# Transition Parameters for Doubly Ionized Lanthanum

Authors: Betül Karaçoban; Leyla Özdemir
Journal: Journal of Atomic, Molecular, and Optical Physics
 (2012)

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## Abstract

The transition parameters such as the wavelengths, weighted oscillator strengths, and transition probabilities (or rates) for the nd(n=5−9)−nf(n=4−8), nd (n=5−9)−np(n=6−9), np (n=6−9)−ns(n=6−10), and ng (n=5−8)−nf(n=4−8) electric dipole (E1) transitions of doubly ionized lanthanum (La III, Z=57) 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.


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## Body

## 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 (E1) in La III (Z=57). 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 (n=5–10), 5p6ns (n=6–10), 5p56s6p, 5p56s4f, 5p55d6p, 5p6nf (n=4–10), 5p6np (n=6–10), 5p54f2, and 5p56p2 configurations outside the core [Cd], and nd, ng (n=5–25), ns (n=6–24), nf (n=4–22), and np (n=6–25) 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 (n=5–25), ns (n=6–24), nf (n=4–22), and np (n=6–25) 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 momentumk and parity π=(-1)k then, the transition is an electric multipole transition (Ek). However, if the photon has parity π=(-1)k+1 the transition is a magnetic multipole transition (Mk).According to HFR method [16], the total transition probability from a state γ'J'M' to all states M levels of γJ is given by
(1)A=64π4e2a02σ33hS∑Mq(J1J'-MqM')2=64π4e2a02σ33h(2J'+1)S,
and absorption oscillator strength is given by
(2)fij=8π2mca02σ3h(2J+1)S=(Ej-Ei)3(2J+1)S,
where, σ=[(Ej-Ei)/hc] has units of kaysers (cm−1) and S=|〈γJ∥P(1)∥γ'J'〉|2 is the electric dipole line strength in atomic units of e2a02. The strongest transition rate (or probability) is electric dipole (E1) radiation. For this reason, the E1 transitions are understood as being “allowed”, whereas high-order transitions are understood as being “forbidden”.In HFR method, for anN electron atom of nuclear charge Z0, the Hamiltonian is expanded as
(3)H=-∑i∇i2-∑i2Z0ri+∑i>j2rij+∑iζi(ri)li·si,
in atomic units, with ri the distance of the ith electron from the nucleus and rij=|ri-rj|. ζi(R)=(α2/2)(1/r)(∂V/∂r) is the spin-orbit term, with α being the fine structure constant and V 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 (Eav) 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 Fk and Gk and spin-orbit integrals ζnl. After radial functions have been obtained based on Hartree-Fock model, the wave function |γJM〉 of the M sublevel of a level labeled γJ is expressed in terms of LS basis states |αLSJM〉 by the formula
(4)|γJM〉=∑αLS|αLSJM〉〈αLSJ∣γJ〉.If determinant wave functions are used for the atom, the total binding energy is given by(5)E=∑i(Eki+Eni+∑j<iEij),
where Eki is the kinetic energy, Eni is the electron-nuclear Coulomb energy, and Eij is the Coulomb interaction energy between electrons i and j  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(7.57), (7.58), and (7.59) in [16].


## 3. Results and Discussion

We calculated the radiative parameters (wavelengths, oscillator strengths, and transition probabilities) for electric dipole (E1) transitions in La III (Z=57) using HFR code [15]. We have taken into account 5p6nd, 5p6ng (n=5–10), 5p6ns (n=6–10), 5p56s6p, 5p56s4f, 5p55d6p, 5p6nf (n=4–10), 5p6np (n=6–10), 5p54f2, and 5p56p2 configurations outside the core [Cd] for calculation A, and nd, ng (n=5–25), ns (n=6–24), nf (n=4–22), and np (n=6–25) configurations outside the core [Xe] for calculation B. Table 1 shows the wavelengths, λ (in Å); the weighted oscillator strengths, gf; the weighted transition rates (or probabilities), gAki (in s-1), for nd (n=5–9)–nf (n=4–8), nd (n=5–9)–np (n=6–9), np (n=6–9)–ns (n=6–10), and ng (n=5–8)–nf (n=4–8) electric dipole (E1) 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 “o”.Table 1
Wavelengthsλ(Å), weighted oscillator strengths gf, and weighted transition probabilities gAki(s−1) for electric dipole (E1) transitions in La III.
