International Journal of Spectroscopy

International Journal of Spectroscopy / 2016 / Article

Research Article | Open Access

Volume 2016 |Article ID 1697561 | 7 pages | https://doi.org/10.1155/2016/1697561

Atomic Structure Calculations for Neutral Oxygen

Academic Editor: Karol Jackowski
Received30 Nov 2015
Revised28 Mar 2016
Accepted04 May 2016
Published25 May 2016

Abstract

Energy levels and oscillator strengths for neutral oxygen have been calculated using the Cowan (CW), SUPERSTRUCTURE (SS), and AUTOSTRUCTURE (AS) atomic structure codes. The results obtained with these atomic codes have been compared with MCHF calculations and experimental values from the National Institute of Standards and Technology (NIST) database.

1. Introduction

Oxygen atom (O I) is the most abundant element after hydrogen and helium in the Universe. Its spectroscopic study is very important for the knowledge of the structure of stars, galaxies and in general the whole Universe. It is also important for studying the life on the earth and the possibility of life on other planets or exoplanets. The studies of earth’s atmosphere and its radiative properties need these data. Industrial and technical applications need the characteristics of this element.

Pradhan and Saraph [1] calculated oscillator strengths for dipole transitions in O I using the SUPERSTRUCTURE (SS) code [2] with spectroscopic type orbitals for 1s, 2s, and 2p and correlation type orbitals for the . Tayal and Henry [3] calculated oscillator strengths and electron collisional excitation cross sections for O I. They used the Hibbert CIV3 atomic structure code [4] with the eight orthogonal one-electron orbitals 1s, 2s, 2p, 3s, 3p, 3d, 4s, and 4p. Using the same CIV3 atomic structure code, Bell and Hibbert [5] calculated oscillator strengths for allowed transitions in O I with more single electron orbitals. Hibbert et al. (HBGV) [6] used the CIV3 code to calculate E1 transitions connecting the and energy levels in O I. Biémont et al. [7] calculate oscillator strengths of astrophysical interest for O I using the CIV3 configuration interaction code and the Hartree-Fock pseudorelativistic (HFR) suite of Cowan (CW) codes [8]. Using the SS code, Biémont and Zeippen [9] calculated oscillator strengths for 2p4-3s and 3s-3p allowed or spin-forbidden transitions in O I. Zheng and Wang [10] used the Weakest Bound Electron Potential Model (WBEPM) theory to calculate radiative lifetime, transition probabilities, and oscillator strengths for atomic carbon and oxygen. Using the Multiconfiguration Hartree-Fock (MCHF) method [11], Tachiev and Froese Fischer (TFF) [12] calculated ab initio Breit-Pauli energy levels and transition rates for nitrogen-like and oxygen-like sequences. Froese Fischer and Tachiev (FFT) [13] calculated Breit-Pauli energy levels, lifetimes, and transition probabilities for the beryllium-like to neon-like sequences in the adjusted with experimental values. Fan et al. [14] used the WBEPMT theory to calculate energy levels of high states in O I. Çelik and Ateş [15] employed the WBEPMT theory to calculate radial transition matrix elements and then atomic transition probabilities for O I.

Using CW or SS or AS codes, we did atomic structure calculations for several atoms and ions [1618] that are needed for ab initio Stark broadening calculations [19, 20] and for emission line ratio calculations [21], but we never compare results obtained by the three codes for the same element.

About O I atomic data in databases, we used the National Institute of Standards and Technology (NIST) data [22] for fine structure energy levels and oscillator strengths. There are energy levels and oscillator strengths of O I without fine structure in the Opacity Project TOPbase [23] and NORAD-Atomic-Data [24] atomic structure databases. TIPbase database [25] of the Opacity Project used NIST data for the fine structure energy levels and Galavis et al. [26] data for the oscillator strengths fine structure data. Galavis et al. [26] used the SS atomic structure code with spectroscopic type orbitals for 1s, 2s, and 2p and correlation type orbitals for , , , and .

