Nötral skandiyum ve itriyumun düşük enerji seviyelerine valans-valans ve öz-valans korelasyon etkilerinin incelenmesi
Investigation of valence-valence and core-valence correlation effects on low-lying energy levels of neutral scandium and yttrium
Yazar: FIFI KARNILA
Danışman: PROF. DR. LEYLA ÖZDEMİR
Sakarya Üniversitesi / Fen Bilimleri Enstitüsü / Fizik Ana Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Fizik ve Fizik Mühendisliği = Physics and Physics Engineering
Dizin: Breit denklemi = Breit equation ; Elektron elektron etkileşimi = Electron electron interaction ; Hartree-Fock teorisi = Hartree-Fock theory ; Konfigürasyon etkileşmesi = Configuration interaction ; Skandiyum = Scandium ; İtriyum = Yttrium

Özet:
Sc I (Z=21) ve Y I (Z=39) için düşük enerji seviyeleri olan açık tabakalarında sırasıyla ndn's2 ve nd2n's (n=3, 4 Sc I için ve n'=4, 5 Y I için) olan konfigürasyonlara sahip geçiş metal elementleridir (Grup III ve periyot 4 ve 5). Bu iki element çoğunlukla aynı cevherlerde bulundukları ve atomik yapıları ve kimyasal özellikleri benzer oldukları için lantanitlerle beraber nadir toprak elementleri olarak da sınıflandırılırlar.
Bu çalışmada, Sc I ve Y I için düşük enerji seviyeleri üzerinde valans-valans (değerlik-değerlik) ve öz-valans (öz-değerlik) korelasyon etkilerini incelemek amaçlandı. Hesaplamalar konfigürasyon etkileşme modelini içeren çok konfigürasyonlu Hartree-Fock (MCHF) yöntem ile yapıldı. Ayrıca, hesaplamalar korelasyon etkilerinin yanı sıra Breit-Paul Hamiltonyeni çerçevesinde relativistik etkileri de içerir. Sc I ve Y I ile ilgili literatür bilgisi birinci bölümde ve kullanılan yöntem ve hesaplama stratejisi ile ilgili bilgi de ikinci bölümde verildi. Son bölümde hesaplama sonuçları tablolarda sunuldu ve sonuçların diğer mevcut çalışma sonuçları ile karşılaştırılması ve bir tartışması verildi. Genel olarak, valans-valans korelasyonlarına göre elde edilen sonuçlar, öz-valans korelasyonuna göre elde edilen sonuçlardan daha iyi olduğu görüldü. Çalışılan atomların dış tabakalarındaki üç elektronun 3d ve 4s (Sc I için) ve 4d ve 5s (Y I için) alt tabakalarına yerleşmeleri karmaşık gözükmese de bu alt tabakaların enerjileri birbirine çok yakındır ve konfigürasyon etkileşimini zorlaştırmaktadır. 
Atomik yapı verileri çok çeşitli araştırma alanları için temel bileşendir. Bu nedenle bu çalışmada nötral skandiyum ve itriyum için verilen enerji seviyelerine ait veriler gelecekte bazı seviye yapılarına ait parametrelerin araştırılması için faydalı olacaktır.

Abstract:
Scandium (Sc) and yttrium (Y) are two Group IIIB and Period 4 and 5 transition metals, respectively. These two elements are categorized as rare earth elements together with the lanthanides, because they are often found in the same core deposits, and they have similar atomic structures and chemical properties as the lanthanides.  Scandium (Sc, Z = 21) has only one long-lived isotope, and has an atomic mass of 44.95591 a.m.u. The electronic configuration for Scandium is [1s22s22p63s23p6]3d14s2. 
Yttrium is a chemical element with the symbol Y (Z = 39), which has a single isotope and has an atomic mass of 88.90584 a.m.u. The electronic configuration for Yittrium is  [1s22s22p63s23p63d104s24d6]4d15s2. There are research about atomic data properties such as energy levels, wavelengths, radiative lifetimes, transition probabilities, and oscillator strengths. 
In some studies, recently research on atomic data related to scandium has been carried out such as Pehlivan et al. (2015) calculated the oscillator strengths of neutral scandium with combined experimental branching fractions with radiative lifetimes from the literature to derive oscillator strengths. It provides the first set of experimental Sc I lines in the near-infrared region for accurate spectral analysis of astronomical objects. In addition, Scott et al. (2015) determine the abundances of all iron group nuclei in the Sun, based on neutral and singly-ionized lines of Sc, Ti, V, Mn, Fe, Co and Ni in the solar spectrum. Lawler et al. (2019) had done the research on scandium in part of iron-group (Fe-group) abundances in metal-poor stars and the laboratory atomic transition probabilities. Liu et al. (2019) also had done the research on the radiative lifetimes of 39 excited levels of Sc I and for the best knowledge, there are no lifetime measurements on the high-lying above 40,603.933 cm-1 in Sc I. Meanwhile, the research on atomic data related to yttrium had been done by Shang Xue et al. (2015) they calculated the radiative lifetimes, branching fractions, transition probabilities and oscillator strengths of some levels for neutral yttrium.