Transition
λ
g
f
gA
ki
Lower level
Upper level
This work
Other works
This work
Other works
This work
Other works
6p2Po1/2
7s2S1/2
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
6p2Po3/2
7s2S1/2
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
6p2Po1/2
6d2D3/2
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
6p2Po3/2
6d2D5/2
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
6p2Po3/2
6d2D3/2
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
6p2Po1/2
8s2S1/2
1466.39A,B
1466.39a
0.071A
0.069a
2.20 × 108 A
2.15 × 108 a
0.064B
2.00 × 108 B
6p2Po3/2
8s2S1/2
1536.13A,B
1536.13a
0.136A
0.132a
3.83 × 108 A
3.73 × 108 a
0.123B
3.48 × 108 B
6p2Po1/2
7d2D3/2
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
6p2Po3/2
7d2D5/2
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
6p2Po3/2
7d2D3/2
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
6p2Po1/2
9s2S1/2
1212.28A,B
1212.28a
0.026A
0.026a
1.19 × 108 A
1.16 × 108 a
0.023B
1.06 × 108 B
6p2Po3/2
9s2S1/2
1259.55A,B
1259.55a
0.051A
0.049a
2.13 × 108 A
2.07 × 108 a
0.045B
1.89 × 108 B
6p2Po1/2
8d2D3/2
1208.79A,B
1208.79a
0.040A
0.041a
1.80 × 108 A
1.86 × 108 a
0.065B
2.95 × 108 B
6p2Po3/2
8d2D5/2
1254.00A,B
1254.00a
0.070A
0.071a
2.98 × 108 A
3.00 × 108 a
0.112B
4.76 × 108 B
6p2Po3/2
8d2D3/2
1255.79A,B
1255.79a
0.008A
0.008a
3.27 × 107 A
3.32 × 107 a
0.012B
5.27 × 107 B
6p2Po1/2
10s2S1/2
1101.01A,B
1101.01a
0.013A
0.013a
7.26 × 107 A
7.07 × 107 a
0.012B
6.39 × 107 B
6p2Po3/2
10s2S1/2
1139.87A,B
1139.87a
0.026A
0.025a
1.31 × 108 A
1.27 × 108 a
0.022B
1.15 × 108 B
6p2Po1/2
9d2D3/2
1099.00A,B
1099.00a
0.015A
0.017a
8.54 × 107 A
9.21 × 107 a
0.029B
16.10 × 107 B
6p2Po3/2
9d2D5/2
1136.80A,B
1136.80a
0.028A
0.029a
1.44 × 108 A
1.50 × 108 a
0.050B
2.61 × 108 B
6p2Po3/2
9d2D3/2
1137.71A,B
1137.71a
0.003A
0.003a
1.58 × 107 A
1.66 × 107 a
0.006B
2.89 × 107 B
6d2D3/2
5f2Fo5/2
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
6d2D5/2
5f2Fo7/2
10287.59A,B
10284.790c
3.515A
—
2.21 × 108 A
—
3.548B
2.24 × 108 B
6d2D5/2
5f2Fo5/2
10373.15A
10370.335c
0.174A
—
1.08 × 107 A
—
10373.12B
0.176B
1.09 × 107 B
6d2D3/2
7p2Po3/2
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
6d2D5/2
7p2Po3/2
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
6d2D3/2
7p2P 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
6d2D3/2
6f2Fo5/2
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
6d2D5/2
6f2Fo7/2
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
6d2D5/2
6f2Fo5/2