In the Chianti project [27], they used the NIST database for experimental energy levels and oscillator strengths. For theoretical energy levels they used the Zatsarinny and Tayal [28] and FFT [13] for the theoretical oscillator strengths.

In this work, we will calculate atomic data for transitions with fine structure in O I using CW and SS and AS codes. Comparison with other theoretical and experimental data available in the literature will be presented.

2. Methods for Calculation

2.1. Hartree-Fock Pseudorelativistic (HFR) Method

In this method a set of orbitals are obtained for each electron configuration by solving the Hartree-Fock equations [8]. A totally antisymmetric wave-function is a combination of single electron solution of the hydrogen atom (Slater determinant): means that the th electron’s space and spin are in the one-electron state . This will automatically satisfy the Pauli principle, because a determinant vanishes if two columns are the same.

Relativistic corrections are introduced by a Breit-Pauli Hamiltonian and treated by the perturbation theory. The relativistic corrections include the Blume-Watson spin-orbit, mass-variation, and one-body Darwin terms. The Blume-Watson spin-orbit term contains the part of the Breit interaction that can be reduced to a one-body operator.

The Cowan (CW) atomic structure suite of codes (RCN, RNC2, RCG, and RCE) uses this HFR method. The three first codes are for ab initio atomic structure calculations and the fourth one (RCE) is used to make least-squares fit calculations using an iterative procedure.

2.2. Thomas-Fermi-Dirac-Amaldi (TFDA) Method

In this method and to have atomic parameters of an atom or ion, a statistical TFDA potential is used. For an atom or ion having protons and electrons, this potential is in the following form [29]:wherewith the constant:and are the orbital scaling parameters.

The function verifies the following equation:with the boundary conditions:The SUPERSTRUCTURE (SS) and AUTOSTRUCTURE (AS) atomic structure codes use this method. Relativistic corrections are also done by a perturbation method using the Breit-Pauli Hamiltonian. The SS atomic structure code used in this work [30] is an updated version of the original one of 1974 [2]. Some relativistic corrections are introduced in this version and orbital scaling parameters are dependent on and [31] and not like the original SS version of 1974, where scaling parameters were depending only on (). The AS code [32, 33] is an extension of the SS code incorporating various improvements and new capabilities like two-body non-fine-structure operators of the Breit-Pauli Hamiltonian and polarization model potentials. Comparing the two atomic structure codes SS and AS we can see that even they used the same techniques in general; they gave different results mainly because they incorporated different relativistic corrections of the Hamiltonian. For the comparison between the two codes, we can refer to the work of Elabidi and Sahal-Bréchot [34] where they studied excitation cross section by electron impact for O V and O VI levels. They showed that the incorporation of the two-body non-fine-structure operators (contact spin-spin, two-body Darwin, and orbit-orbit) in AS and not in the initial SS code is the main reason of the different results obtained by the two codes.

3. Results and Discussion

3.1. Energy Levels

We performed ab initio calculations of energy levels for O I using the three atomic structure codes CW, SS, and AS with the 5 configurations expansion 2p4, 2p3 3s, 2p3 3p, 2p3 3d, and 2p3 4s. This same set of configurations expansion was used by Tachiev and Froese Fischer (TFF) in the ab initio calculations [12] and by Froese Fischer and Tachiev in the adjusted with experimental values calculations [13]. For the SS and AS atomic codes, the scaling parameters are determined variationally by minimizing the sum of all the nonrelativistic term energies (Table 1).


Scaling parameters1s2s2p3s3p3d4s

(SS)1.231031.23103 1.15865 1.231031.15865 0.92431 1.23103
(AS)1.55498 1.16135 1.20894 1.07693 2.388710.91505 2.33806

In Tables 26, calculated fine structure energy levels are presented. The obtained values are compared with the NIST atomic database [22] and with Tachiev and Froese Fischer ab initio calculations [12] using the Multiconfiguration Hartree-Fock (MCHF) method [11].


