KR VII için elektrik dipol (E1), elektrik kuadrupol (E2) ve manyetik dipol (M1) geçişleri = Electric dipole (E1), electric quadrupole (E2) and magnetic dipole (M1) transitions for KR VII

Abstract

Bu çalışmada altı kez iyonize olmuş çinko benzeri kripton (Z=36, Kr VII) için bazı enerji seviyeleri ve bu seviyeler arasındaki elektrik dipol (E1), elektrik kuadrupol (E2) ve manyetik dipol (M1) ışımalı geçişlerine ait dalga boyu (λ (Å)), geçiş olasılığı (Aij (s-1)), salınıcı şiddeti (fji) ve çizgi şiddeti (Sij (a.b)) gibi atomik geçiş parametreleri hesaplandı. Enerji seviyeleri için hesaplamalar yapılırken farklı hamiltonyenlere sahip iki yöntem olan, tamamen relativistik çok konfigürasyonlu Dirac-Fock (MCDF) yöntemini temel alan genel amaçlı relativistik atomik yapı paketi (GRASP) ve çok konfigürasyonlu Hartree-Fock (MCHF) yöntemi kullanıldı. MCDF hesabı sonucunda elde edilen enerji seviyelerine, QED ve Breit düzeltmelerinin bir katkı olarak nasıl etki ettiği incelendi. İzinli (E1) ve yasaklı (E2 ve M1) geçişlerine ait atomik parametreler için yapılan hesaplamalarda ise enerji seviyeleri için MCDF hesabından elde edilen sonuçların mevcut literatür ile daha iyi uyumlu olmasından dolayı bu yöntem kullanıldı. İlk bölümde, yapılan bu çalışmanın kapsamı ve amacı ile birlikte çinko benzeri altı kez iyonlaşmış kriptona (Kr VII) ait atomik parametreler için ulaşılabilir literatürde var olan deneysel ve teorik olan çalışmalar; ikinci bölümde ise çok-elektronlu atomlar, MCDF ve MCHF yöntemi, Breit düzeltmeleri, QED katkıları ve ışımalı geçişler hakkında özet bilgiler; son bölümde ise bu çalışmada yapılan hesaplamalar sonucunda elde edilen atomik veriler tablo ve grafikler halinde sunulmaktadır. Bu sonuçlar, mevcut literatürde var olan deneysel ve teorik değerler ile tablo ve grafiklerde karşılaştırmalı bir şekilde sunuldu ve hata hesabı yapıldı. Yapılan karşılaştırmalar sonucunda, bu çalışmadan elde edilen hesaplama sonuçlarının daha önce yapılan çalışmalar ile oldukça iyi uyum içerisinde olduğu görüldü. Ayrıca, altı kez iyonlaşmış çinko benzeri kripton (Kr VII) iyonu için özellikle yasaklı geçişlere ait ulaşılabilir mevcut literatür tarandığında daha önce herhangi bir veri sunulmadığı görülmektedir. Bu nedenle, bu çalışmada mevcut literatürde sınırlı sayıda bulunan verileri, yapılan hesaplamalardan elde edilen yeni veriler ile genişletmek ve özellikle geçişlere ait bazı parametrelerin literatüre ilk kez kazandırılması amaçlanmaktadır.