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
6d2D3/2
8p2Po3/2
2954.63A
2953.77a
0.009A
0.008a
6.82 × 106 A
5.87 × 106 a
2954.64B
0.008B
6.18 × 106 B
6d2D5/2
8p2Po3/2
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
6d2D3/2
8p2Po1/2
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
6d2D3/2
7f2Fo5/2
2239.04A
2238.35a
0.339A
0.358a
4.51 × 108 A
4.76 × 108 a
2239.05B
0.356B
4.74 × 108 B
6d2D5/2
7f2Fo7/2
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
6d2D5/2
7f2Fo5/2
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
6d2D3/2
9p2Po3/2
2195.18A
2194.50a
0.003A,B
0.002a
4.15 × 106 A
3.28 × 106 a
2195.19B
3.58 × 106B
6d2D3/2
9p2Po1/2
2213.95A,B
2213.26a
0.015A
0.012a
2.02 × 107 A
1.60 × 107 a
0.013B
1.75 × 107 B
6d2D5/2
9p2Po3/2
2216.28A,B
2215.58a
0.027A
0.021a
3.62 × 107 A
2.87 × 107 a
0.023B
3.13 × 107 B
6d2D3/2
8f2Fo5/2
1923.33A
1923.33a
0.178A
0.185a
3.22 × 108 A
3.33 × 108 a
1923.34B
0.188B
3.39 × 108 B
6d2D5/2
8f2Fo7/2
1938.53A,B
1938.53a
0.253A
0.262a
4.49 × 108 A
4.65 × 108 a
0.267B
4.73 × 108 B
6d2D5/2
8f2Fo5/2
1939.51A,B
1939.51a
0.013A,B
0.013a
2.24 × 107 A
2.32 × 107 a
2.36 × 107 B
6f2Fo5/2
6g2G7/2
8290.18A
8287.76a
8.903A
8.527a
8.64 × 108 A,B
8.28 × 108 a
8290.16B
8287.752c
8.904B
6f2Fo7/2
6g2G9/2
8323.43A
8321.16a
11.495A
11.009a
1.11 × 109 A,B
1.06 × 109 a
8323.34B
8321.107c
11.496B
6f2Fo7/2
6g2G7/2
8323.98A
8321.63a
0.328A,B
0.315a
3.16 × 107 A,B
3.03 × 107 a
8323.97B
6f2Fo5/2
7g2G7/2
5147.17A,B
5145.72a
1.282A
1.239a
3.23 × 108 A,B
3.12 × 108 a
5145.729c
1.283B
6f2Fo7/2
7g2G9/2
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
6f2Fo7/2
7g2G7/2
5160.18A
5158.76a
0.047A,B
0.046a
1.19 × 107 A,B
1.15 × 107 a
5160.19B
6f2Fo5/2
8g2G7/2
4130.43A,B
4129.24a
0.411A,B
0.394a
1.61 × 108 A,B
1.54 × 108 a
6f2Fo7/2
8g2G9/2
4138.59A
4137.43a
0.531A
0.509a
2.07 × 108 A,B
1.98 × 108 a
4138.58B
4137.428c
0.532B
6f2Fo7/2
8g2G7/2
4138.80A
4137.64a
0.015A,B
0.015a
5.91 × 106 A,B
5.67 × 106 a
4138.81B
6f2Fo5/2
9d2D3/2
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
6f2F°5/2
9d2D5/2
5498.45A
5496.88a
0.009A,B
0.009a
2.08 × 106 A
2.06 × 106 a
5498.43B
2.02 × 106B
6f2Fo7/2
9d2D5/2
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
6s2S1/2
6p2Po3/2
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
6s2S1/2
6p2Po1/2
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
6s2S1/2
7p2Po3/2
1236.55A,B
1236.55a
0.002A
0.006a
0.70 × 107 A
2.39 × 107 a
0.001B
0.27 × 107 B
6s2S1/2
7p2Po1/2
1255.63A,B
1255.63a
0.001A
