Journal of Atomic, Molecular, and Optical PhysicsVolume 2012 (2012), Article ID 246105, 15 pagesdoi:10.1155/2012/246105

Research Article

Transition Parameters for Doubly Ionized Lanthanum

Betül Karaçoban and Leyla Özdemir

Department of Physics, Sakarya University, 54187 Sakarya, Turkey

Received 6 July 2012; Accepted 8 August 2012

Academic Editor: Alan Migdall

Copyright © 2012 Betül Karaçoban and Leyla Özdemir. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The transition parameters such as the wavelengths, weighted oscillator strengths, and transition probabilities (or rates) for the nd , nd , np , and ng electric dipole (E1) transitions of doubly ionized lanthanum (La III, ) have been calculated using the relativistic Hartree-Fock (HFR) method. In this method, configuration interaction and relativistic effects have been included in the computations combined with a least squares fitting of the Hamiltonian eigenvalues to the observed energy levels. We have compared the results obtained from this work with the previously available calculations and experiments in literature. We have also reported new transitions with the weighted transition probabilities greater than or equal to 10⁵.

1. Introduction

The radiative properties of the lanthanides and their ions have been rather little considered. This can be explained by the fact that these atoms or ions are characterized by complex electronic structures with an unfilled 4f subshell, which makes the calculations very difficult, and that the laboratory analyses are still extremely fragmentary or even missing for many ions. Owing to the importance of rare earth elements in astrophysics, especially in relation to nucleosynthesis and star formation (notably the lanthanides in chemically peculiar (CP) stars) [7], there is a growing need for accurate spectroscopic data, that is, wavelengths, radiative transition rates, oscillator strengths, branching fractions, radiative lifetimes, hyperfine structure, and isotope shift data for lanthanide atoms and ions.

The lanthanum atom is the first member of the rare earth elements. Doubly ionized lanthanum (La III) is characterized by a simple atomic structure with core [Xe] and only one outer electron. There is substantial spectroscopic literature concerning La III, though less than the neutral or singly ionized species. The available theoretical and experimental works on energy levels, radiative lifetimes, and transition parameters for La III can be found in the literature [1–3, 5, 6, 8–13]. These works were reported in our previous work in detail [14].

Up till now the wavelengths, oscillator strengths, and transition probabilities available for La III were obtained by experimental, semiempirical, or pure theoretical approaches. Sixty-five spectral lines of La III in the 2000–12000 Å interval were reported by Odabasi [2]. Sugar and Kaufman [13] observed forty-five La III spectral lines in the interval from 700 to 2000 Å. Johansson and Litzén [5] recorded wavelengths of 5d–4f lines of La III. Relativistic single-configuration Hartree-Fock oscillator strengths for 6s–6p transitions in La III were reported by Migdalek and Baylis [4]. Migdalek and Wyrozumska [3] have calculated oscillator strengths obtained using the relativistic model-potential approach in there different versions: a model-potential without valence-core electron exchange but with core-polarization included (RMP + CP), with semiclassical exchange and core-polarization (RMP + SCE + CP), and with empirically adjusted exchange and core-polarization (RMP + EX + CP) for the 6s–6p, 5d–6p, 5d–4f, 5d–5f, 5d–6f, 6p–6d, and 6p–7d transition arrays. The single-configuration relativistic Hartree-Fock ionization potentials of La III were computed by Migdalek and Bojara [9]. Biémont et al. [1] have performed oscillator strengths and transition probabilities in La III by relativistic Hartree-Fock method with core-polarization.

Our aim here is to determine the transition parameters, such as the wavelengths, oscillator strengths, and transition probabilities, for electric dipole transitions () in La III (). These calculations have been performed by using code [15] developed Cowan for relativistic Hartree-Fock (HFR) [16] calculations. This code considers the correlation effects and relativistic corrections. These effects contribute importantly to the physical and chemical properties of atoms or ions, especially lanthanides. The ground-state level of doubly ionized lanthanum is [Xe] 5d ²D3/2. We have taken into account 5p⁶nd, 5p⁶ng (), 5p⁶ns (), 5p⁵6s6p, 5p⁵6s4f, 5p⁵5d6p, 5p⁶nf (), 5p⁶np (), 5p⁵4, and 5p⁵6p² configurations outside the core [Cd], and nd, ng (), ns (), nf (), and np () configurations outside the core [Xe] in La III. The configuration sets that we used have been denoted by A and B, respectively, and are given in tables and text. We presented the energies, the Landé g-factors, and the lifetimes for nd, ng (), ns (), nf (), and np () excited levels of La III [14]. In addition, we have reported various atomic structure calculations such as energy levels, transition energies, hyperfine structure, lifetimes, and electric dipole transitions for some lanthanides (La I−III, Lu I−III, and Yb I−III) [17–27].

2. Calculation Method

An electromagnetic transition between two states is characterized by the angular momentum and the parity of the corresponding photon. If the emitted or absorbed photon has angular momentum and parity then, the transition is an electric multipole transition (). However, if the photon has parity the transition is a magnetic multipole transition ().

According to HFR method [16], the total transition probability from a state to all states levels of is given by and absorption oscillator strength is given by where, has units of kaysers (cm⁻¹) and is the electric dipole line strength in atomic units of . The strongest transition rate (or probability) is electric dipole () radiation. For this reason, the transitions are understood as being “allowed”, whereas high-order transitions are understood as being “forbidden”.

In HFR method, for an electron atom of nuclear charge , the Hamiltonian is expanded as in atomic units, with the distance of the th electron from the nucleus and . is the spin-orbit term, with being the fine structure constant and the mean potential field due to the nucleus and other electrons.

In this method, one calculates single-configuration radial functions for a spherically symmetrised atom (center-of-gravity energy of the configuration) based on Hartree-Fock method. The radial wave functions are also used to obtain the atom’s total energy () including approximate relativistic and correlation energy corrections. Relativistic terms in the potential function give approximate relativistic corrections to the radial functions, as well as improved relativistic energy corrections in heavy atoms. In addition, a correlation term is included to make the potential function more negative, thereby helping to bind negative ions. These radial functions are also used to calculate Coulomb integrals and and spin-orbit integrals . After radial functions have been obtained based on Hartree-Fock model, the wave function of the sublevel of a level labeled is expressed in terms of basis states by the formula

If determinant wave functions are used for the atom, the total binding energy is given by where is the kinetic energy, is the electron-nuclear Coulomb energy, and is the Coulomb interaction energy between electrons and   averaged over all possible magnetic quantum numbers.

In this method, relativistic corrections have been limited to calculations to the mass-velocity and the Darwin corrections by using the relativistic correction to total binding energy. The total binding energy can be given in by formulas , , and in [16].

3. Results and Discussion

We calculated the radiative parameters (wavelengths, oscillator strengths, and transition probabilities) for electric dipole () transitions in La III () using HFR code [15]. We have taken into account 5p⁶nd, 5p⁶ng (), 5p⁶ns (), 5p⁵6s6p, 5p⁵6s4f, 5p⁵5d6p, 5p⁶nf (), 5p⁶np (), 5p⁵4, and 5p⁵6p² configurations outside the core [Cd] for calculation A, and nd, ng (), ns (), nf (), and np () configurations outside the core [Xe] for calculation B. Table 1 shows the wavelengths, (in Å); the weighted oscillator strengths, gf; the weighted transition rates (or probabilities), (in ), for nd ()–nf (), nd ()–np (), np ()–ns (), and ng ()–nf () electric dipole () transitions. The data obtained are too much. For this reason, we have here presented just a part of the results. The comparing values for these exist in literature. Therefore, it is also made a comparison with other calculations and experiments in Table 1. We have also reported the wavelengths, the weighted oscillator strengths, and the weighted transition probabilities that are greater than or equal to 10⁵ for some new transitions (680 Å ≤ λ ≤ 8600 Å) in Table 2. References for other comparison values are indicated below the tables with a lowercase superscript; odd-parity states are indicated by the superscript “”.

