151,153,155sm çekirdeklerinde düşük enerjili elektromanyetik dipol modların teorik olarak araştırılması
Theoretical investigation of low energy electromagnetic dipole modes in 151,153,155sm nuclei
Yazar: YASEMİN KARADEMİRCİ KÖMÜRCÜ
Danışman: DOÇ. DR. EMRE TABAR
Sakarya Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Ana Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Fizik ve Fizik Mühendisliği = Physics and Physics Engineering

Özet:
Çalışmanın konusunu yakın geçmişte 151,153,155Sm deforme çekirdeklerinde gözlenen düşük enerjili manyetik dipol (M1) ve elektrik dipol (E1) uyarılmaları için ilk ayrıntılı teorik hesaplamaların yapılması oluşturmaktadır. M1 uyarılmalarının hesabında Dönme Değişmez Kuaziparçacık Nükleer Model (RI-QPNM), E1 uyarılmalarının hesabında ise Öteleme ve Galileo Değişmez Kuaziparçacık Nükleer Model (TGI-QPNM) kullanılmıştır. Her iki teoride de nükleonler arasındaki monopol çiftlenimler hesaba katılmış ve ortalama alan potansiyeli olarak deforme Woods-Saxon potansiyeli kullanılmıştır. RI-QPNM'de M1 uyarılmalarının oluşumundan nükleonlar arasındaki spin-spin etkileşmeleri sorumlu iken TGI-QPNM'de E1 uyarılmaları dipol-dipol etkileşmeleri tarafından üretilir. Her iki teoride de ortalama alan yaklaşımı nedeniyle çekirdek hamiltoniyeninin kırılan simetrilerinin onarılmasında Pyatov Metodu kullanılmıştır. 
RI- ve TGI-QPNM kullanılarak 151,153,155Sm çekirdeklerinde hem M1 hem de E1 uyarılmaları için indirgenmiş geçiş olasılıkları, radyasyon genişlikleri, indirgenmiş radyasyon genişlikleri, seviye yapıları, tesir kesitleri ve ortalama enerji değerleri hesaplanmış, elde edilen sonuçlar Oslo metoduyla belirlenen deneysel veriyle karşılaştırılmıştır. RI- ve TGI-QPNM 2-5 MeV enerji aralığında ölçülen toplam radyasyon genişliklerini, uyarılmalara ait ortalama enerjileri ve tesir kesiti değerlerini başarıyla açıklamıştır. Beklendiği gibi bu enerji aralığındaki M1 geçişleri baskın biçimde orbital karakterlidir. Mikroskopik yapı hesaplamaları söz konusu enerjilerde M1 uyarılmalarının, E1 uyarılmalarının aksine kolektif yapıda olduklarını ortaya koymaktadır. 
Bu tez ile 151,153,155Sm çekirdeklerinin düşük enerjili M1 ve E1 uyarılma özellikleri üzerine ilk ayrıntılı teorik çalışma gerçekleştirilmiştir. Elde edilen sonuçlar iyi deforme tek kütle numaralı lantanit ve aktinit çekirdeklerinde gözlenen M1 ve E1 uyarılmalarını başarıyla açıklayan RI- ve TGI-QPNM'in aynı başarıyı zayıf deforme 151,153,155Sm çekirdeklerine de taşıdığını göstermektedir.

Abstract:
In recent years, determining the response of deformed nuclei to electromagnetic probes become a most powerful tool for exploring nuclear structure. Interaction between the nucleus and the external electromagnetic field leads to the occurrence of different collective modes with different multipolarities in the nucleus. These collective modes are of great importance in understanding the complex structure of atomic nuclei and in testing theoretical models. The most recent examples of these collective modes are electric dipole (E1) and magnetic dipole (M1) excitations occurring in the low energy region (2-4 MeV) of deformed nuclei.
Although there are many theoretical approaches in the literature to explain the low-energy E1 and M1 excitations observed in even-even deformed nuclei, there are a limited number of theories to explain these excitations in odd-A deformed nuclei. One of these theories, which are actively used, is the Rotational Invariant (RI-) / Translational and Galileo Invariant (TGI-) QPNM, which considers quasiparticle and phonon interactions. RI-QPNM successfully explains the M1 excitation properties of odd-A deformed nuclei, and TGI-QPNM successfully explains the E1 excitation properties. Since it is impossible to determine the parity of the levels observed in experiments with odd-mass deformed nuclei, E1 excitations cannot be distinguished from M1 excitations. In this respect, calculations with TGI- and RI-QPNM in odd-A nuclei are important to determine the character of transitions and shed light on the experimentalists. Therefore, extending TGI-QPNM calculations to different nuclei is of great importance. 151,153,155Sm nuclei, with their recent experimental data, are good candidates for this purpose. 