0.003a
0.33 × 107 A
1.14 × 107 a
0.0003B
0.13 × 107 B
7s2S1/2
7p2Po3/2
8254.85A
8252.53a
2.418A
2.279a
2.37 × 108 A,B
2.23 × 108 a
8254.77B
8252.603c
2.424B
7s2S1/2
7p2Po1/2
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
7s2S1/2
8p2Po3/2
2951.72A,B
2950.843c
0.002A,B
—
1.81 × 106 A
—
1.54 × 106B
7s2S1/2
8p2Po1/2
3007.07A
3006.186c
0.001A,B
—
8.57 × 105 A
—
3007.08B
7.27 × 105 B
7p2Po1/2
8s2S1/2
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
7p2Po3/2
8s2S1/2
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
7p2Po1/2
7d2D3/2
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
7p2Po3/2
7d2D5/2
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
7p2Po3/2
7d2D3/2
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
7p2Po1/2
9s2S1/2
3197.77A
3196.85a
0.089A,B
0.092a
5.77 × 107 A,B
5.98 × 107 a
3197.78B
3196.844c
7p2Po3/2
9s2S1/2
3328.60A
3327.64a
0.170A,B
0.176a
1.02 × 108 A,B
1.06 × 108 a
3328.61B
3327.655c
7p2Po1/2
8d2D3/2
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
7p2Po3/2
8d2D5/2
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
7p2Po3/2
8d2D3/2
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
7p2Po1/2
10s2S1/2
2524.74A,B
2523.98a
0.031A,B
0.033a
3.25 × 107 A
3.44 × 107 a
3.27 × 107 B
7p2Po3/2
10s2S1/2
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
7p2Po1/2
9d2D3/2
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
7p2Po3/2
9d2D5/2
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
7p2Po3/2
9d2D3/2
2594.36A,B
2593.58a
0.016A
0.015a
1.59 × 107 A
1.47 × 107 a
0.017B
1.69 × 107 B
7d2D3/2
7f2Fo5/2
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
7d2D5/2
7f2Fo7/2
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
7d2D5/2
7f2Fo5/2
6133.39A
6131.67a
0.037A
0.043a
6.51 × 106 A
7.55 × 106 a
6133.35B
0.041B
7.24 × 106B
7d2D3/2
8f2Fo5/2
4194.71A
4193.51a
0.260A
0.292a
0.99 × 108 A
1.11 × 108 a
4194.72B
0.283B
1.07 × 108 B
7d2D5/2
8f2Fo7/2
4226.33A
4225.12a
0.370A
0.414a
1.38 × 108 A
1.54 × 108 a
4226.29B
0.402B
1.50 × 108 B
7d2D5/2
8f2Fo5/2
4230.95A
4229.73a
0.018A
0.021a
6.89 × 106 A
7.70 × 106 a
4230.92B
0.020B
7.47 × 106B
7d2D3/2
9p2Po3/2
5746.85A
5745.26a
0.008A
0.007a
1.67 × 106 A
1.49 × 106 a
5746.90B
0.007B
1.48 × 106B
7d2D5/2
9p2Po3/2
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
7d2D3/2
9p2Po1/2
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
7f2Fo5/2
8g2G7/2
8293.36A
8291.04a
1.513A,B
1.485a
1.47 × 108 A,B
1.44 × 108 a
8293.35B
7f2Fo7/2
8g2G9/2
8315.16A