Table 1: Wavelengths λ(Å), weighted oscillator strengths , and weighted transition probabilities gA (s⁻¹) for electric dipole () transitions in La III.

Transition

ki

Lower level
Upper level
This work
Other works
This work
Other works
This work
Other works

6p ²Po1/2
7s ²S1/2
2479.41A,B
2478.66a
0.489A
0.475a
5.31 × 108 A
5.16 × 108 a

2478.652c
0.463B

5.03 × 108 B

6p ²Po3/2
7s ²S1/2
2685.55A,B
2684.75a
0.904A
0.878a
8.36 × 108 A
8.12 × 108 a

2684.757c
0.855B

7.91 × 108 B

6p ²Po1/2
6d ²D3/2
2477.36A
2476.60a
2.474A
2.365a
2.69 × 109 A
2.57 × 109 a

2477.35B
2476.599c
2.651B
2.142d
2.88 × 109 B
2.27 × 109 b

6p ²Po3/2
6d ²D5/2
2652.29A
2651.50a
4.168A
3.976a
3.95 × 109 A
3.77 × 109 a

2652.28B
2651.501c
4.457B
3.972d
4.23 × 109 B
3.66 × 109 b

6p ²Po3/2
6d ²D3/2
2683.14A
2682.34a
0.458A
0.437a
4.24 × 108 A
4.05 × 108 a

2683.13B
2682.345c
0.489B
0.444d
4.54 × 108 B
4.01 × 108 b

6p ²Po1/2
8s ²S1/2
1466.39A,B
1466.39a
0.071A
0.069a
2.20 × 108 A
2.15 × 108 a

0.064B

2.00 × 108 B

6p ²Po3/2
8s ²S1/2
1536.13A,B
1536.13a
0.136A
0.132a
3.83 × 108 A
3.73 × 108 a

0.123B

3.48 × 108 B

6p ²Po1/2
7d ²D3/2
1459.45A,B
1459.45a
0.158A
0.156a
4.96 × 108 A
4.88 × 108 a

0.216B
0.137d
6.76 × 108 B
4.26 × 108 b

6p ²Po3/2
7d ²D5/2
1523.75A,B
1523.75a
0.277A
0.269a
7.95 × 108 A
7.71 × 108 a

0.372B
0.211d
10.70 × 108 B
6.02 × 108 b

6p ²Po3/2
7d ²D3/2
1528.51A,B
1528.51a
0.031A
0.030a
8.71 × 107 A
8.49 × 107 a

0.041B
0.022d
11.80 × 107 B
6.23 × 107 b

6p ²Po1/2
9s ²S1/2
1212.28A,B
1212.28a
0.026A
0.026a
1.19 × 108 A
1.16 × 108 a

0.023B

1.06 × 108 B

6p ²Po3/2
9s ²S1/2
1259.55A,B
1259.55a
0.051A
0.049a
2.13 × 108 A
2.07 × 108 a

0.045B

1.89 × 108 B

6p ²Po1/2
8d ²D3/2
1208.79A,B
1208.79a
0.040A
0.041a
1.80 × 108 A
1.86 × 108 a

0.065B

2.95 × 108 B

6p ²Po3/2
8d ²D5/2
1254.00A,B
1254.00a
0.070A
0.071a
2.98 × 108 A
3.00 × 108 a

0.112B

4.76 × 108 B

6p ²Po3/2
8d ²D3/2
1255.79A,B
1255.79a
0.008A
0.008a
3.27 × 107 A
3.32 × 107 a

0.012B

5.27 × 107 B

6p ²Po1/2
10s ²S1/2
1101.01A,B
1101.01a
0.013A
0.013a
7.26 × 107 A
7.07 × 107 a

0.012B

6.39 × 107 B

6p ²Po3/2
10s ²S1/2
1139.87A,B
1139.87a
0.026A
0.025a
1.31 × 108 A
1.27 × 108 a

0.022B

1.15 × 108 B

6p ²Po1/2
9d ²D3/2
1099.00A,B
1099.00a
0.015A
0.017a
8.54 × 107 A
9.21 × 107 a

0.029B

16.10 × 107 B

6p ²Po3/2
9d ²D5/2
1136.80A,B
1136.80a
0.028A
0.029a
1.44 × 108 A
1.50 × 108 a

0.050B

2.61 × 108 B

6p ²Po3/2
9d ²D3/2
1137.71A,B
1137.71a
0.003A
0.003a
1.58 × 107 A
1.66 × 107 a

0.006B

2.89 × 107 B

6d ²D3/2
5f ²Fo5/2
9926.70A
9924.04a
2.549A
2.370a
1.73 × 108 A
1.60 × 108 a

9926.74B
9923.989c
2.574B

1.74 × 108 B

6d ²D5/2
5f ²Fo7/2
10287.59A,B
10284.790c
3.515A
—
2.21 × 108 A
—

3.548B

2.24 × 108 B

6d ²D5/2
5f ²Fo5/2
10373.15A
10370.335c
0.174A
—
1.08 × 107 A
—

10373.12B

0.176B

1.09 × 107 B

6d ²D3/2
7p ²Po3/2
8277.67A,B
8275.41a
0.243A
0.240a
2.37 × 107 A
2.34 × 107 a

8275.388c
0.250B

2.43 × 107 B

6d ²D5/2
7p ²Po3/2
8585.81A
8583.42a
2.115A
2.081a
1.91 × 108 A
1.88 × 108 a

8585.76B
8583.453c
2.165B

1.96 × 108 B

6d ²D3/2
7p ²P o1/2
9215.20A
9212.68a
1.094A
1.077a
8.59 × 107 A
8.46 × 107 a

9215.23B
9212.628c
1.121B

8.80 × 107 B

6d ²D3/2
6f ²Fo5/2
3076.05A
3075.17a
0.733A
0.822a
5.17 × 108 A
5.80 × 108 a

3076.06B
3075.173c
0.790B

5.57 × 108 B

6d ²D5/2
6f ²Fo7/2
3112.88A,B
3111.97a
1.037A
1.161a
7.14 × 108 A
7.99 × 108 a

3111.969c
1.116B

7.68 × 108 B

6d ²D5/2
6f ²Fo5/2
3117.63A,B
3116.74a
0.052A
0.058a
3.55 × 107 A
3.98 × 107 a

3116.738c
0.056B

3.82 × 107 B

6d ²D3/2
8p ²Po3/2
2954.63A
2953.77a
0.009A
0.008a
6.82 × 106 A
5.87 × 106 a

2954.64B

0.008B

6.18 × 106 B

6d ²D5/2
8p ²Po3/2
2992.97A,B
2992.10a
0.079A
0.068a
5.89 × 107 A
5.08 × 107 a

2992.098c
0.072B

5.35 × 107 B

6d ²D3/2
8p ²Po1/2
3010.10A
3009.22a
0.044A
0.038a
3.23 × 107 A
2.77 × 107 a

3010.11B
3009.223c
0.040B

2.92 × 107 B

6d ²D3/2
7f ²Fo5/2
2239.04A
2238.35a
0.339A
0.358a
4.51 × 108 A
4.76 × 108 a

2239.05B

0.356B

4.74 × 108 B

6d ²D5/2
7f ²Fo7/2
2259.31A,B
2258.61a
0.480A
0.507a
6.28 × 108 A
6.62 × 108 a

2258.609c
0.504B

6.59 × 108 B

6d ²D5/2
7f ²Fo5/2