The subject of the present thesis is to perform the first theoretical calculations for low energy M1 and E1 excitations recently observed in deformed 151,153,155Sm nuclei. The RI-QPNM is used to calculate M1 excitations, and the TGI-QPNM is used to calculate E1 excitations. Both theories consider monopole pairing between nucleons, and the deformed Woods-Saxon potential is used as the mean-field potential. In both theories, the Pyatov Method was used to repair the broken symmetries of the nuclear Hamiltonian due to the mean field approximation. While the spin-spin interactions between nucleons are responsible for forming M1 excitations in RI-QPNM, E1 excitations are generated by the dipole-dipole interactions in TGI-QPNM. One of the essential inputs in numerical calculations is the strength parameters of these interactions. The value of the spin-spin strength parameter (χσ) was determined as χσ=30 MeV/A by comparing the theoretical and experimental intrinsic magnetic moment (gK) values of these nuclei. This value is also compatible with the χσ values we determined for other odd-neutron nuclei in the rare earth region. The strength parameter (χ1) of the dipole-dipole interaction was chosen as χ1=300A-5/3 MeVfm-2, depending on our previous studies. This value explains well the E1 transitions observed in spherical and deformed even-even nuclei. In addition, using this χ1 value, E1 excitations measured in 2-20 MeV in several odd-mass nuclei in the rare earth region have been successfully reproduced.
By using the RI- and TGI-QPNM, the level structures, reduced transition probabilities, radiation widths, reduced radiation widths and cross sections for both M1 and E1 excitations in 151,153,155Sm nuclei were calculated, and the obtained results were compared with the experimental data determined based on the Oslo method. 
Firstly, the results obtained from experimental and different theoretical approaches for the ground-states of 151,153,155Sm nuclei were compared with the QPNM calculation results. Particle-Rotor Model (PRM) calculations reveal that the ground state of 151Sm is an admixture of IKπ=5/2 5/2- [523] and IKπ=5/2 3/2- [532] states. This result is also supported by experimental data obtained from the 149,151Sm(t, p) reaction. Our calculations based on QPNM for the ground-state of 151Sm prove that the energy values of the 5/2-[523] and 3/2-[532] levels are very close, and therefore they mix.
150Nd (α, n)153Sm transfer reaction show that the ground state of 153Sm nucleus is a admixture of 3/2+ [651] and 1/2+ [660] configurations. PRM model calculations also supported this structure. However, the results of 152Sm(n, γ)153Sm and 154Sm(d, t)153Sm reactions indicated that the ground state of this nucleus is an admixture of 3/2+ [651] and 3/2+ [402] configurations. These observations were also confirmed by the Nilsson Model calculations considering Coriolis interactions and QRPA calculations based on the Woods-Saxon potential. Our calculations in the QPNM framework show that the 3/2+ [651] level is formed because of the splitting of the i13/2 spherical shell due to deformation. It is known that Coriolis forces strongly mix the levels with quantum numbers {[660]↑, [400]↑} and {[402]↓, [651]↑} belonging to the i13/2 spherical shell. Therefore, both the 3/2+{[651]↑+[642]↑} and 3/2+ {[651]↑+[660]↑} configurations suggested for the ground -state are unlikely to occur. Our QPNM calculations show that the energy difference between the [651]↑ and [402]↓ levels is smaller than the energy difference between the [651]↑ and [660]↑, and [651]↑ and [642]↑ levels for 153Sm. Since Coriolis forces are very effective at close levels, mixing amplitudes of [651]↑ and [402]↓ will be larger; therefore, we may say that the best approximation for the ground-state of the 153Sm nucleus is the 3/2+[651]↑+[402]↓ configuration. 
From RI-QPNM calculations, it has been determined that low energy M1 excitations in 151,153155Sm nuclei have orbital character. This is in line with the available data in the literature for other even-even and odd-mass deformed nuclei in the rare earth region. The orbital nature of low energy M1 transitions in 151,153155Sm nuclei indicates that these transitions are scissor-mode excitations.
As expected, the observed total dipole radiation widths for 151,153,155Sm nuclei are slightly lower than the predicted values. This is due to the enormous level density of the odd-mass nuclei, leading to fragmentation in the dipole strength. Some fragmented levels' strength is below the detector's sensitivity and escapes from detection. 