8312.96a
1.956A,B
1.919a
1.89 × 108 A,B
1.85 × 108 a
8315.11B
7f2Fo7/2
8g2G7/2
8316.03A
8313.81a
0.056A,B
0.055a
5.39 × 106 A,B
5.29 × 106 a
8316.04B
5f2Fo5/2
7d2D5/2
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
5f2Fo5/2
7d2D3/2
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
5f2Fo7/2
7d2D5/2
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
5f2Fo5/2
5g2G7/2
4484.21A
4482.98a
8.886A
8.277a
2.95 × 109 A,B
2.75 × 109 a
4484.25B
4482.967c
8.889B
5f2Fo7/2
5g2G9/2
4500.32A
4499.06a
11.478A
10.692a
3.78 × 109 A,B
3.52 × 109 a
4500.34B
4499.050c
11.482B
5f2Fo7/2
5g2G7/2
4500.39A
4499.15a
0.328A,B
0.306a
1.08 × 108 A,B
1.01 × 108 a
4500.43B
5f2Fo5/2
8d2D5/2
3086.28A
3085.38a
0.004A,B
0.005a
2.98 × 106 A
3.13 × 106 a
3086.29B
3085.379c
2.80 × 106B
5f2Fo5/2
8d2D3/2
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
5f2Fo7/2
8d2D5/2
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
5f2Fo5/2
6g2G7/2
2898.73A
2897.88a
0.866A,B
0.786a
6.87 × 108 A,B
6.24 × 108 a
2898.74B
2897.875c
5f2Fo7/2
6g2G9/2
2905.42A
2904.57a
1.120A,B
1.016a
8.85 × 108 A,B
8.03 × 108 a
2905.41B
2904.576c
5f2Fo7/2
6g2G7/2
2905.49A,B
2904.63a
0.032A,B
0.029a
2.53 × 107 A,B
2.29 × 107 a
5f2Fo5/2
9d2D5/2
2461.70A,B
2460.95a
0.001A,B
0.002a
1.51 × 106 A
1.67 × 106 a
1.41 × 106B
5f2F o5/2
9d2D3/2
2465.97A,B
2465.22a
0.019A
0.021a
2.11 × 107 A
2.33 × 107 a
0.018B
1.96 × 107 B
5f2F o7/2
9d2D5/2
2466.59A
2465.82a
0.027A
0.030a
3.01 × 107 A
3.33 × 107 a
2535.57B
0.025B
2.80 × 107 B
5f2Fo5/2
7g2G7/2
2388.71A
2387.99a
0.226A,B
0.196a
2.64 × 108 A,B
2.29 × 108 a
2388.72B
2387.988c
5f2Fo7/2
7g2G9/2
2393.23A
2392.49a
0.292A,B
0.254a
3.41 × 108 A,B
2.96 × 108 a
2393.22B
2392.492c
5f2Fo7/2
7g2G7/2
2393.30A,B
2392.57a
0.008A,B
0.007a
9.73 × 106 A,B
8.45 × 106 a
5f2Fo5/2
8g2G7/2
2143.81A,B
2143.13a
0.089A,B
0.074a
1.29 × 108 A,B
1.08 × 108 a
5f2F o7/2
8g2G9/2
2147.44A,B
2146.77a
0.115A,B
0.096a
1.67 × 108 A,B
1.39 × 108 a
5f2Fo7/2
8g2G7/2
2147.50A,B
2146.83a
0.003A,B
0.003a
4.77 × 106 A,B
3.98 × 106 a
5g2G9/2
7f2Fo7/2
8116.78A
8114.48a
0.018A,B
0.021a
1.79 × 106 A,B
2.11 × 106 a
8116.75B
8114.415c
5g2G7/2
7f2Fo5/2
8138.27A
8136.00a
0.014A,B
0.016a
1.37 × 106 A,B
1.62 × 106 a
8138.19B
8135.964c
5g2G9/2
8f2Fo7/2
5090.54A
5089.12a
0.003A,B
0.003a
6.83 × 105 A
7.82 × 105 a
5090.51B
6.86 × 105B
5g2G7/2
8f2Fo5/2
5097.17A
5095.70a
0.002A,B
0.002a
5.25 × 105 A
6.01 × 105 a
5097.11B
5.27 × 105B
5d2D3/2
4f2Fo5/2
13898.50A
13894.47f
0.072A
0.031d
2.51 × 106 A
—
13898.06B