In this work, we calculate the valence-valence and core-valence correlation effects on the energy levels for neutral scandium and neutral yttrium using MCHF atomic structure package. In the MCHF method developed by Fischer, the electron correlations are computed by wave function expansions composed of a large set of one-electron basis functions generated by electron replacement. In addition, the relative contributions are considered in the framework of Breit-Pauli Hamiltonian. For a part from increasing the number of orthogonality constraints, the complexity of the latter is independent of the number of the electrons. There is no additional difficulty in solving equations for large numbers of the electrons. however, the correct definition 
of electron correlation is highly dependent on the number of electrons and the corresponding occupied shells. 
Atomic theory is based on the independent particle model, in which each electron is thought to move at an effective potential in the nucleus and the average effect of repulsive interactions between an electron and other electrons. If the interaction in the movement of electrons is neglected, it is assumed that each electron moves independently in a field determined by other electrons. These effects between electrons are called "correlation effects" and the error in energy is defined as "correlation energy" by neglecting the correlation effects. The various Φi Slater determinants differ in the selection of spin-orbitals occupied by electrons, and therefore correspond to different placements. This approach is known as the configuration-interaction (CI) method.
We have given various configuration sets including valence-valence and core-valence correlation effects, and the results obtained have been presented in the tables. For these atoms, there are available data based on the literature and the results thats obtained in this work have been compared with the literature data from the National Institute of Standards and Technology (NIST).
For neutral scandium, there are 157 levels were obtained in this work. Energies have been separately presented for even-parity and odd-parity levels. The calculations have been indicated numbers according to various configuration sets both valence-valence and core-valence correlations. In some calculations, level energies that obtained in this work are better than others. For the example in the first even-parity level of 3d4s2 (179,54 cm-1) in the fourth calculation is close to the NIST (168,3371 cm-1) and another work (173,90 cm-1). For the other levels those are also close to the literatures are 3d2(3F)4s, 3d2(1D)4s, 3d2(3P)4s, and 3d2(1G)4s. Meanwhile for the other levels are far from the literatures. In this work the error percentage has been considered in the fourth calculation. There are 17 levels of value those are close to the NIST. For the example in the level of 3d2(3F)4s has the smallest error percentage of all the levels. Those are in (J=3/2) has 1.9%, (J=5/2) has 1.8%, (J=7/2) has 1.8%, and (J=9/2) has 1.7%. The third calculation results for odd-parity levels are better than other calculations. For the example, in the first odd-parity level of 3d4s(3D)4p in tem of 4F is close to the literatures. For the other levels those are also close to the literatures are 3d4s(3D)4p, 3d4s(1D)4p, 3d4s(3D)4p, 3d2(3F)4p, 3d2(3P)4p, 3d2(1D)4p, and 3d2(1G)4p. Meanwhile for the other levels are far from the literatures. These levels belong to the part of the valence-valence correlation calculation. The calculation of the error percentage in the third calculation there are 28 levels of value those are close to the NIST. For the example in the level of 3d4s(3D)4p has the smallest error percentage of all the levels. Those are in (J=3/2) has 1.1% (J=3/2) has 1.1%, (J=5/2) has 0.6%, and (J=7/2) has 0.5%).
For neutral yttrium there are 171 levels have been obtained based on the calculation and the results have been presented in the tables. For even parity levels, the values from third calculation are close to the literature. In this calculation, for the first level of 4d5s2 is close to the NIST. For the other levels those are also close to the NIST are in levels of 4d2(3F)5s, 4d2(3P)5s, 4d2(1D)5s, 4d2(1D)5s, 4d2(3P)5s, 4d2(1S)5s, 4d3, 5p2(3P)5s, 5p2(3P)4d, 5s27s, and 5p2(3P)4d, but for the other levels are far from the literature. The calculation of the error percentage in the third calculation of the energy level values that has the smallest error percentage is in the configuration of 5p2 (3P)5s, 
those are in (J=1/2) has 1.9%, (J=3/2) has 1.8%, and (J=3/2) has 1.6%. For odd parity, that has the values close to the literature are obtained in the fourth calculation. In this calculation, the first level of 5s25p is close to NIST value (10529.169 cm-1). For the other levels those are also close to the literatures are 4d5s(3D)5p, 4d5s(1D)5p, 4d2(3F)5p, 4d2 (3P)5p, 4d2(1D)5p, 4d2(1G)5p, and 4d5s(3D)6p. The calculation of the error percentage of the energy level values in the fourth calculation have been obtained 53 energy levels are close to the NIST. For the example in the level of 4d5s(1D)5p has the smallest error percentage those are in (J=5/2) has 0.4%, and (J=7/2) has 0.7%. 
In the general, the results obtained according to valence- valence correlation are better than according to the core-valence correlation. however, we inform that we have not widely selected configuration set for core-valence correlations because of the computational restriction for both atoms.  Although these configurations are not difficult to saturate three-electron CI space, the energies of the 3d and 4s subshells are very close and mixing of configurations is stronger than usual for Sc I. We think in this case also will occur for 4d and 5s. In addition, we have not considered all interactions for Breit - Pauli Hamiltonyen due to widely interaction integrals produced, so the spin-orbit interactions only considered in some cases, particularly in the core-valence correlation calculation. 
Accurate atomic structure data is an essential important for a wide range of research fields. Therefore, energy levels presented for Sc I and Y I from this work will be useful for research of some parameters belong to level structures.