Aktinitler bölgesindeki tek-A'lı deforme çekirdeklerin elektrik dipol uyarılmalarının teorik olarak incelenmesi
Theoretical investigation of electric dipole excitations in deformed odd-mass nuclei in the actinide region
Yazar: ELİF KEMAH
Danışman: PROF. DR. HAKAN YAKUT
Sakarya Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Ana Bilim Dalı
Derece: Doktora, 2023
Konu: Fizik ve Fizik Mühendisliği = Physics and Physics Engineering

Özet:
Bu tez çalışmasında, 229,231,233Th, 233,235,237,239U, 237Np ve 239,243Pu aktinit çekirdeklerinde 20 MeV'e kadar ki enerjilerde elektrik dipol (E1) uyarılmalarının araştırılması, E1 cüce ve dev dipol rezonanslarının ilk teorik sonuçlarının sunulması ve sonuçların mevcut deneysel verilerle karşılaştırılması amaçlanmaktadır. Bu izotopların seçilmesindeki motivasyon, teorik olarak tek-A'lı aktinit çekirdeklerinde E1 uyarılmalarının ve rezonans özelliklerinin daha önce çalışılmamış olması ve mevcut deneysel verilerin test edilmesinde öteleme ve Galileo değişmez (TGI) kuaziparçacık fonon nükleer modelinin (QPNM) başarısının belirlenmesidir. 
QPNM hesaplamalarında önemli bir problem, nükleer ortalama alan yaklaşımlarının nükleer Hamiltoniyenin kendiliğinden simetri kırılmasına yol açması ve bu durumda sıfır enerjili sahte durumların gerçek dipol durumlarına karışmasıdır. Kırılan simetrilerin restore edilmesi, nükleer elektromanyetik spektrumda belirli dipol uyarılmalarının gerçek doğasını anlamak açısından önem taşır. Bu tez kapsamında, E1 spektrumlarının mikroskopik analizleri için kırılan simetrilerin restore edilmesine yönelik ayrılabilir etkin kuvvetlerin kullanıldığı TGI-QPNM yaklaşımı formülüze edilmiş ve aktinitler bölgesi tek-A'lı deforme çekirdeklerine uygulanmıştır. 233,235,237,239U, 237Np ve 243Pu çekirdekleri için TGI-QPNM ile elde edilen sonuçlar, kırılan öteleme ve Galileo değişmezlik simetrilerinin restore edilmediği yaklaşımın (NTGI-QPNM) sonuçlarıyla karşılaştırılmıştır. Kırılan simetrilerin restore edilmesi ile gerçek titreşim durumlarına karışan sahte haller yalıtılmış olduğundan E1 geçiş gücü dağılımı ve toplam kuralları gibi niceliklerin güvenilir bir şekilde hesaplanması mümkün olmuştur.
Tez çalışması kapsamında ürettilen makalelerde, 229,231,233Th, 233,235,237,239U, 237Np ve 239,243Pu  aktinit çekirdeklerinde, TGI-QPNM yaklaşımı kullanılarak E1 dipol gücü başarıyla tahmin edilmiştir. Bu çalışmalarda aynı zamanda Dönme Değişmez (RI)-QPNM yaklaşımı kullanılarak 229,231,233Th, 233,235,237,239U ve 239,243Pu  aktinit çekirdekleri için M1 uyarılmaları  başarıyla tanımlanmıştır. İncelenen deforme aktinit çekirdeklerde GDR, çekirdeğin simetri eksenine paralel (ΔK = 0) ve dikey (ΔK = 1) salınımlara karşılık gelen iki Lorentziyel dağılım şeklini almaktadır. Hesaplamalarda elde edilen PDR gücü, incelenen çekirdeklerin dipol spektrumunda TGI-QPNM fotosoğurma tesir kesitlerinin sadece %1-3'lük kısmını kapsamaktadır. Bunun yanısıra, NRF deneylerinde tek-A'lı aktinit çekirdekleri (235U, 237Np ve 239Pu) için M1 ve E1 geçişleri birbirinden ayırt edilemezken, mevcut tez çalışmasındaki RI- ve TGI- QPNM  hesaplamaları ile dipol kuvvetinin doğası hakkında önemli tahminler yapılabilmektedir. Bu yaklaşımlar, 231-233Th, 237,239U ve 243Pu çekirdeklerinin dipol modlarının araştırılmasında kullanılmış ve sonuçlar Oslo metodunun verileriyle karşılaştırılmıştır.