2261.00A,B
2260.30a
0.024A
0.025a
3.13 × 107 A
3.30 × 107 a

2260.295c
0.025B

3.29 × 107 B

6d ²D3/2
9p ²Po3/2
2195.18A
2194.50a
0.003A,B
0.002a
4.15 × 106 A
3.28 × 106 a

2195.19B

3.58 × 106B

6d ²D3/2
9p ²Po1/2
2213.95A,B
2213.26a
0.015A
0.012a
2.02 × 107 A
1.60 × 107 a

0.013B

1.75 × 107 B

6d ²D5/2
9p ²Po3/2
2216.28A,B
2215.58a
0.027A
0.021a
3.62 × 107 A
2.87 × 107 a

0.023B

3.13 × 107 B

6d ²D3/2
8f ²Fo5/2
1923.33A
1923.33a
0.178A
0.185a
3.22 × 108 A
3.33 × 108 a

1923.34B

0.188B

3.39 × 108 B

6d ²D5/2
8f ²Fo7/2
1938.53A,B
1938.53a
0.253A
0.262a
4.49 × 108 A
4.65 × 108 a

0.267B

4.73 × 108 B

6d ²D5/2
8f ²Fo5/2
1939.51A,B
1939.51a
0.013A,B
0.013a
2.24 × 107 A
2.32 × 107 a

2.36 × 107 B

6f ²Fo5/2
6g ²G7/2
8290.18A
8287.76a
8.903A
8.527a
8.64 × 108 A,B
8.28 × 108 a

8290.16B
8287.752c
8.904B

6f ²Fo7/2
6g ²G9/2
8323.43A
8321.16a
11.495A
11.009a
1.11 × 109 A,B
1.06 × 109 a

8323.34B
8321.107c
11.496B

6f ²Fo7/2
6g ²G7/2
8323.98A
8321.63a
0.328A,B
0.315a
3.16 × 107 A,B
3.03 × 107 a

8323.97B

6f ²Fo5/2
7g ²G7/2
5147.17A,B
5145.72a
1.282A
1.239a
3.23 × 108 A,B
3.12 × 108 a

5145.729c
1.283B

6f ²Fo7/2
7g ²G9/2
5159.84A
5158.39a
1.658A
1.602a
4.15 × 108 A
4.01 × 108 a

5159.82B
5158.410c
1.659B

4.16 × 108 B

6f ²Fo7/2
7g ²G7/2
5160.18A
5158.76a
0.047A,B
0.046a
1.19 × 107 A,B
1.15 × 107 a

5160.19B

6f ²Fo5/2
8g ²G7/2
4130.43A,B
4129.24a
0.411A,B
0.394a
1.61 × 108 A,B
1.54 × 108 a

6f ²Fo7/2
8g ²G9/2
4138.59A
4137.43a
0.531A
0.509a
2.07 × 108 A,B
1.98 × 108 a

4138.58B
4137.428c
0.532B

6f ²Fo7/2
8g ²G7/2
4138.80A
4137.64a
0.015A,B
0.015a
5.91 × 106 A,B
5.67 × 106 a

4138.81B

6f ²Fo5/2
9d ²D3/2
5519.77A
5518.19a
0.132A
0.130a
2.89 × 107 A
2.85 × 107 a

5519.75B
5518.187c
0.128B

2.79 × 107 B

6f ²F°5/2
9d ²D5/2
5498.45A
5496.88a
0.009A,B
0.009a
2.08 × 106 A
2.06 × 106 a

5498.43B

2.02 × 106B

6f ²Fo7/2
9d ²D5/2
5513.29A,B
5511.76a
0.188A
0.186a
4.14 × 107 A
4.09 × 107 a

5511.721c
0.182B

4.01 × 107 B

6s ²S1/2
6p ²Po3/2
3172.60A,B
3171.69a
1.673A
1.527a
1.11 × 109 A
1.01 × 109 a

3171.735c
1.935B
1.418d
1.28 × 109 B
9.40 × 108 b

1.868e

6s ²S1/2
6p ²Po1/2
3518.16A
3517.16a
0.754A
0.689a
4.06 × 108 A
3.71 × 108 a

3518.15B
3517.217c
0.872B
0.640d
4.70 × 108 B
3.45 × 108 b

0.850e

6s ²S1/2
7p ²Po3/2
1236.55A,B
1236.55a
0.002A
0.006a
0.70 × 107 A
2.39 × 107 a

0.001B

0.27 × 107 B

6s ²S1/2
7p ²Po1/2
1255.63A,B
1255.63a
0.001A
0.003a
0.33 × 107 A
1.14 × 107 a

0.0003B

0.13 × 107 B

7s ²S1/2
7p ²Po3/2
8254.85A
8252.53a
2.418A
2.279a
2.37 × 108 A,B
2.23 × 108 a

8254.77B
8252.603c
2.424B

7s ²S1/2
7p ²Po1/2
9186.87A
9184.34a
1.086A
1.024a
8.59 × 107 A
8.09 × 107 a

9186.92B
9184.380c
1.089B

8.61 × 107 B

7s ²S1/2
8p ²Po3/2
2951.72A,B
2950.843c
0.002A,B
—
1.81 × 106 A
—

1.54 × 106B

7s ²S1/2
8p ²Po1/2
3007.07A
3006.186c
0.001A,B
—
8.57 × 105 A
—

3007.08B

7.27 × 105 B

7p ²Po1/2
8s ²S1/2
5890.23A
5888.63a
0.716A
0.718a
1.38 × 108 A
1.38 × 108 a

5890.25B
5888.620c
0.714B

1.37 × 108 B

7p ²Po3/2
8s ²S1/2
6349.93A
6348.21a
1.329A
1.331a
2.20 × 108 A
2.20 × 108 a

6349.97B
6348.213c
1.324B

2.19 × 108 B

7p ²Po1/2
7d ²D3/2
5779.74A
5778.14a
3.095A
2.967a
6.18 × 108 A
5.92 × 108 a

5779.71B
5778.138c
3.045B

6.08 × 108 B

7p ²Po3/2
7d ²D5/2
6143.64A
6141.99a
5.238A
5.024a
9.26 × 108 A
8.88 × 108 a

6143.71B
6141.987c
5.157B

9.11 × 108 B

7p ²Po3/2
7d ²D3/2
6221.70A
6219.99a
0.575A
0.551a
9.91 × 107 A
9.50 × 107 a

6221.69B
6219.999c
0.566B

9.75 × 107 B

7p ²Po1/2
9s ²S1/2
3197.77A
3196.85a
0.089A,B
0.092a
5.77 × 107 A,B
5.98 × 107 a

3197.78B
3196.844c

7p ²Po3/2
9s ²S1/2
3328.60A
3327.64a
0.170A,B
0.176a
1.02 × 108 A,B
1.06 × 108 a

3328.61B
3327.655c

7p ²Po1/2
8d ²D3/2
3173.60A
3172.69a
0.274A
0.260a
1.81 × 108 A
1.72 × 108 a

3173.61B
3172.689c
0.284B

1.89 × 108 B

7p ²Po3/2
8d ²D5/2
3290.05A
3289.11a
0.476A
0.452a
2.94 × 108 A
2.79 × 108 a

3290.07B
3289.110c
0.494B

3.05 × 108 B

7p ²Po3/2
8d ²D3/2
3302.41A
3301.47a
0.053A
0.050a
3.22 × 107 A
3.06 × 107 a

3302.43B
3301.481c
0.055B

3.35 × 107 B

7p ²Po1/2
10s ²S1/2
2524.74A,B
2523.98a
0.031A,B
0.033a
3.25 × 107 A
3.44 × 107 a