ConfigurationTermJE(NIST)E(CW)E(SS)E(AS)E(TFF)

2s22p43P200000
2s22p43P1158141171204156
2s22p43P0227210255303223
2s22p41D21586814941188811736416122
2s22p41S03379337013457464214033844


ConfigurationTermJE(NIST)E(CW)E(SS)E(AS)E(TFF)

2s22p3(4S°)3s527376870285503426740974012
2s22p3(4S°)3s317679572704545467036576910
2s22p3(2D°)3s33101135964758076999037
2s22p3(2D°)3s32101148964748076899036
2s22p3(2D°)3s31101155964738076799035
2s22p3(2D°)3s121026629768482871100502
2s22p3(2P°)3s32113911113471100024119170
2s22p3(2P°)3s31113921113469100023119169
2s22p3(2P°)3s30113928113468100022119168
2s22p3(2P°)3s11115918114666101453121545


ConfigurationTermJE(NIST)E(CW)E(SS)E(TFF)

2s22p3(4S°)3p5P186626831486227686645
2s22p3(4S°)3p5P286628831496227986647
2s22p3(4S°)3p5P386631831526228486650
2s22p3(4S°)3p3P188631855166749588590
2s22p3(4S°)3p3P288631855196749288591
2s22p3(4S°)3p3P088631855146749788591
2s22p3(2D°)3p1P111320410893591748
2s22p3(2D°)3p3D311329510887791674
2s22p3(2D°)3p3D211329510887191665
2s22p3(2D°)3p3D111329810886491655
2s22p3(2D°)3p3F411371410907592012
2s22p3(2D°)3p3F311372110907292007
2s22p3(2D°)3p3F211372710906992003
2s22p3(2D°)3p1F311399610931892419
2s22p3(2D°)3p1D2116631113447101312
2s22p3(2P°)3p3D3127283126148111485
2s22p3(2P°)3p3D2127288126149111486
2s22p3(2P°)3p3D1127292126149111485
2s22p3(2P°)3p1P1127668126335111820
2s22p3(2P°)3p1D2128595127944115611
2s22p3(2P°)3p1S0130943132423111145
2s22p3(2D°)3p3P111127496720
2s22p3(2D°)3p3P211128096730
2s22p3(2D°)3p3P011127296715
2s22p3(2P°)3p3P1127427113836
2s22p3(2P°)3p3P2127418113812
2s22p3(2P°)3p3P0127432113848


ConfigurationTermJE(NIST)E(CW)E(SS)E(AS)E(TFF)

2s22p3(4S°)3d549742194227727218975597147
2s22p3(4S°)3d539742194227727218975597147
2s22p3(4S°)3d529742194227727218975597147
2s22p3(4S°)3d519742194227727218975597147
2s22p3(4S°)3d509742194227727218975497148
2s22p3(4S°)3d319748894299728208983697205
2s22p3(4S°)3d329748894299728208983697205
2s22p3(4S°)3d339748994299728218983697205
2s22p3()3d32123297120045102401120957
2s22p3()3d31123356120049102405120959
2s22p3()3d30123387120050102406120961
2s22p3()3d34124214119938102042120523
2s22p3()3d33124219119935102039120520
2s22p3()3d32124224119934102037120518
2s22p3(2D°)3d34124239119945102051120530
2s22p3(2D°)3d35124240119946102053120531
2s22p3()3d10124243119935102037120519
2s22p3()3d33124247119957102070120544
2s22p3(2D°)3d33124253119944102051120529
2s22p3()3d32124258119958102072120545
2s22p3()3d14124259119952102061120538
2s22p3()3d31124264119959102072120546
2s22p3()3d11124274120043103055120030
2s22p3()3d12124319120017102181120609
2s22p3()3d13124327120033102174120629
2s22p3()3d31124336120002102133120577
2s22p3(2P°)3d12137928137105121625141057
2s22p3(2P°)3d30137947137093121609141050
2s22p3(2P°)3d31137947137094121611141052
2s22p3(2P°)3d32137947137097121615141054
2s22p3(2P°)3d31137963137117121642141063
2s22p3(2P°)3d32137963137119121645141066
2s22p3(2P°)3d33137963137121121647141067
2s22p3(2P°)3d11137981137186121755141153
2s22p3(2P°)3d34137084121596141041
2s22p3(2P°)3d33137085121597141041
2s22p3(2P°)3d32137085121597141041
2s22p3(2P°)3d13137136121667141098


