Norah Alonizan,^{1}Rabia Qindeel,^{1} and Nabil Ben Nessib^{1}
^{1}Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
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 2p^{4}-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 [16–18] 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 2p^{4}, 2p^{3} 3s, 2p^{3} 3p, 2p^{3} 3d, and 2p^{3} 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 parameters
1s
2s
2p
3s
3p
3d
4s
(SS)
1.23103
1.23103
1.15865
1.23103
1.15865
0.92431
1.23103
(AS)
1.55498
1.16135
1.20894
1.07693
2.38871
0.91505
2.33806
In Tables 2–6, 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].
Configuration
Term
J
E(NIST)
E(CW)
E(SS)
E(AS)
E(TFF)
2s^{2}2p^{4}
^{3}P
2
0
0
0
0
0
2s^{2}2p^{4}
^{3}P
1
158
141
171
204
156
2s^{2}2p^{4}
^{3}P
0
227
210
255
303
223
2s^{2}2p^{4}
^{1}D
2
15868
14941
18881
17364
16122
2s^{2}2p^{4}
^{1}S
0
33793
37013
45746
42140
33844
Configuration
Term
J
E(NIST)
E(CW)
E(SS)
E(AS)
E(TFF)
2s^{2}2p^{3}(^{4}S°)3s
^{5}S°
2
73768
70285
50342
67409
74012
2s^{2}2p^{3}(^{4}S°)3s
^{3}S°
1
76795
72704
54546
70365
76910
2s^{2}2p^{3}(^{2}D°)3s
^{3}D°
3
101135
96475
80769
99037
—
2s^{2}2p^{3}(^{2}D°)3s
^{3}D°
2
101148
96474
80768
99036
—
2s^{2}2p^{3}(^{2}D°)3s
^{3}D°
1
101155
96473
80767
99035
—
2s^{2}2p^{3}(^{2}D°)3s
^{1}D°
2
102662
97684
82871
100502
—
2s^{2}2p^{3}(^{2}P°)3s
^{3}P°
2
113911
113471
100024
119170
—
2s^{2}2p^{3}(^{2}P°)3s
^{3}P°
1
113921
113469
100023
119169
—
2s^{2}2p^{3}(^{2}P°)3s
^{3}P°
0
113928
113468
100022
119168
—
2s^{2}2p^{3}(^{2}P°)3s
^{1}P°
1
115918
114666
101453
121545
—
Configuration
Term
J
E(NIST)
E(CW)
E(SS)
E(TFF)
2s^{2}2p^{3}(^{4}S°)3p
^{5}P
1
86626
83148
62276
86645
2s^{2}2p^{3}(^{4}S°)3p
^{5}P
2
86628
83149
62279
86647
2s^{2}2p^{3}(^{4}S°)3p
^{5}P
3
86631
83152
62284
86650
2s^{2}2p^{3}(^{4}S°)3p
^{3}P
1
88631
85516
67495
88590
2s^{2}2p^{3}(^{4}S°)3p
^{3}P
2
88631
85519
67492
88591
2s^{2}2p^{3}(^{4}S°)3p
^{3}P
0
88631
85514
67497
88591
2s^{2}2p^{3}(^{2}D°)3p
^{1}P
1
113204
108935
91748
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}D
3
113295
108877
91674
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}D
2
113295
108871
91665
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}D
1
113298
108864
91655
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}F
4
113714
109075
92012
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}F
3
113721
109072
92007
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}F
2
113727
109069
92003
—
2s^{2}2p^{3}(^{2}D°)3p
^{1}F
3
113996
109318
92419
—
2s^{2}2p^{3}(^{2}D°)3p
^{1}D
2
116631
113447
101312
—
2s^{2}2p^{3}(^{2}P°)3p
^{3}D
3
127283
126148
111485
—
2s^{2}2p^{3}(^{2}P°)3p
^{3}D
2
127288
126149
111486
—
2s^{2}2p^{3}(^{2}P°)3p
^{3}D
1
127292
126149
111485
—
2s^{2}2p^{3}(^{2}P°)3p
^{1}P
1
127668
126335
111820
—
2s^{2}2p^{3}(^{2}P°)3p
^{1}D
2
128595
127944
115611
—
2s^{2}2p^{3}(^{2}P°)3p
^{1}S
0
130943
132423
111145
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}P
1
—
111274
96720
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}P
2
—
111280
96730
—
2s^{2}2p^{3}(^{2}D°)3p
^{3}P
0
—
111272
96715
—
2s^{2}2p^{3}(^{2}P°)3p
^{3}P
1
—
127427
113836
—
2s^{2}2p^{3}(^{2}P°)3p
^{3}P
2
—
127418
113812
—
2s^{2}2p^{3}(^{2}P°)3p
^{3}P
0
—
127432
113848
—
Configuration
Term
J
E(NIST)
E(CW)
E(SS)
E(AS)
E(TFF)
2s^{2}2p^{3}(^{4}S°)3d
^{5}D°
4
97421
94227
72721
89755
97147
2s^{2}2p^{3}(^{4}S°)3d
^{5}D°
3
97421
94227
72721
89755
97147
2s^{2}2p^{3}(^{4}S°)3d
^{5}D°
2
97421
94227
72721
89755
97147
2s^{2}2p^{3}(^{4}S°)3d
^{5}D°
1
97421
94227
72721
89755
97147
2s^{2}2p^{3}(^{4}S°)3d
^{5}D°
0
97421
94227
72721
89754
97148
2s^{2}2p^{3}(^{4}S°)3d
^{3}D°
1
97488
94299
72820
89836
97205
2s^{2}2p^{3}(^{4}S°)3d
^{3}D°
2
97488