3.27 × 107 B

7p ²Po3/2
10s ²S1/2
2605.59A
2604.82a
0.060A,B
0.064a
5.91 × 107 A
6.25 × 107 a

2605.60B
2604.827c

5.94 × 107 B

7p ²Po1/2
9d ²D3/2
2514.19A,B
2513.43a
0.083A
0.077a
8.72 × 107 A
8.10 × 107 a

2513.432c
0.088B

9.27 × 107 B

7p ²Po3/2
9d ²D5/2
2589.64A,B
2588.86a
0.145A
0.134a
1.44 × 108 A
1.33 × 108 a

2588.867c
0.153B

1.53 × 108 B

7p ²Po3/2
9d ²D3/2
2594.36A,B
2593.58a
0.016A
0.015a
1.59 × 107 A
1.47 × 107 a

0.017B

1.69 × 107 B

7d ²D3/2
7f ²Fo5/2
6057.51A
6055.85a
0.518A
0.604a
0.94 × 108 A
1.10 × 108 a

6057.56B
6055.838c
0.578B

1.05 × 108 B

7d ²D5/2
7f ²Fo7/2
6121.04A
6119.27a
0.735A
0.854a
1.31 × 108 A
1.52 × 108 a

6121.00B
6119.254c
0.818B

1.46 × 108 B

7d ²D5/2
7f ²Fo5/2
6133.39A
6131.67a
0.037A
0.043a
6.51 × 106 A
7.55 × 106 a

6133.35B

0.041B

7.24 × 106B

7d ²D3/2
8f ²Fo5/2
4194.71A
4193.51a
0.260A
0.292a
0.99 × 108 A
1.11 × 108 a

4194.72B

0.283B

1.07 × 108 B

7d ²D5/2
8f ²Fo7/2
4226.33A
4225.12a
0.370A
0.414a
1.38 × 108 A
1.54 × 108 a

4226.29B

0.402B

1.50 × 108 B

7d ²D5/2
8f ²Fo5/2
4230.95A
4229.73a
0.018A
0.021a
6.89 × 106 A
7.70 × 106 a

4230.92B

0.020B

7.47 × 106B

7d ²D3/2
9p ²Po3/2
5746.85A
5745.26a
0.008A
0.007a
1.67 × 106 A
1.49 × 106 a

5746.90B

0.007B

1.48 × 106B

7d ²D5/2
9p ²Po3/2
5815.10A
5813.45a
0.073A
0.066a
1.45 × 107 A
1.30 × 107 a

5815.07B
5813.447c
0.065B

1.29 × 107 B

7d ²D3/2
9p ²Po1/2
5877.26A
5875.63a
0.040A
0.036a
7.83 × 106 A
6.98 × 106 a

5877.31B
5875.632c
0.036B

6.92 × 106B

7f ²Fo5/2
8g ²G7/2
8293.36A
8291.04a
1.513A,B
1.485a
1.47 × 108 A,B
1.44 × 108 a

8293.35B

7f ²Fo7/2
8g ²G9/2
8315.16A
8312.96a
1.956A,B
1.919a
1.89 × 108 A,B
1.85 × 108 a

8315.11B

7f ²Fo7/2
8g ²G7/2
8316.03A
8313.81a
0.056A,B
0.055a
5.39 × 106 A,B
5.29 × 106 a

8316.04B

5f ²Fo5/2
7d ²D5/2
5469.30A
5467.81a
0.037A
0.035a
8.26 × 106 A
7.89 × 106 a

5469.35B
5467.812c
0.035B

7.77 × 106B

5f ²Fo5/2
7d ²D3/2
5531.09A
5529.54a
0.514A
0.490a
1.12 × 108 A
1.07 × 108 a

5531.07B
5529.542c
0.482B

1.05 × 108 B

5f ²Fo7/2
7d ²D5/2
5493.40A
5491.90a
0.738A
0.704a
1.63 × 108 A
1.56 × 108 a

5493.43B
5491.902c
0.693B

1.53 × 108 B

5f ²Fo5/2
5g ²G7/2
4484.21A
4482.98a
8.886A
8.277a
2.95 × 109 A,B
2.75 × 109 a

4484.25B
4482.967c
8.889B

5f ²Fo7/2
5g ²G9/2
4500.32A
4499.06a
11.478A
10.692a
3.78 × 109 A,B
3.52 × 109 a

4500.34B
4499.050c
11.482B

5f ²Fo7/2
5g ²G7/2
4500.39A
4499.15a
0.328A,B
0.306a
1.08 × 108 A,B
1.01 × 108 a

4500.43B

5f ²Fo5/2
8d ²D5/2
3086.28A
3085.38a
0.004A,B
0.005a
2.98 × 106 A
3.13 × 106 a

3086.29B
3085.379c

2.80 × 106B

5f ²Fo5/2
8d ²D3/2
3097.15A
3096.26a
0.059A
0.062a
4.13 × 107 A
4.33 × 107 a

3097.16B
3096.255c
0.056B

3.88 × 107 B

5f ²Fo7/2
8d ²D5/2
3093.93A
3093.03a
0.085A
0.089a
5.91 × 107 A
6.21 × 107 a

3093.94B
3093.028c
0.080B

5.56 × 107 B

5f ²Fo5/2
6g ²G7/2
2898.73A
2897.88a
0.866A,B
0.786a
6.87 × 108 A,B
6.24 × 108 a

2898.74B
2897.875c

5f ²Fo7/2
6g ²G9/2
2905.42A
2904.57a
1.120A,B
1.016a
8.85 × 108 A,B
8.03 × 108 a

2905.41B
2904.576c

5f ²Fo7/2
6g ²G7/2
2905.49A,B
2904.63a
0.032A,B
0.029a
2.53 × 107 A,B
2.29 × 107 a

5f ²Fo5/2
9d ²D5/2
2461.70A,B
2460.95a
0.001A,B
0.002a
1.51 × 106 A
1.67 × 106 a

1.41 × 106B

5f ²F o5/2
9d ²D3/2
2465.97A,B
2465.22a
0.019A
0.021a
2.11 × 107 A
2.33 × 107 a

0.018B

1.96 × 107 B

5f ²F o7/2
9d ²D5/2
2466.59A
2465.82a
0.027A
0.030a
3.01 × 107 A
3.33 × 107 a

2535.57B

0.025B

2.80 × 107 B

5f ²Fo5/2
7g ²G7/2
2388.71A
2387.99a
0.226A,B
0.196a
2.64 × 108 A,B
2.29 × 108 a

2388.72B
2387.988c

5f ²Fo7/2
7g ²G9/2
2393.23A
2392.49a
0.292A,B
0.254a
3.41 × 108 A,B
2.96 × 108 a

2393.22B
2392.492c

5f ²Fo7/2
7g ²G7/2
2393.30A,B
2392.57a
0.008A,B
0.007a
9.73 × 106 A,B
8.45 × 106 a

5f ²Fo5/2
8g ²G7/2
2143.81A,B
2143.13a
0.089A,B
0.074a
1.29 × 108 A,B
1.08 × 108 a

5f ²F o7/2
8g ²G9/2
2147.44A,B
2146.77a
0.115A,B
0.096a
1.67 × 108 A,B
1.39 × 108 a

5f ²Fo7/2
8g ²G7/2
2147.50A,B
2146.83a
0.003A,B
0.003a
4.77 × 106 A,B
3.98 × 106 a