0.074B
2.54 × 106B
5d2D5/2
4f2Fo7/2
14099.97A
14096.18f
0.102A
0.046d
3.44 × 106 A
—
14100.19B
0.104B
3.48 × 106B
5d2D5/2
4f2Fo5/2
17882.04A
17878.09f
0.004A,B
0.002d
8.41 × 104 A
—
17883.69B
8.52 × 104 B
5d2D5/2
6p2Po3/2
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
5d2D3/2
6p2Po3/2
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
5d2D3/2
6p2Po1/2
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
5d2D3/2
5f2Fo5/2
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
5d2D5/2
5f2Fo7/2
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
5d2D5/2
5f2Fo5/2
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
5d2D3/2
7p2Po3/2
1058.63A,B
1058.63a
0.013A,B
0.010a
7.84 × 107 A
5.72 × 107 a
8.02 × 107 B
5d2D3/2
7p2Po1/2
1072.59A,B
1072.59a
0.067A,B
0.048a
3.77 × 108 A
2.75 × 108 a
3.86 × 108 B
5d2D5/2
7p2Po3/2
1076.91A,B
1076.91a
0.116A
0.085a
6.70 × 108 A
4.89 × 108 a
0.119B
6.86 × 108 B
5d2D3/2
6f2Fo5/2
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
5d2D5/2
6f2Fo7/2
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
5d2D5/2
6f2Fo5/2
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
5d2D3/2
8p2Po3/2
860.39A,B
860.39a
0.005A,B
0.003a
4.24 × 107 A
2.76 × 107 a
4.36 × 107 B
5d2D3/2
8p2Po1/2
865.04A,B
865.04a
0.024A,B
0.015a
2.08 × 108 A
1.36 × 108 a
2.15 × 108 B
5d2D5/2
8p2Po3/2
872.43A,B
872.43a
0.043A,B
0.027a
3.65 × 108 A
2.38 × 108 a
3.77 × 108 B
5d2D3/2
7f2Fo5/2
787.14A,B
787.14a
0.303A
0.203a
3.24 × 109 A
2.18 × 109 a
0.305B
3.28 × 109 B
5d2D5/2
7f2Fo7/2
796.99A,B
796.99a
0.430A,B
0.286a
4.51 × 109 A,B
3.00 × 109 a
5d2D5/2
7f2F o5/2
797.20A,B
797.20a
0.021A,B
0.014a
2.26 × 108 A,B
1.50 × 108 a
5d2D3/2
9p2Po3/2
781.65A,B
781.65a
0.002A,B
0.001a
2.52 × 107 A
1.54 × 107 a
2.62 × 107 B
5d2D3/2
9p2Po1/2
784.01A,B
784.01a
0.012A,B
0.007a
12.50 × 107 A
7.61 × 107 a
13.01 × 107 B
5d2D5/2
9p2Po3/2
791.57A,B
791.57a
0.021A,B
0.013a
2.19 × 108 A
1.33 × 108 a
2.27 × 108 B
5d2D3/2
8f2Fo5/2
744.19A,B
744.19a
0.176A,B
0.110a
2.12 × 109 A,B
1.33 × 109 a
5d2D5/2
8f2Fo7/2
753.03A,B
753.03a
0.249A
0.155a
2.92 × 109 A,B
1.83 × 109 a
0.248B
5d2D5/2
8f2Fo5/2
753.18A,B
753.18a
0.012A,B
0.008a
1.46 × 108 A,B
9.14 × 107 a
4f2Fo5/2
6d2D5/2
1322.42A,B
1322.42a
0.000A,B
0.002a
0.12 × 106 A
7.00 × 106 a
0.17 × 106B
4f2Fo5/2
6d2D3/2
1330.04A,B
1330.04a
0.001A,B
0.026a
0.22 × 107 A
9.64 × 107 a
0.23 × 107 B
4f2Fo7/2
6d2D5/2
1349.18A,B
1349.18a
0.001A,B
0.036a
3.07 × 106 A
1.32 × 108 a
3.16 × 106B
4f2Fo5/2
5g2G7/2
929.72A,B
929.72a
