Investigation of excited level properties with i^π=1^- in nuclei having particle-hole symmetry (130≤a≤170)

In recent years, various software and codes have been used to describe the properties of nuclear structure and the fundamental interactions between nucleons in parallel with the development of technology. Theories and experimental systems are being developed. The most fundamental application of the experimental approach is to expose a nucleus to an external influence. Studying nuclear excitations resulting from the nucleus's response to this influence provides valuable information about the nucleus's structure and nuclear binding. Investigating the data obtained from the excited levels of the nucleus as a function of particle-hole symmetry is one of the fundamental tasks of nuclear structure physics. It has been observed that previous studies on nucleus pairs or triplets with particle-hole symmetry have focused only on the properties of electric quadrupole transitions lying on the yrast band, and the properties of electric dipole (I^π=1^-) transitions in these nuclei have not been studied so far. In the studies conducted, it has been determined that low-energy excited energy levels exhibit similar properties in nucleus pairs or triplets with particle-hole symmetry. Electric dipole excitations provide valuable information about the nucleus's fundamental properties, deformation, and nuclear astrophysics. In this study, the boundaries of similar level structures in nuclei with particle-hole symmetry were investigated by extending them to higher energy levels where electric dipole excitations occur, and how far they continue. In this treatise, the electric dipole excitations of nuclei with even mass numbers located in the actinide and transition metal regions of the periodic table, which have particle-hole symmetry, were theoretically investigated and compared separately for K=0 and K=1 branches using the Translationally-Invariant Quasiparticle Random Phase Approximation (TGI-QRPA) model, where the broken symmetry of the average potential is restored, and the results were compared with experimental data using the TALYS and EMPIRE reaction codes, yielding results highly consistent with experimental data. In this study, the electric dipole excitations of double-double deformed nucleus pairs with particle-hole symmetry, with spin and parity I^π=1^-, were investigated within the framework of the Quasiparticle Random Phase Approximation (QRPA) for Base Hal excitations (Low Lying Excitations -LLE) between 0-4 MeV, Pygmy Dipole Resonances (Pygme Dipole Resonances-PDR) between 4-8 MeV, and Giant Dipole Resonances (Giant Dipole Resonance-GDR) between 8-20 MeV. In this approach, separable interactions for isoscalar and isovector components were determined self-consistently for the restoration of broken symmetry of the average potential. The model containing a single parameter for isovector dipole-dipole interaction explains the asymmetric structure of GDR in deformed nuclei, its energies for K=0 and K=1 branches, in good agreement with experimental data. For the nuclei with particle-hole symmetry in the mass region of 130 ≤ A ≤ 170, the reduced transition probabilities (B(E1)) and energy (ω_i) values for the I^π K=1^- 1 and I^π K=1^- 0 transitions were calculated within the model framework for the nuclear geometries and deformations, and the excitation characteristics of the giant dipole resonance, electric base state, and pygmy dipole resonance, and B(E1) values for pseudo mirror nuclei were investigated. It was observed that the ΔK=1 transition is dominant in the GDR region for the deformed nuclei. The calculated total photoabsorption cross section (σ_abs) for deformed nuclei showed peak values in the energy ranges of 11-12 MeV and 15-16 MeV for K=0 and K=1 branches, respectively, which are consistent with experimental and other theoretical studies. Additionally, some characteristic features of electric dipole transitions, such as asymptotic quantum numbers [Nn_z ΛΣ], radiation widths Γ(E1), reduced radiation widths red(E1), and integrated cross sections σ_0, σ_(-1), σ_(-2) were investigated. Within the scope of this treatise, the relationship between the B(E1) values of pseudo mirror nuclei with particle-hole symmetry in the mass region of 130 ≤ A ≤ 170, including 132Sm-164Yb, 134Sm-162Yb, 136Sm-160Yb, 132Nd-164Hf, 132Ce-164W, 136Nd-160Hf, 166Hf-162Yb, 168Hf-160Er, 170Yb-160Dy, 170Hf-158Dy, and 166Er-162Dy, and the reduced transition probabilities (B(E1)) and energy (ω_i) values for the I^π K=1^- 1 transitions were theoretically calculated using the Translationally-Invariant Quasiparticle Random Phase Approximation (TGI-QRPA) model, where the broken symmetry of the average potential is restored. It was observed that the ΔK=1 branch is dominant in the GDR region for the investigated deformed nuclei. The calculated total photoabsorption cross section (σabs) for deformed nuclei showed asymmetric structures in the spectrum, with peak values in the energy ranges of 10-12 MeV and 14-16 MeV for K=0 and K=1 branches, respectively, which are consistent with experimental and other theoretical studies. Additionally, some characteristic features of electric dipole transitions, such as asymptotic quantum numbers [Nn_z ΛΣ], radiation widths Γ (E1), and reduced radiation widths Γred (E1), were investigated. Furthermore, the results obtained from TALYS and EMPIRE reaction codes, which are highly consistent with experimental data, were compared with the TGI-QRPA calculations. The structure and properties of the atomic nucleus, a complex, multi-body structure consisting of two different fermions, continue to attract the attention of researchers. Exploring various symmetries facilitates overcoming the challenges in understanding the nucleus's structure. One of these symmetries is isospin symmetry. Isospin symmetries give rise to three phenomena in nuclear structure physics; mirror nuclei, valence mirror nuclei, and pseudo-mirror nuclei. As can be understood from these three structures, the nuclear force does not make any distinction between neutrons and protons and the vacancies belonging to these particles. Pseudo-mirror nuclei, which were the subject of this treatise, have been studied by various researchers from the 1980s to the present day. With the increasing experimental data, systematic information about pseudo-mirror nuclei has also increased. While initial studies focused only on the energies of the same spin-quantum numbered levels belonging to the yrast band, later studies addressed the values of reduced transition probabilities for these levels and found a systematic between these transitions. Considering that the levels in the yrast band are thought to be composed of quadrupole interactions, the question arises as to how symmetries behave in dipole-dipole interactions, and thus, the subject of this treatise emerged. In this context, this problem was investigated through the pseudo-mirror nuclei 132Sm-164Yb, 134Sm-162Yb, 136Sm-160Yb, 132Nd-164Hf, 132Ce-164W, 136Nd-160Hf, 166Hf-162Yb, 168Hf-160Er, 170Yb-160Dy, 170Hf-158Dy, and 166Er-162Dy. In the findings section, the B(E1), energy-weighted B(E1), average energy, radiation width, reduced radiation width, and photoabsorption cross-section values were given for the pseudo-mirror nuclei 132Sm-164Yb, 134Sm-162Yb, 136Sm-160Yb, 132Nd-164Hf, 132Ce-164W, 136Nd-160Hf, 166Hf-162Yb, 168Hf-160Er, 170Yb-160Dy, 170Hf-158Dy, and 166Er-162Dy in the energy ranges of 0-4 MeV, 4-8 MeV, and 8-20 MeV. As seen from the findings, in pseudo-mirror nuclei with similar masses, it was observed that the degenerate structures in the low-energy region due to quadrupole interactions continue in the high-energy levels due to dipole interactions. The overlap is seen in the photoabsorption cross-sections calculated using QRPA and TALYS, and also, the ratios of the total B(E1) values of pseudo-mirror nuclei are clustered around 1, just like the ratios of B(E2) values in the low-energy region. In pseudo-mirror nuclei where the difference in mass numbers increases, deviations were observed in the photoabsorption cross-sections calculated using QRPA and TALYS, and also, the ratios of the total B(E1) values of pseudo-mirror nuclei differed. The investigation of this difference using microscopic models will form the basis for our group's future studies.