5g ²G9/2
7f ²Fo7/2
8116.78A
8114.48a
0.018A,B
0.021a
1.79 × 106 A,B
2.11 × 106 a

8116.75B
8114.415c

5g ²G7/2
7f ²Fo5/2
8138.27A
8136.00a
0.014A,B
0.016a
1.37 × 106 A,B
1.62 × 106 a

8138.19B
8135.964c

5g ²G9/2
8f ²Fo7/2
5090.54A
5089.12a
0.003A,B
0.003a
6.83 × 105 A
7.82 × 105 a

5090.51B

6.86 × 105B

5g ²G7/2
8f ²Fo5/2
5097.17A
5095.70a
0.002A,B
0.002a
5.25 × 105 A
6.01 × 105 a

5097.11B

5.27 × 105B

5d ²D3/2
4f ²Fo5/2
13898.50A
13894.47f
0.072A
0.031d
2.51 × 106 A
—

13898.06B

0.074B

2.54 × 106B

5d ²D5/2
4f ²Fo7/2
14099.97A
14096.18f
0.102A
0.046d
3.44 × 106 A
—

14100.19B

0.104B

3.48 × 106B

5d ²D5/2
4f ²Fo5/2
17882.04A
17878.09f
0.004A,B
0.002d
8.41 × 104 A
—

17883.69B

8.52 × 104 B

5d ²D5/2
6p ²Po3/2
2298.44A,B
2297.74a
1.172A
1.120a
1.48 × 109 A
1.41 × 109 a

2297.737c
1.315B
1.050d
1.66 × 109 B
1.33 × 109 b

2298.44g

5d ²D3/2
6p ²Po3/2
2216.76A
2216.07a
0.135A
0.129a
1.83 × 108 A
1.75 × 108 a

2216.75B
2216.067c
0.151B
0.115d
2.06 × 108 B
1.56 × 108 b

5d ²D3/2
6p ²Po1/2
2380.10A
2379.37a
0.629A
0.601a
7.41 × 108 A
7.07 × 108 a

2380.09B
2379.374c
0.705B
0.576d
8.31 × 108 B
6.78 × 108 b

2380.10g

5d ²D3/2
5f ²Fo5/2
1081.61A,B
1081.61a
1.649A
1.377a
9.40 × 109 A
7.85 × 109 a

1.640B
1.604d
9.35 × 109 B
9.06 × 109 b

5d ²D5/2
5f ²Fo7/2
1099.73A,B
1099.73a
2.317A
1.935a
1.28 × 1010A
1.07 × 1010 a

2.304B
2.325d
1.27 × 1010B
1.28 × 1010 b

5d ²D5/2
5f ²Fo5/2
1100.70A,B
1100.70a
0.115A,B
0.097a
6.37 × 108 A
5.32 × 108 a

0.119d
6.34 × 108 B
6.49 × 108 b

5d ²D3/2
7p ²Po3/2
1058.63A,B
1058.63a
0.013A,B
0.010a
7.84 × 107 A
5.72 × 107 a

8.02 × 107 B

5d ²D3/2
7p ²Po1/2
1072.59A,B
1072.59a
0.067A,B
0.048a
3.77 × 108 A
2.75 × 108 a

3.86 × 108 B

5d ²D5/2
7p ²Po3/2
1076.91A,B
1076.91a
0.116A
0.085a
6.70 × 108 A
4.89 × 108 a

0.119B

6.86 × 108 B

5d ²D3/2
6f ²Fo5/2
870.40A,B
870.40a
0.614A,B
0.446a
5.41 × 109 A
3.93 × 109 a

0.480d
5.40 × 109 B
4.21 × 109 b

5d ²D5/2
6f ²Fo7/2
882.34A,B
882.34a
0.865A,B
0.629a
7.42 × 109 A
5.39 × 109 a

0.696d
7.41 × 109 B
5.95 × 109 b

5d ²D5/2
6f ²Fo5/2
882.72A,B
882.72a
0.043A,B
0.031a
3.71 × 108 A
2.69 × 108 a

0.035d
3.70 × 108 B
2.99 × 108 b

5d ²D3/2
8p ²Po3/2
860.39A,B
860.39a
0.005A,B
0.003a
4.24 × 107 A
2.76 × 107 a

4.36 × 107 B

5d ²D3/2
8p ²Po1/2
865.04A,B
865.04a
0.024A,B
0.015a
2.08 × 108 A
1.36 × 108 a

2.15 × 108 B

5d ²D5/2
8p ²Po3/2
872.43A,B
872.43a
0.043A,B
0.027a
3.65 × 108 A
2.38 × 108 a

3.77 × 108 B

5d ²D3/2
7f ²Fo5/2
787.14A,B
787.14a
0.303A
0.203a
3.24 × 109 A
2.18 × 109 a

0.305B

3.28 × 109 B

5d ²D5/2
7f ²Fo7/2
796.99A,B
796.99a
0.430A,B
0.286a
4.51 × 109 A,B
3.00 × 109 a

5d ²D5/2
7f ²F o5/2
797.20A,B
797.20a
0.021A,B
0.014a
2.26 × 108 A,B
1.50 × 108 a

5d ²D3/2
9p ²Po3/2
781.65A,B
781.65a
0.002A,B
0.001a
2.52 × 107 A
1.54 × 107 a

2.62 × 107 B

5d ²D3/2
9p ²Po1/2
784.01A,B
784.01a
0.012A,B
0.007a
12.50 × 107 A
7.61 × 107 a

13.01 × 107 B

5d ²D5/2
9p ²Po3/2
791.57A,B
791.57a
0.021A,B
0.013a
2.19 × 108 A
1.33 × 108 a

2.27 × 108 B

5d ²D3/2
8f ²Fo5/2
744.19A,B
744.19a
0.176A,B
0.110a
2.12 × 109 A,B
1.33 × 109 a

5d ²D5/2
8f ²Fo7/2
753.03A,B
753.03a
0.249A
0.155a
2.92 × 109 A,B
1.83 × 109 a

0.248B

5d ²D5/2
8f ²Fo5/2
753.18A,B
753.18a
0.012A,B
0.008a
1.46 × 108 A,B
9.14 × 107 a

4f ²Fo5/2
6d ²D5/2
1322.42A,B
1322.42a
0.000A,B
0.002a
0.12 × 106 A
7.00 × 106 a

0.17 × 106B

4f ²Fo5/2
6d ²D3/2
1330.04A,B
1330.04a
0.001A,B
0.026a
0.22 × 107 A
9.64 × 107 a

0.23 × 107 B

4f ²Fo7/2
6d ²D5/2
1349.18A,B
1349.18a
0.001A,B
0.036a
3.07 × 106 A
1.32 × 108 a

3.16 × 106B

4f ²Fo5/2
5g ²G7/2
929.72A,B
929.72a
0.058A
0.040a
4.49 × 108 A
3.06 × 108 a

0.060B

4.63 × 108 B

4f ²Fo7/2
5g ²G9/2
942.86A,B
942.86a
0.074A
0.051a
5.58 × 108 A
3.81 × 108 a

0.077B

5.76 × 108 B

4f ²Fo7/2
5g ²G7/2
942.87A,B
942.87a
0.002A,B
0.001a
1.60 × 107 A
1.09 × 107 a

1.65 × 107 B

4f ²Fo5/2
6g ²G7/2
835.02A,B
835.02a
0.046A
0.030a
4.44 × 108 A
2.87 × 108 a

0.048B

4.58 × 108 B

4f ²Fo7/2
6g ²G9/2
845.61A,B
845.61a
0.059A
0.038a
5.54 × 108 A
3.58 × 108 a

0.061B

5.72 × 108 B

4f ²Fo7/2
6g ²G7/2
845.62A,B
845.62a
0.002A,B
0.001a
1.59 × 107 A
1.02 × 107 a

1.63 × 107 B

4f ²Fo5/2
7g ²G7/2
786.64A,B
786.64a
0.033A
0.021a
3.56 × 108 A
2.23 × 108 a

0.034B

3.68 × 108 B

4f ²Fo7/2
7g ²G9/2
796.03A,B
796.03a
0.042A
0.026a
4.44 × 108 A
2.78 × 108 a

0.044B

4.60 × 108 B

4f ²Fo5/2
8g ²G7/2
758.12A,B
758.12a
0.023A
0.014a
2.73 × 108 A
1.67 × 108 a

0.024B

2.82 × 108 B

4f ²Fo7/2
8g ²G9/2
766.83A,B
766.83a
0.030A
0.018a
3.41 × 108 A
2.09 × 108 a

0.031B

3.54 × 108 B

8s ²S1/2
9p ²Po3/2
5641.62A,B
5640.03a
0.005A
0.003a
10.20 × 105 A
5.58 × 105 a

0.004B

9.34 × 105B

8s ²S1/2
9p ²Po1/2
5767.24A
5765.63a
0.002A,B
0.001a
4.76 × 105 A
2.61 × 105 a

5767.25B

4.37 × 105B

8p ²Po1/2
8d ²D3/2
10940.83A
10937.898c
3.508A
—
1.95 × 108 A
—

10940.86B

3.439B

1.92 × 108 B

8p ²Po1/2
9d ²D3/2
5745.68A
5744.08a
0.337A
0.334a
6.81 × 107 A
6.75 × 107 a

5745.66B
5744.088c
0.347B

7.01 × 107 B

8p ²Po3/2
9d ²D5/2
5934.37A,B
5932.73a
0.588A
0.582a
1.12 × 108 A
1.10 × 108 a

5932.706c
0.604B

1.14 × 108 B

8p ²Po3/2
9d ²D3/2
5959.22A
5957.57a
0.065A
0.064a
1.22 × 107 A
1.21 × 107 a

5959.21B

0.067B

1.26 × 107 B

8p ²Po1/2
10s ²S1/2
5801.06A
5799.48a
0.112A
0.115a
2.23 × 107 A
2.27 × 107 a

5801.07B

0.113B

2.24 × 107 B

8p ²Po3/2
10s ²S1/2
6018.81A
6017.18a
0.217A
0.221a
3.99 × 107 A
4.06 × 107 a

6018.84B
6017.114c
0.218B

4.01 × 107 B

aReference [1], breference (in [1]), creference [2], dreference [3, RMP + EX + CP ], ereference [4, RHF + CP (a)], freference [5], greference [6].