ConfigurationTermJE(NIST)E(CW)E(SS)E(AS)E(TFF)

2s22p3(4S°)4s5295477924257107011055895576
2s22p3(4S°)4s3196225930537275712224296264
2s22p3(2D°)4s33122420118248100741144123
2s22p3(2D°)4s32122433118247100740144121
2s22p3(2D°)4s31122441118246100739144121
2s22p3()4s12122798118560101552149959
2s22p3(2P°)4s30135682135369120288164620
2s22p3(2P°)4s31135682135370120289164621
2s22p3(2P°)4s32135682135372120291164623
2s22p3(2P°)4s11136353135684121113170467

For the fundamental configuration 2s2 2p4, CW code gives 7% difference from NIST values, while SS and AS codes give, respectively, 15% and 19% difference from NIST values. With CW code and for the other four excited configurations (2p3  ,  , and 2p3 4s), the agreement with NIST values is about 3%, while SS and AS give an agreement of about 20% with the NIST values except for 2p3 3s where the agreement of AS with NIST is 4% and 7% for 2p3 3d. AS gives bad energy levels (one hundred greater values) for the 2p3 3p configuration comparing to the other data and the calculated values are not reported in Table 4. TFF energy levels are less than 1% near the NIST values but there are many missed values (they give energy levels for only 24% of the NIST data for the 4 excited configurations 2p3  ).

We obtain six energy levels for the 2p3 3p configuration (2p3(2D°)3p 3P0,1,2 and 2p3(2P°)3p 3P0,1,2) and four new energy levels for the 2p3 3d configuration (2p3(2P°)3d 3F2,3,4 and 2p3(2P°)3d 1F3) which are not in the NIST atomic database (see the end of Tables 4 and 5).

3.2. Oscillator Strengths

We have also computed oscillator strengths for three multiplets of the transition 2p4-2p3 3s, four multiplets of the transition 2p3 3s-2p3 3p, one multiplet of the transition 2p4-3d, and four multiplets of the transition 2p3 3p-2p3 3d using the atomic structure codes CW, SS, and AS (see Tables 710). They are compared with those of FFT [13] and HBGV [6] and tabulated in NIST [22]. Our calculations with CW code give an agreement of about 2% with NIST values while FFT gives 8% with the NIST ones. The HBGV values have an agreement of 2% with the NIST ones but many data are missing.


Termsλ ()gf(NIST)gf(CW)gf(SS)gf(AS)gf(FFT)gf(HBGV)

3P-3131306.03
3P-3331304.86
3P-3531302.17
1D-3531641.31
1S-3132324.74


Termsλ ()gf(NIST)gf(CW)gf(SS)gf(AS)gf(FFT)gf(HBGV)

5S°-5537775.39
5S°-5557774.17
5S°-5577771.94
5S°-3536726.54
5S°-3556726.28
3S°-53310169.35
3S°-53510167.26
3S°-3318446.25
3S°-3338446.76
3S°-3358446.36


Termsλ ()gf(NIST)gf(CW)gf(SS)gf(AS)gf(FFT)gf(HBGV)

3P-3571025.76
3P-3551025.76
3P-3531025.76
3P-3351027.43
3P-3331027.43
3P-3131028.16
3P-5571026.47
3P-5551026.47
3P-5531026.47
3P-5351028.12
3P-5331028.12
3P-5131028.83

Wavelengths are from FFT.

Termsλ ()gf(NIST)gf(CW)gf(SS)gf(AS)gf(FFT)gf(HBGV)

5P-3579204.93
5P-5319260.81
5P-5339260.85
5P-5359260.94
5P-5539262.58
5P-5559262.67
5P-5579262.78
5P-5759265.83
5P-5779265.93
5P-5799266.01
3P-33511286.32
3P-33311286.41
3P-35711286.91
3P-35511287.03
3P-35311287.12