94299
72820
89836
97205
2s^{2}2p^{3}(^{4}S°)3d
^{3}D°
3
97489
94299
72821
89836
97205
2s^{2}2p^{3}()3d
^{3}P°
2
123297
120045
102401
120957
—
2s^{2}2p^{3}()3d
^{3}P°
1
123356
120049
102405
120959
—
2s^{2}2p^{3}()3d
^{3}P°
0
123387
120050
102406
120961
—
2s^{2}2p^{3}()3d
^{3}F°
4
124214
119938
102042
120523
—
2s^{2}2p^{3}()3d
^{3}F°
3
124219
119935
102039
120520
—
2s^{2}2p^{3}()3d
^{3}F°
2
124224
119934
102037
120518
—
2s^{2}2p^{3}(^{2}D°)3d
^{3}G°
4
124239
119945
102051
120530
—
2s^{2}2p^{3}(^{2}D°)3d
^{3}G°
5
124240
119946
102053
120531
—
2s^{2}2p^{3}()3d
^{1}S°
0
124243
119935
102037
120519
—
2s^{2}2p^{3}()3d
^{3}D°
3
124247
119957
102070
120544
—
2s^{2}2p^{3}(^{2}D°)3d
^{3}G°
3
124253
119944
102051
120529
—
2s^{2}2p^{3}()3d
^{3}D°
2
124258
119958
102072
120545
—
2s^{2}2p^{3}()3d
^{1}G°
4
124259
119952
102061
120538
—
2s^{2}2p^{3}()3d
^{3}D°
1
124264
119959
102072
120546
—
2s^{2}2p^{3}()3d
^{1}P°
1
124274
120043
103055
120030
—
2s^{2}2p^{3}()3d
^{1}D°
2
124319
120017
102181
120609
—
2s^{2}2p^{3}()3d
^{1}F°
3
124327
120033
102174
120629
—
2s^{2}2p^{3}()3d
^{3}S°
1
124336
120002
102133
120577
—
2s^{2}2p^{3}(^{2}P°)3d
^{1}D°
2
137928
137105
121625
141057
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}P°
0
137947
137093
121609
141050
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}P°
1
137947
137094
121611
141052
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}P°
2
137947
137097
121615
141054
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}D°
1
137963
137117
121642
141063
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}D°
2
137963
137119
121645
141066
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}D°
3
137963
137121
121647
141067
—
2s^{2}2p^{3}(^{2}P°)3d
^{1}P°
1
137981
137186
121755
141153
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}F°
4
—
137084
121596
141041
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}F°
3
—
137085
121597
141041
—
2s^{2}2p^{3}(^{2}P°)3d
^{3}F°
2
—
137085
121597
141041
—
2s^{2}2p^{3}(^{2}P°)3d
^{1}F°
3
—
137136
121667
141098
—
Configuration
Term
J
E(NIST)
E(CW)
E(SS)
E(AS)
E(TFF)
2s^{2}2p^{3}(^{4}S°)4s
^{5}S°
2
95477
92425
71070
110558
95576
2s^{2}2p^{3}(^{4}S°)4s
^{3}S°
1
96225
93053
72757
122242
96264
2s^{2}2p^{3}(^{2}D°)4s
^{3}D°
3
122420
118248
100741
144123
—
2s^{2}2p^{3}(^{2}D°)4s
^{3}D°
2
122433
118247
100740
144121
—
2s^{2}2p^{3}(^{2}D°)4s
^{3}D°
1
122441
118246
100739
144121
—
2s^{2}2p^{3}()4s
^{1}D°
2
122798
118560
101552
149959
—
2s^{2}2p^{3}(^{2}P°)4s
^{3}P°
0
135682
135369
120288
164620
—
2s^{2}2p^{3}(^{2}P°)4s
^{3}P°
1
135682
135370
120289
164621
—
2s^{2}2p^{3}(^{2}P°)4s
^{3}P°
2
135682
135372
120291
164623
—
2s^{2}2p^{3}(^{2}P°)4s
^{1}P°
1
136353
135684
121113
170467
—
For the fundamental configuration 2s^{2} 2p^{4}, 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 (2p^{3} , , and 2p^{3} 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 2p^{3} 3s where the agreement of AS with NIST is 4% and 7% for 2p^{3} 3d. AS gives bad energy levels (one hundred greater values) for the 2p^{3} 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 2p^{3} ).
We obtain six energy levels for the 2p^{3} 3p configuration (2p^{3}(^{2}D°)3p ^{3}P_{0,1,2} and 2p^{3}(^{2}P°)3p ^{3}P_{0,1,2}) and four new energy levels for the 2p^{3} 3d configuration (2p^{3}(^{2}P°)3d ^{3}F_{2,3,4} and 2p^{3}(^{2}P°)3d ^{1}F_{3}) 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 2p^{4}-2p^{3} 3s, four multiplets of the transition 2p^{3} 3s-2p^{3} 3p, one multiplet of the transition 2p^{4}-3d, and four multiplets of the transition 2p^{3} 3p-2p^{3} 3d using the atomic structure codes CW, SS, and AS (see Tables 7–10). 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.