Table 2: New (Å), , and (s⁻¹) for electric dipole () transitions in La III.

Transition
λ
gf
gA ki

Lower level
Upper level

5d ²D3/2
12f ²Fo5/2
682.99B
0.039B
5.62 × 108 B

5d ²D5/2
12f ²Fo7/2
690.53B
0.056B
7.77 × 108 B

5d ²D5/2
12f ²Fo5/2
690.55B
0.003B
3.89 × 107 B

5d ²D3/2
11f ²Fo5/2
690.98B
0.053B
7.46 × 108 B

5d ²D5/2
11f ²Fo7/2
698.69B
0.075B
1.03 × 109 B

5d ²D5/2
11f ²Fo5/2
698.72B
0.004B
5.15 × 107 B

5d ²D3/2
12p ²Po3/2
701.16B
0.001B
8.21 × 106 B

5d ²D3/2
12p ²Po1/2
701.60B
0.003B
4.10 × 107 B

5d ²D3/2
10f ²Fo5/2
702.10A,B
0.074A
1.00 × 109 A

0.075B
1.02 × 109 B

5d ²D5/2
12p ²Po3/2
709.13B
0.005B
7.14 × 107 B

5d ²D5/2
10f ²Fo7/2
710.05A,B
0.104A
1.38 × 109 A

0.106B
1.41 × 109 B

5d ²D5/2
10f ²Fo5/2
710.09A,B
0.005A,B
6.92 × 107 A

7.03 × 107 B

5d ²D3/2
11p ²Po3/2
716.83B
0.001B
1.15 × 107 B

5d ²D3/2
11p ²Po1/2
717.49B
0.004B
5.76 × 107 B

5d ²D5/2
11p ²Po3/2
725.17B
0.008B
1.00 × 108 B

4f ²Fo5/2
10g ²G7/2
729.02A
0.013A,B
1.57 × 108 A

727.97B

1.67 × 108 B

4f ²Fo7/2
10g ²G7/2
737.09A
0.001A,B
5.70 × 106A

736.01B

5.97 × 106 B

4f ²Fo7/2
10g ²G9/2
737.09A
0.016A
1.97 × 108 A

736.01B
0.017B
2.09 × 108 B

4f ²Fo5/2
9g ²G7/2
742.58A
0.017A
2.06 × 108 A

740.62B
0.018B
2.15 × 108 B

5d ²D3/2
10p ²Po3/2
740.94A
0.001A,B
1.60 × 107 A

740.93B

1.70 × 107 B

5d ²D3/2
10p ²Po1/2
742.00A
0.007A,B
7.99 × 107 A

741.97B

8.44 × 107 B

4f ²Fo7/2
9g ²G7/2
750.95A
0.001A,B
7.44 × 106 A

748.94B

7.72 × 106 B

4f ²Fo7/2
9g ²G9/2
750.95A
0.022A
2.58 × 108 A

748.94B
0.023B
2.70 × 108 B

5d ²D5/2
10p ²Po3/2
749.86A
0.012A,B
1.39 × 108 A

749.84B

1.47 × 108 B

6p ²Po1/2
12d ²D3/2
978.38B
0.006B
4.54 × 107 B

6p ²Po1/2
11d ²D3/2
1002.77B
0.010B
6.50 × 107 B

6p ²Po3/2
12d ²D5/2
1008.75B
0.011B
7.46 × 107 B

6p ²Po3/2
12d ²D3/2
1008.94B
0.001B
8.29 × 106 B

6p ²Po3/2
11d ²D5/2
1034.62B
0.017B
1.06 × 108 B

6p ²Po3/2
11d ²D3/2
1034.89B
0.002B
1.18 × 107 B

6p ²Po1/2
10d ²D3/2
1061.80A
0.008A
4.59 × 107 A

1039.29B
0.016B
9.83 × 107 B

6p ²Po3/2
10d ²D5/2
1097.43A
0.014A
7.83 × 107 A

1073.42B
0.028B
1.61 × 108 B

6p ²Po3/2
10d ²D3/2
1097.89A
0.002A
8.55 × 106A

1073.84B
0.003B
1.78 × 107 B

6d ²D3/2
12f ²Fo5/2
1561.65B
0.036B
9.96 × 107 B

6d ²D5/2
12f ²Fo7/2
1572.18B
0.052B
1.39 × 108 B

6d ²D5/2
12f ²Fo5/2
1572.29B
0.002B
6.97 × 106B

6d ²D3/2
11f ²Fo5/2
1604.09B
0.050B
1.31 × 108 B

6d ²D5/2
11f ²Fo7/2
1615.16B
0.072B
1.83 × 108 B

6d ²D5/2
11f ²Fo5/2
1615.32B
0.004B
9.15 × 106 B

6d ²D3/2
12p ²Po1/2
1662.51B
0.002B
5.62 × 106 B

6d ²D3/2
10f ²Fo5/2
1665.31A
0.080A
1.93 × 108 A

1665.37B
0.073B
1.76 × 108 B

6d ²D5/2
12p ²Po3/2
1672.06B
0.004B
9.94 × 106B

6d ²D5/2
10f ²Fo7/2
1677.17A,B
0.114A
2.70 × 108 A

0.104B
2.46 × 108 B

6d ²D5/2
10f ²Fo5/2
1677.42A,B
0.006A
1.35 × 107 A

0.005B
1.23 × 107 B

6d ²D3/2
11p ²Po1/2
1754.58B
0.004B
7.85 × 106 B

6d ²D5/2
11p ²Po3/2
1764.04B
0.006B
1.39 × 107 B

6d ²D3/2
10p ²Po3/2
1901.87A
0.002A
2.94 × 106A

1901.69B
0.001B
2.31 × 106 B

6d ²D3/2
10p ²Po1/2
1908.76A
0.008A
1.45 × 107 A

1908.57B
0.006B
1.14 × 107 B

6d ²D5/2
10p ²Po3/2
1917.68A
0.014A
2.57 × 107 A

1917.49B
0.011B
2.03 × 107 B

5f ²Fo5/2
10g ²G7/2
1926.41A
0.025A,B
4.50 × 107 A

1919.09B

4.53 × 107 B

5f ²Fo7/2
10g ²G7/2
1929.39A
0.001A,B
1.66 × 106 A

1922.05B

1.67 × 106 B

5f ²Fo7/2
10g ²G9/2
1922.05A
0.032A,B
5.85 × 107 A

1929.39B

5.80 × 107 B

5f ²Fo5/2
12d ²D3/2
1931.60B
0.003B
5.03 × 106 B

5f ²Fo7/2
12d ²D5/2
1933.92B
0.004B
7.16 × 106 B

7p ²Po1/2
12d ²D3/2
1961.07B
0.014B
2.38 × 107 B

7p ²Po3/2
12d ²D5/2
2008.77B
0.024B
3.99 × 107 B

7p ²Po3/2
12d ²D3/2
2009.50B
0.003B
4.43 × 106 B

5f ²Fo5/2
9g ²G7/2
2024.06A
0.044A,B
7.09 × 107 A

2009.57B

7.26 × 107 B

5f ²Fo7/2
9g ²G7/2
2027.35A
0.002A,B
2.61 × 106 A

2012.81B

2.67 × 106 B

5f ²Fo7/2
9g ²G9/2
2027.34A
0.056A
9.15 × 107 A

2012.81B
0.057B
9.36 × 107 B

5f ²Fo5/2
11d ²D3/2
2029.02B
0.004B
7.36 × 106 B

5f ²Fo7/2
11d ²D5/2
2031.29B
0.006B
1.05 × 107 B

7p ²Po1/2
11d ²D3/2
2061.56B
0.022B
3.47 × 107 B

7p ²Po3/2
11d ²D5/2
2114.03B
0.039B
5.80 × 107 B

7p ²Po3/2
11d ²D3/2
2115.16B
0.004B
6.43 × 106 B

5f ²Fo5/2
10d ²D5/2
2284.24A
0.001A,B
7.40 × 105 A

2182.60B

8.22 × 105 B

5f ²Fo5/2
10d ²D3/2
2286.23A
0.008A,B
1.03 × 107 A

2184.34B

1.15 × 107 B

5f ²Fo7/2
10d ²D5/2
2288.43A
0.012A,B
1.47 × 107 A

2186.43B

1.63 × 107 B

7p ²Po1/2
10d ²D3/2
2327.62A
0.034A
4.21 × 107 A

2222.09B
0.040B
5.41 × 107 B

7p ²Po3/2
10d ²D5/2
2393.98A
0.060A
7.01 × 107 A

2282.58B
0.070B
8.98 × 107 B

7p ²Po3/2
10d ²D3/2
2396.17A
0.007A
7.73 × 106 A

2284.49B
0.008B
9.95 × 106 B

7d ²D3/2
12f ²Fo5/2
2786.97B
0.045B
3.86 × 107 B

7d ²D5/2
12f ²Fo7/2
2802.54B
0.064B
5.42 × 107 B

7d ²D5/2
12f ²Fo5/2
2802.90B
0.003B
2.71 × 106 B

7d ²D3/2
11f ²Fo5/2
2925.08B
0.064B
4.98 × 107 B

7d ²D5/2
11f ²Fo7/2
2942.09B
0.091B
7.00 × 107 B

7d ²D5/2
11f ²Fo5/2
2942.64B
0.004B
3.50 × 106 B

7d ²D3/2
12p ²Po3/2
3116.57B
0.001B
4.10 × 105 B

7d ²D3/2
12p ²Po1/2
3125.35B
0.003B