Abstract:
Within the scope of this thesis, electric dipole transitions between ground and excited states of 229,231,233Th, 233,235,237,239U, 237Np, and 239,243Pu isotopes were analyzed for energies up to 20 MeV using the TGI-QPNM method for the first time. The obtained results were evaluated in conjunction with existing experimental data.
In this thesis work, the significant outcomes derived from the TGI-QPNM analysis for 229,231,233Th, 233,235,237,239U, 237Np, and 239,243Pu isotopes are as follows:
• In the calculations performed using the Pyatov method, symmetry violations were considered, and the results indicated that the zero-energy spurious states only mix with the real E1 excitation resonance region in the energy range of 7-12 MeV, with a contribution of no more than 20%.
• The results obtained demonstrate that the restoration of translation and Galilean Invariance and the departure of spurious states from the real vibrational states lead to the saturation of EWSR when virtual states are separated from genuine vibration states (see Figure 3.22).
• The TGI-QPNM approach provided photoscission cross-section values and impact parameter moments for the GDR energy region of 233,235U, 237Np, and 239Pu nuclei, showing a successful agreement of approximately 85-90% with experimental cross-section data for these nuclei.
• For 229,231,233Th, 233,235,237,239U,237Np, and 239,243Pu nuclei, the TGI-QPNM approach adheres to the TRK sum rule for the total cross-section (σ0) and slightly exceeds this value by about 5-15% for 235U, 237Np, and 239Pu. These results indicate the possibility of rare but observable E1 transitions at high energies.
• The TGI-QPNM calculations for the nuclei studied within this thesis suggest a weak E1 transition strength in the scissor resonance energy range. Furthermore, in the calculations for low-energy dipole excitations in 231,233Th, 237,239U, and 243Pu nuclei, the RI-QPNM results for M1 transition strength and width (1.5–4 MeV energy region) have been found to be slightly lower compared to the Oslo data. A possible explanation for this inconsistency could be that the scissor resonance in the Oslo method is constructed not only on the ground state of the nuclear nucleus but also on all excited states.
• The investigation of deformed actinide nuclei in this thesis work reveals that the deformation effect leads to a separation between the ΔK = 0 and ΔK = 1 branches of the GDR, exhibiting different behaviors. The ΔK = 0 and ΔK = 1 branches of GDR were observed at excitation energies above 8 MeV, with the ΔK = 0 branch spreading to a lower energy region than the ΔK = 1 branch. However, for the PDR, the ΔK = 0 E1 strength is found to be dominant in the energy range between 7 and 8 MeV compared to the ΔK = 1 E1 strength. These results support the notion that PDR could be a distinct resonance type independent of GDR.
The TGI-QPNM analyses conducted for 229,231,233Th, 233,235,237,239U, 233,235,237,239Np, and 239,241,243,245Pu isotopes (see Appendices B, C, and D) have contributed to identifying the systematic features of these nuclei as follows:
• In the systematic GDR distribution of the studied isotopes, 229,231,233Th, and 239,241,243,245Pu isotopes exhibit a leftward shift of 0.5-1 MeV due to changes in the mass number, while 233,235,237,239U isotopes show a rightward shift of 0.5-1 MeV based on mass number variations. Np isotopes, however, display relatively minor changes in the GDR spectrum.
• Based on the results of the RA (GDR area ratio) values obtained from the PDR analysis of odd-A actinide nuclei (see Appendices C), it can be inferred that these nuclei have a prolate geometrical shape with RA values less than 1.
