose nature is unknown. PDR is the product of the vibrations of core nucleons and the excess neutrons against each other and is located around the neutron binding energy (6-9 MeV). GDR occurs due to the vibrations of the centers of mass of neutron and proton systems against each other and is located at an excitation energy of 13-16 MeV. In this thesis, the Translational and Galileo Invariant (TGI-) Quasiparticle-Phonon Nuclear Model (QPNM) was formulated to theoretically examine the electric dipole excitations (E1) of odd-A deformed nuclei. The translational and Galileo symmetry of the odd-A nucleus, broken due to the mean-field approximation of the QPNM Hamiltonian, was repaired with the help of the Pyatov-Salamov restoration method. To test the reliability of the model, B(E1) reduced electric dipole transition probabilities, electric dipole radiation widths, gΓ_0^red (E1) reduced electric dipole radiation widths, and integral properties of 161,163Dy, 165Ho, 167Er, 169Tm, and 175Lu deformed nuclei were calculated and compared with experimental data. Fine structure and total properties of E1 excitations of 161,163Dy, 165Ho, 167Er, 169Tm, and 175Lu deformed nuclei were calculated with TGI-QPNM. The obtained results were compared with experimental data. Theoretical results reveal that there are also significant dipole (M1) excitations in the low energy region of the mentioned nuclei in addition to magnetic E1 excitations. For all nuclei examined, the addition of the E1 spectrum to the M1 spectrum in the 2-4 MeV energy range increased the agreement between experiment and theory in terms of the distribution of dipole states. The results obtained show that the assumption that all dipole transitions in the low energy region have M1 character, which is used in many studies to compare experimental and theoretical results, is not a very realistic assumption. Because TGI-QPNM predicts the existence of significant E1 transitions in this energy region. In fact, E1 transitions with magnitudes very close to the total M1 transitions calculated in the 2-4 MeV energy range have been predicted in some nuclei. According to the calculation results, the one-phonon Iπ= 1+ levels of the dipole force in the 2-4 MeV energy range are more fragmented than the one-phonon Iπ= 1− levels. This thesis is important because it reveals the existence of PDR and GDR in odd-A deformed nuclei at energies above 4 MeV. B(E1) reduced electric dipole transition probabilities of the PDR region (4-9 MeV), which is expected to be observed near the neutron dissociation energy (Sn) and whose nature has not yet been determined, were obtained by TGI-QPNM. It has been found that transitions in the branch are more dominant in the 4-9 MeV energy range. From the results obtained, it can be seen that the E1 transitions in the PDR region exhibit a collective structure, the QPRA phonons consist of a large number of two-quasiparticle states, and one type of nucleon (especially two-quasineutron) is generally dominant. It is still debated whether PDR is a new excitation mode or just the low-energy tail of GDR. Experimental studies carried out in recent years for many dual-mass nuclei to understand the nature of this mode show that the E1 strength distribution at energies around Sn consists of two parts. These studies show dipole transitions up to approximately 6 MeV excitation energy can be observed with both isoscalar and isovector probes. On the other hand, dipole transitions occurring after 6 MeV excitation energy can be observed with isovector probes. The typical result of a series of theoretical studies examining these two modes is that isoscalar E1 transitions are a new excitation mode of the PDR. In contrast, isovector E1 transitions are the low-energy tail of the GDR. The peak energies, radiation widths, photo-absorption cross sections, and integrated moments (σ−2, σ−1, σ0) in the GDR region (9-20 MeV) of the investigated nuclei were calculated. The theoretical photo-absorption cross-section results are split in and branches and a two-peaked resonance shape is formed. The theoretical results obtained are in good agreement with existing experimental data. It was found that transitions in the K=1 branch were more dominant in the 9-20 MeV energy range. Theoretical results obtained for the GDR show that, just like in the PDR region, the E1 transitions in the GDR region exhibit a collective structure. On the other hand, unlike the PDR region, both types of nucleons (two-quazineutrons and two-quasiprotons) contribute to the microscopic structure. This difference between the two-quasiparticle configurations of core nuclei may help distinguish GDR and PDR regions. This thesis study and the results obtained will fill a significant blank in the literature. Especially in recent years, both experimental and theoretical studies have gained momentum, and an important step has been taken in understanding the pygmy dipole resonance, whose nature has not been fully resolved. PDR has become a fundamental nuclear mode due to its relationship with astrophysical events. This mode can significantly impact reaction rates in the astrophysical r-process, which synthesizes approximately 50% of elements heavier than iron. A small dipole force around the Sn energy will enormously increase the neutron capture cross-sections. The dipole strength in the PDR region affects the synthesis of nuclei in supernova explosions, the photo-disintegration of ultrahigh-energy cosmic rays, and may be necessary for the production of neutrons in stars. It is thought that theoretical predictions will shed light on the observations obtained by experimental research groups, help explain these observations, and encourage new experimental studies in this field.