2.03 × 106 B

7d ²D3/2
10f ²Fo5/2
3135.24A,B
0.103A
6.99 × 107 A

0.096B
6.53 × 107 B

7d ²D5/2
12p ²Po3/2
3136.51B
0.005B
3.62 × 106B

7d ²D5/2
10f ²Fo7/2
3154.57A
0.146A
9.78 × 107 A

3154.55B
0.137B
9.16 × 107 B

7d ²D5/2
10f ²Fo5/2
3155.45A
0.007A,B
4.89 × 106 A

3155.42B

4.58 × 106 B

6f ²Fo5/2
10g ²G7/2
3392.75A
0.098A
5.70 × 107 A

3370.11B
0.099B
5.82 × 107 B

6f ²Fo7/2
10g ²G7/2
3398.40A
0.004A,B
2.10 × 106 A

3375.69B

2.14 × 106 B

6f ²Fo7/2
10g ²G9/2
3398.41A
0.127A
7.35 × 107 A

3375.69B
0.128B
7.50 × 107 B

6f ²Fo5/2
12d ²D5/2
3406.76B
0.001B
4.58 × 105 B

6f ²Fo5/2
12d ²D3/2
3408.88B
0.011B
6.40 × 106 B

6f ²Fo7/2
12d ²D5/2
3412.46B
0.016B
9.11 × 106 B

7d ²D3/2
11p ²Po3/2
3452.08B
0.001B
5.78 × 105 B

7d ²D3/2
11p ²Po1/2
3467.38B
0.005B
2.85 × 106 B

7d ²D5/2
11p ²Po3/2
3476.57B
0.009B
5.09 × 106 B

8p ²Po1/2
12d ²D3/2
3493.71B
0.028B
1.54 × 107 B

8p ²Po3/2
12d ²D5/2
3569.21B
0.050B
2.60 × 107 B

8p ²Po3/2
12d ²D3/2
3571.54B
0.005B
2.88 × 106 B

6f ²Fo5/2
9g ²G7/2
3707.80A
0.181A
8.76 × 107 A

3659.44B
0.183B
9.13 × 107 B

6f ²Fo7/2
9g ²G7/2
3714.55A
0.007A,B
3.23 × 106 A

3666.01B

3.36 × 106 B

6f ²Fo7/2
9g ²G9/2
3714.49A
0.234A
1.13 × 108 A

3666.01B
0.237B
1.18 × 108 B

6f ²Fo5/2
11d ²D5/2
3720.97B
0.001B
6.83 × 105 B

6f ²Fo5/2
11d ²D3/2
3724.47B
0.020B
9.54 × 106 B

6f ²Fo7/2
11d ²D5/2
3727.77B
0.028B
1.36 × 107 B

8p ²Po1/2
11d ²D3/2
3825.97B
0.050B
2.30 × 107 B

8p ²Po3/2
11d ²D5/2
3915.63B
0.089B
3.86 × 107 B

8p ²Po3/2
11d ²D3/2
3919.50B
0.010B
4.28 × 106 B

7d ²D3/2
10p ²Po3/2
4093.95A
0.003A
1.05 × 106 A

4093.09B
0.002B
8.64 × 105 B

7d ²D3/2
10p ²Po1/2
4126.00A
0.013A
5.11 × 106 A

4125.12B
0.011B
4.22 × 106 B

7d ²D5/2
10p ²Po3/2
4128.47A
0.023A
9.13 × 106 A

4127.55B
0.019B
7.59 × 106 B

6f ²Fo5/2
10d ²D5/2
4685.40A
0.003A,B
8.22 × 105 A

4276.87B

1.10 × 106 B

6f ²Fo5/2
10d ²D3/2
4693.78A
0.038A
1.14 × 107 A

4283.55B
0.042B
1.54 × 107 B

6f ²Fo7/2
10d ²D5/2
4696.17A
0.054A
1.63 × 107 A

4285.85B
0.060B
2.19 × 107 B

8p ²Po1/2
10d ²D3/2
4856.14A
0.091A
2.57 × 107 A

4418.37B
0.110B
3.74 × 107 B

8p ²Po3/2
10d ²D5/2
4998.26A
0.160A
4.26 × 107 A

4536.05B
0.192B
6.22 × 107 B

8p ²Po3/2
10d ²D3/2
5007.81A
0.018A
4.69 × 106 A

4543.57B
0.021B
6.88 × 106 B

8d ²D3/2
12f ²Fo5/2
4613.96B
0.058B
1.82 × 107 B

8d ²D5/2
12f ²Fo7/2
4637.33B
0.083B
2.57 × 107 B

8d ²D5/2
12f ²Fo5/2
4638.30B
0.004B
1.28 × 106 B

8d ²D3/2
11f ²Fo5/2
5005.22B
0.086B
2.30 × 107 B

8d ²D5/2
11f ²Fo7/2
5032.28B
0.123B
3.23 × 107 B

8d ²D5/2
11f ²Fo5/2
5033.88B
0.006B
1.61 × 106 B

6g ²G9/2
12f ²Fo7/2
5136.94B
0.001B
1.75 × 105 B

6g ²G7/2
12f ²Fo5/2
5137.90B
0.001B
1.35 × 105 B

8d ²D3/2
12p ²Po3/2
5593.28B
0.001B
1.96 × 105 B

8d ²D3/2
12p ²Po1/2
5621.62B
0.005B
9.65 × 105 B

6g ²G9/2
11f ²Fo7/2
5626.07B
0.001B
2.71 × 105 B

6g ²G7/2
11f ²Fo5/2
5627.78B
0.001B
2.09 × 105 B

8d ²D5/2
12p ²Po3/2
5629.09B
0.008B
1.73 × 106 B

8d ²D3/2
10f ²Fo5/2
5653.76A
0.144A
3.02 × 107 A

5653.69B
0.138B
2.87 × 107 B

8d ²D5/2
10f ²Fo7/2
5687.53A
0.203A
4.23 × 107 A

5687.46B
0.196B
4.03 × 107 B

8d ²D5/2
10f ²Fo5/2
5690.36A
0.010A,B
2.11 × 106 A

5690.29B

2.01 × 106 B

7f ²Fo5/2
10g ²G7/2
5773.05A
0.247A
4.95 × 107 A

5707.79B
0.250B
5.13 × 107 B

7f ²Fo7/2
10g ²G7/2
5784.03A
0.009A,B
1.82 × 106 A

5718.53B

1.89 × 106 B

7f ²Fo7/2
10g ²G9/2
5784.05A
0.320A
6.38 × 107 A

5718.53B
0.324B
6.61 × 107 B

7f ²Fo5/2
12d ²D5/2
5813.72B
0.002B
4.69 × 105 B

7f ²Fo5/2
12d ²D3/2
5819.89B
0.033B
6.55 × 106 B

7f ²Fo7/2
12d ²D5/2
5824.86B
0.047B
9.33 × 106 B

9p ²Po1/2
12d ²D3/2
5996.59B
0.061B
1.12 × 107 B

9p ²Po3/2
12d ²D5/2
6131.85B
0.107B
1.89 × 107 B

9p ²Po3/2
12d ²D3/2
6138.72B
0.012B
2.10 × 106 B

6g ²G9/2
10f ²Fo7/2
6457.77A
0.003A,B
4.51 × 105 A

6457.76B

4.59 × 105 B

6g ²G7/2
10f ²Fo5/2
6461.09A
0.002A,B
3.48 × 105 A

6461.03B

3.53 × 105 B

7f ²Fo5/2
9g ²G7/2
6748.79A
0.512A
7.50 × 107 A

6590.26B
0.525B
8.07 × 107 B

7f ²Fo7/2
9g ²G7/2
6763.80A
0.019A,B
2.76 × 106 A

6604.58B

2.97 × 106 B

7f ²Fo7/2
9g ²G9/2
6763.63A
0.663A
9.66 × 107 A

6604.58B
0.679B
1.04 × 108 B

8d ²D3/2
11p ²Po3/2
6775.04B
0.002B
2.86 × 105 B

7f ²Fo5/2
11d ²D5/2
6792.55B
0.005B
7.23 × 105 B

7f ²Fo5/2
11d ²D3/2
6804.23B
0.070B
1.01 × 107 B

7f ²Fo7/2
11d ²D5/2
6807.77B
0.100B
1.44 × 107 B

8d ²D5/2
11p ²Po3/2
6827.66B
0.017B
2.52 × 106 B

8d ²D3/2
11p ²Po1/2
6834.22B
0.010B
1.39 × 106 B

9p ²Po1/2
11d ²D3/2
7046.99B
0.130B
1.75 × 107 B

9p ²Po3/2
11d ²D5/2
7230.87B
0.228B
2.91 × 107 B

9p ²Po3/2
11d ²D3/2
7244.09B
0.025B
3.21 × 106 B

9d ²D3/2
12f ²Fo5/2
7457.70B
0.079B
9.47 × 106 B

9d ²D5/2
12f ²Fo7/2
7494.42B
0.112B
1.33 × 107 B

9d ²D5/2
12f ²Fo5/2
7496.98B
0.006B
6.66 × 105 B

7g ²G9/2
12f ²Fo7/2
8263.95B
0.003B
2.86 × 105 B

7g ²G7/2
12f ²Fo5/2
8266.14B
0.002B
2.21 × 105 B

9d ²D3/2
11f ²Fo5/2
8536.25B
0.124B
1.14 × 107 B

9d ²D5/2
11f ²Fo7/2
8583.10B
0.176B
1.60 × 107 B

9d ²D5/2
11f ²Fo5/2
8587.74B
0.009B
7.97 × 105 B