The atomic data of ionized noble gases play a significant role in spectroscopy of astrophysical and laboratory plasmas, calculation of elemental abundances, modeling of stellar atmospheres, laser physics, industrial research, planetary science and in general, in all laboratory plasma applications. In this study, some energy levels and atomic transition parameters such as wavelength, (λ (Å)), transition probability, (Aij (s-1)), oscillator strength, (fji), and line strength, (Sij (a.b)) for six times ionized zinc-like krypton (Z=36, Kr VII) were calculated. Two methods with different hamiltonians, namely the General-purpose Relativistic Atomic Structure Package (GRASP) based on the fully relativistic multiconfiguration Dirac-Fock (MCDF) method and the multiconfiguration Hartree-Fock (MCHF) method, were used for calculations of energy levels. We analyzed how the Quantum Electrodynamics (QED-self-energy and vacuum polarization) and Breit corrections (magnetic interaction between the electrons and retardation effects of the electron-electron interaction) contribute to the energy levels obtained from the MCDF calculation. The MCDF method was used in the calculations for the atomic parameters of the allowed (electric dipole-E1) and forbidden (electric quadrupole-E2 and magnetic dipole-M1) transitions for Zn-like krypton (Kr VII). In the first part, together with the scope and purpose of this study, the experimental and theoretical studies available in the literature for the atomic parameters of six times ionized krypton (Kr VII) are presented; in the second part, summary information about multielectron atoms, MCDF and MCHF methods, Breit effects, QED contributions and radiative transitions are presented; in the last section, the atomic data obtained as a result of the calculations performed in this study are presented in tables and graphs. These results are presented in tables and graphs in comparison with the experimental and theoretical values in the available literature and percentage error calculation is performed. As a result of the comparisons, it was seen that the calculation results obtained from this study are in good agreement with the previous studies. Table 3.1 presents the configuration sets which were used in the MCHF and MCDF calculations for the Kr VII ion. Using the configuration sets given in Table 3.1 for the Kr VII ion, 55 and 81 energy levels were obtained for MCDF and MCHF, respectively. The obtained results for the energy levels are in good agreement with existing experimental and theoretical data in the literature. Percentage errors were calculated to show the compatibility of the results obtained with the data available in the literature. The percentage differences results (min-max) values were calculated in the range of (0.21-7.09) for MCDF and (0.06-28.8) for MCHF. A clearer comparison of the results obtained with both MCDF and MCHF in this study with other existing results is given in Figure 3.1. It is also seen in this figure that the energy levels obtained are in good agreement with the existing values in the literature. The R2 values for the energy levels were calculated as 0.9984 for MCDF and 0.9352 for MCHF. Since these values are very close to 1, it shows that the results obtained in this study are good. R2 values are given above the associated graphs. When the energy values for the zinc-like, six times ionized krypton (Kr VII) were examined, it was seen that the results obtained from the MCDF calculation were in better agreement with the comparison values. For this reason, the E1 transitions between the energy levels obtained from the MCDF calculation were calculated and 257 transitions were obtained. Transition parameters such as wavelength, (λ (Å)), transition probability, (Aij (s-1)), oscillator strength, (fji), and line strength, (Sij (a.b)), of electric dipole (E1) radiative transitions for the Kr VII ion, and their comparison values in the literature are presented in Table 3.2. It is seen that the MCDF calculation results in this study are in good agreement with the comparison values. While calculating the percentage differences results of the transition parameters, the study by NIST [41] for wavelength, Liang and colleagues [24] for transition probabilities, oscillator strengths and line strengths were preferred as reference due to the abundance of data in the existing literature. Percentage differences (min-max) values were calculated in the range of (0.001-0.164) for wavelength, (0.02-1.61) for transition probabilities, (0.01-1.66) for oscillator strengths and (0.02-1.9) for line strengths. The fact that these ranges are quite small and close to each other shows the accuracy of the results obtained in this study. A comparison between the results of this study and the data available in the literature is also given in Figure 3.2. for wavelength, Figure 3.3. for transition probability, Figure 3.4. for oscillator strengths and Figure 3.5. for line strengths. The R2 values were calculated as 0.9989 for wavelength, 0.9844 for transition probabilities, 0.9965 for oscillator strengths, and 0.9859 for line strengths. These values are quite small and very close to 1, indicating that the results obtained in this study are good. R2 values are shown above the related graphs. The new data obtained as a result of the MCDF calculation without comparison value for the E1 transition parameters for the Kr VII ion are presented in the Table 3.3. As a result of the MCDF calculations performed in this study, for six times ionized krypton (Kr VII), the transition parameters such as wavelength, (λ (Å)), transition probability, (Aij (s-1)), oscillator strength, (fji), and line strength, (Sij (a.b)) for electric quadrupole (E2) and magnetic dipole (M1) transitions, 540 and 372 transitions were obtained, respectively. These transitions are given in Table 3.4 for E2 and Table 3.5 for M1. In the tables, the first and second columns represent the lower and upper levels for these forbidden transitions (E2 and M1), the third column represents the wavelength, the fourth column represents the transition probabilities, the fifth column represents the oscillator strengths, and the sixth column represents the line strengths values. A search of the available literature revealed no theoretical or experimental data on the forbidden transitions (E2 and M1) for the six times ionized krypton (Kr VII). Therefore, the transition parameters for forbidden transitions of Kr VII ion are presented for the first time in this study. Due to the limited number of previous theoretical and experimental calculations related to six times ionized krypton (Kr VII), it is believed that the comprehensive computational results obtained in this study could provide valuable data, especially for astrophysical research, technological advancements, and scientific developments. For the Kr VII ion, there are no previously presented data, especially for the forbidden transitions. In this study, it is aimed to extend the limited data in the existing literature with new data obtained from the calculations and to introduce some parameters to the literature for the first time.