• Regarding the total E1 transitions up to 20 MeV excitation energy (see Appendix C):
a. The total E1 strength for the 229,231,233Th isotope series remains relatively constant (63.50; 69.00; 66.50 e2fm2), and the average resonance energy is consistent (11.87; 11.83; 11.37 MeV) within the 0-20 MeV energy range. However, the total E1 strength increases (1.72; 2.06; 2.83 MeV), and the average resonance energy is approximately 7 MeV in the 5-8 MeV energy range, which is the PDR energy region.
b. The 233,235,237,239U isotope series exhibit variability in the total E1 strength (69.40; 76.90; 72.70; 76.80 e2fm2) without a clear trend within the 0-20 MeV energy range, while the average resonance energy remains relatively constant (11.63; 12.06; 12.02; 11.82 MeV). In the PDR energy region, the total E1 strength decreases (2.09; 1.99; 1.79; 1.63 MeV), and the average resonance energy is approximately 7 MeV.
c. The 233,235,237,239Np isotope series show variability in both the total E1 strength (69.00; 75.90; 75.40; 76.00 e2fm2) and the average resonance energy (11.97; 12.60; 12.48; 12.32 MeV) within the 0-20 MeV energy range. Similar variability is observed in the PDR energy region, where the total E1 strength (2.04; 1.31; 1.41; 1.33 MeV) and average resonance energy display a trendless variation around 7 MeV.
d. The 239,241,243Pu isotope series exhibit variable total E1 strength values (75.40; 78.20; 71.80 e2fm2) within the 0-20 MeV energy range, without a pronounced pattern, and the average resonance energy (12.00; 11.82; 11.62 MeV) decreases. Similarly, in the PDR energy region, the total E1 strength (1.60; 1.58; 1.82 MeV) and average resonance energy show irregular variations around 7 MeV.
• When evaluating the underlying configurations of the maximum structures observed in the PDR and GDR spectral distributions of 229, 231,233Th, 233,235,237,239U, and 239,243Pu (see Appendix D):
a. In the case of 229,231,233Th isotopes, E1 excitations corresponding to the ΔK=0 branch, with a high transition probability approximately 2-3 MeV above the Sn values (in the PDR energy region), are present. The phonons contributing to the excited energies, listed in Table D.1, include configurations involving either two-quasineutron or two-quasiproton states. The GDR's first peak in 229Th and 231Th nuclei, which is dominated by ΔK=0 excitations, primarily involves two-quasiproton configurations. On the other hand, phonons contributing to the second peak (ΔK=±1 excitations) include approximately 40% two-quasineutron and 60% two-quasiproton configurations. In contrast, the GDR's first peak in 233Th nucleus is mainly associated with two-quasiproton configurations, while the second peak has a predominance of two-quasineutron configurations, distinguishing it from the other two isotopes.
b. In the 233,235,237,239U and 239,243Pu nuclei, the phonons contributing to the PDR energy region are dominated by either purely two-quasineutron or purely two-quasiproton configurations. Regarding the GDR, both the ΔK=0 and ΔK=±1 excitations, contributing to the first and second peaks, respectively, consist of approximately 40% two-quasineutron and 60% two-quasiproton configurations.
Considering the structural characteristics of the investigated nuclei, the analyses performed on single-A actinide nuclei support the microscopic TGI-QPNM method consistently describing the excitation events of axially deformed systems, such as the collective vibrations of neutron and proton excess systems (PDR) and the neutron-proton oscillations (GDR), in line with the macroscopic definitions. The analyses of these nuclei also reveal that the PDR mode is less collective compared to the GDR mode, possesses weaker B(E1) strength, and exhibits a distinct structure characterized by a mononucleon nature.
The studies conducted within this thesis, employing the TGI-QPNM method for the investigation of E1 dipole excitations in odd-A actinide nuclei, have contributed to the literature in the field of nuclear structure physics and engineering. This novel theoretical approach stands out for its potential to accurately characterize the excitation events of axially deformed systems and its applicability to various mass regions on the nuclear chart. However, it is acknowledged that the existing experimental data are limited compared to the calculations. Therefore, further experimental studies are necessary to enhance the understanding of E1 dipole excitations and enable more detailed analyses. Given the critical role of nuclear materials such as Th, U, Np, and Pu in nuclear energy and technology, these studies are expected to make significant contributions to the future development of the nuclear energy sector.