Electron correlation effects and relativistic effects play an important role in the spectra of heavy elements. To accurately predict the radiative atomic properties for heavy atoms such as La III, complex configuration interactions and relativistic effects must be considered simultaneously. Although Cowan’s approach is based on Schrödinger’s equation, it includes the most important relativistic effects like mass-velocity corrections and Darwin contributions. Also, for complex atoms, it is important to allow for spin-orbit interaction, which represents the magnetic interaction energy between electron’s spin magnetic moment and the magnetic field that the electron sees due to its orbital motion through the electric field of the nucleus. These contributions are considered as perturbations. Thus, to solve the Schrödinger equation with this Hamiltonian, we define a new angular momentum operator in an intermediate coupling scheme.

In calculations, the eigenvalues of Hamiltonian were optimized to the observed energy levels via a least-squares fitting procedure using experimentally determined energy levels, specifically all of the levels from the NIST compilation [28]. The scaling factors of the Slater parameters ( and ) and of configuration interaction integrals (), not optimized in the least-squares fitting, were chosen equal to 0.85, while the spin-orbit parameters were left at their initial values. This low value of the scaling factors has been suggested by Cowan for neutral heavy elements [15, 16].

We obtained 7785 and 4278 possible transitions between odd- and even-parity levels in the calculations A and B, respectively. The results obtained are in excellent agreement with those of other works except some transitions. For some transitions, although the agreement is less in the weighted oscillator strengths and the weighted transition probabilities, it is very good in the wavelengths. Most of results related to low-lying levels obtained from this work are in agreement with literature [1–6]. The differences between our HFR results and other works for and have been found in the 0–10% range for the transitions np ()–ns (), nd (), in the 0.5–9% range for the transitions nd ()–nf (), np (), and in the 1.5–20% range for the transitions nf ()–nd (), ng (). But the agreement is less in the weighted oscillator strengths and the weighted transition probabilities for 5d and 4f transitions. In fact, except the transitions 6p ²3/2–9d ²D3/2, 5d ²D3/2–9p ²1/2, 4f ²7/2–5g ²G7/2, 4f ²7/2–6g ²G7/2, and 4f ²5/2–8g ²G7/2,9/2, we found the values 1.064 (in calculation A) and 1.078 (in calculation B) for the mean ratio (this work)/ [1]. Except the transitions 5d–9p, 4f–7g, 8g, 8s–9p, and 4f–6d, we found also the values 1.084 (in calculation A) and 1.126 (in calculation B) for the mean ratio (this work)/ [1]. The transition results obtained from the calculation A agree with other works. This calculation includes core correlation (including excitation from 5p shell in core). These results obtained from HFR calculations may be better in case that the increasing number of configurations including the excitations from core. It is noted that there are no exist the works, especially experimental, on La III recently in available literature. A detailed comparison needs new experimental works. Most of our results are excellent in agreement, expect the transition results to 4f and 5d levels (for and results), generally. It is well known that these levels interact strongly with core.

In conclusion, the main purpose of this paper was to perform HFR calculations for obtaining the description of La III spectrum. Accurate atomic structure data is an essential ingredient for a wide range of research fields. Areas from plasma research applications in nuclear fusion to lighting research, as well as astrophysics and cosmology, depend on such data. In spectrum synthesis works, particularly for CP stars, accurate data for transition probabilities (rates) and oscillator strengths for lanthanide atoms are needed to establish reliable abundances for these species. The agreement is excellent, especially for wavelengths, when our HFR results are compared with other available works in literature for the radiative transitions for La III. So, we may mention that new results presented in Table 2 for the transitions between some highly levels in this work are also reliable. There are a few experimental or theoretical radiative transition data for La III in literature. Consequently, we hope that our results, especially the new results in Table 2, which are obtained using the HFR method will be useful for research fields, technological applications, and other works in the future for La III spectra.

Acknowledgment

The authors are very grateful to the anonymous reviewer for stimulating comments and valuable suggestions, which resulted in improvements to this paper.

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