The analysis of the numerical results reveals that the fragmentation mechanism in the E1 and M1 strength distributions in 151,153,155Sm nuclei is the same. ΔK=±1 component of E1 (M1) operator in an odd-A nucleus can connect {K_0 〖,I〗_0=K_0 } ground state to the states having (K_f 〖,I〗_f )=(K_0-1〖,I〗_0-1),(K_f 〖,I〗_f )=(K_0-1〖,I〗_0 ),(K_f 〖,I〗_f )=(K_0-1〖,I〗_0+1),(K_f 〖,I〗_f )=(K_0+1〖,I〗_0+1) quantum numbers. Thus, each E1 (M1) transition of the ΔK=±1 branch in the even-even core is distributed to 4 different E1 (M1) levels in the adjacent odd-A nucleus. On the other hand, ΔK=0 component of E1 (M1) operator can connect {K_0 〖,I〗_0=K_0 } ground state to the states having (K_f 〖,I〗_f )=(K_0 〖,I〗_0 )   and (K_f 〖,I〗_f )=(K_0+1〖,I〗_0 ) quantum numbers. Thus, each E1 (M1) transition of the ΔK=0 branch in the even-even core is shared by two levels in the adjacent odd-A nucleus. For this reason, dipole levels in the energy spectra of odd-A nuclei are more fragmented compared to neighbouring even-even nuclei.
Theoretical results obtained for M1 and E1 excitations in the low energy region of 151,153155Sm nuclei showed that excitations in the 2-4 MeV energy range predominantly belong to the ΔK=±1 branch. Few ΔK=0 transitions occur in this energy range. When the structure of the E1 and M1 levels in the studied nuclei are examined, it is seen that they are predominantly quasiparticle-phonon mixtures. On the other hand, when the structure of core phonons contributing to the E1 levels of 151,153,155Sm nuclei is examined, it is seen that they all consist of two-quasineutron or two-quasiproton pairs. This shows that the low energy E1 excitation levels of 151,153,155Sm nuclei are not in a collective structure. However, since the core phonons contributing to M1 levels in the same energy range in these nuclei are the superposition of many quasiparticle pairs, M1 excitations exhibit a collective characteristic.
A critical situation in our results is that selection of 5/2[523] or 3/2[532] as the ground state configuration in the 151Sm, and 3/2[402] or 3/2 [651] as the ground state configuration in the 153Sm does not affect the distribution of E1 and M1 levels in the energy spectrum in these nuclei. The distributions of Γ0(E1↑) and Γ0(M1↑) are almost identical for both configurations in 151,153Sm. The main reason is that changing the ground state configuration changes only the base quasiparticle in the wavefunction and the quasiparticle level that combines with the phonon. In RI-QPNM and TGI-QPNM, the root of the base quasiparticle state (single-quasiparticle level in the wave function) occurs at energies below 1.5 MeV. As a rule, levels above this energy are of the quasiparticle⊗phonon structure. Since the dominant component in the quasiparticle⊗phonon levels is the phonons of the core, the energies to be found will be around the phonon energies found for the core nucleus. In addition, the transition probabilities and radiation width distributions to be calculated for the quasiparticle⊗phonon levels will be close to the distributions in the core. However, the M1 and E1 levels will be more fragmented in odd-A nuclei for the reasons we mentioned earlier. 
RI- and TGI-QPNM successfully have explained the summed radiation widths, average energies of excitations, and cross-section values measured in the 2-5 MeV energy range. Microscopic structure calculations reveal that M1 excitations in this energy range are collective, unlike E1 excitations.
The experimental data we compare with our theoretical results are based on the Oslo Method. In the Oslo method, dipole levels built on excited states can be separated from the experimental spectrum. Whereas dipole transitions from the ground state to the excited states are calculated in RI-QPNM and TGI-QPNM. Despite this, consistent agreement has been achieved between experiment and theory. However, to compare with our TGI-QPNM and RI-QPNM results, we look forward to performing Nuclear Resonance Fluorescence (NRF) experiments for 151,153,155Sm nuclei, in which dipole transitions from the ground state to excited states can be measured and fine structure can be determined for these transitions.
With this thesis, the first theoretical study on low energy M1 and E1 excitation properties of 151,153,155Sm nuclei was carried out. The results show that RI- and TGI-QPNM, which successfully explained the M1 and E1 excitations observed in well-deformed odd mass lanthanide and actinide nuclei, also carried the same success to weakly deformed 151,153,155Sm nuclei.