0.058A
0.040a
4.49 × 108 A
3.06 × 108 a
0.060B
4.63 × 108 B
4f2Fo7/2
5g2G9/2
942.86A,B
942.86a
0.074A
0.051a
5.58 × 108 A
3.81 × 108 a
0.077B
5.76 × 108 B
4f2Fo7/2
5g2G7/2
942.87A,B
942.87a
0.002A,B
0.001a
1.60 × 107 A
1.09 × 107 a
1.65 × 107 B
4f2Fo5/2
6g2G7/2
835.02A,B
835.02a
0.046A
0.030a
4.44 × 108 A
2.87 × 108 a
0.048B
4.58 × 108 B
4f2Fo7/2
6g2G9/2
845.61A,B
845.61a
0.059A
0.038a
5.54 × 108 A
3.58 × 108 a
0.061B
5.72 × 108 B
4f2Fo7/2
6g2G7/2
845.62A,B
845.62a
0.002A,B
0.001a
1.59 × 107 A
1.02 × 107 a
1.63 × 107 B
4f2Fo5/2
7g2G7/2
786.64A,B
786.64a
0.033A
0.021a
3.56 × 108 A
2.23 × 108 a
0.034B
3.68 × 108 B
4f2Fo7/2
7g2G9/2
796.03A,B
796.03a
0.042A
0.026a
4.44 × 108 A
2.78 × 108 a
0.044B
4.60 × 108 B
4f2Fo5/2
8g2G7/2
758.12A,B
758.12a
0.023A
0.014a
2.73 × 108 A
1.67 × 108 a
0.024B
2.82 × 108 B
4f2Fo7/2
8g2G9/2
766.83A,B
766.83a
0.030A
0.018a
3.41 × 108 A
2.09 × 108 a
0.031B
3.54 × 108 B
8s2S1/2
9p2Po3/2
5641.62A,B
5640.03a
0.005A
0.003a
10.20 × 105 A
5.58 × 105 a
0.004B
9.34 × 105B
8s2S1/2
9p2Po1/2
5767.24A
5765.63a
0.002A,B
0.001a
4.76 × 105 A
2.61 × 105 a
5767.25B
4.37 × 105B
8p2Po1/2
8d2D3/2
10940.83A
10937.898c
3.508A
—
1.95 × 108 A
—
10940.86B
3.439B
1.92 × 108 B
8p2Po1/2
9d2D3/2
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
8p2Po3/2
9d2D5/2
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
8p2Po3/2
9d2D3/2
5959.22A
5957.57a
0.065A
0.064a
1.22 × 107 A
1.21 × 107 a
5959.21B
0.067B
1.26 × 107 B
8p2Po1/2
10s2S1/2
5801.06A
5799.48a
0.112A
0.115a
2.23 × 107 A
2.27 × 107 a
5801.07B
0.113B
2.24 × 107 B
8p2Po3/2
10s2S1/2
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
Newλ(Å), gf, and gAki (s−1) for electric dipole (E1) transitions in La III.
Transition
λ
gf
gA
ki
Lower level
Upper level
5d2D3/2
12f2Fo5/2
682.99B
0.039B
5.62 × 108 B
5d2D5/2
12f2Fo7/2
690.53B
0.056B
7.77 × 108 B
5d2D5/2
12f2Fo5/2
690.55B
0.003B
3.89 × 107 B
5d2D3/2
11f2Fo5/2
690.98B
0.053B
7.46 × 108 B
5d2D5/2
11f2Fo7/2
698.69B
0.075B
1.03 × 109 B
5d2D5/2
11f2Fo5/2
698.72B
0.004B
5.15 × 107 B
5d2D3/2
12p2Po3/2
701.16B
0.001B
8.21 × 106 B
5d2D3/2
12p2Po1/2
701.60B
0.003B
4.10 × 107 B
5d2D3/2
10f2Fo5/2
702.10A,B
0.074A
1.00 × 109 A
0.075B
1.02 × 109 B
5d2D5/2
12p2Po3/2
709.13B
0.005B
7.14 × 107 B
5d2D5/2
10f2Fo7/2
710.05A,B
0.104A
1.38 × 109 A
0.106B
1.41 × 109 B
5d2D5/2
10f2Fo5/2
710.09A,B
0.005A,B
6.92 × 107 A
7.03 × 107 B
5d2D3/2
11p2Po3/2
716.83B
0.001B
1.15 × 107 B
5d2D3/2
11p2Po1/2
717.49B
0.004B
5.76 × 107 B
5d2D5/2
11p2Po3/2
725.17B
0.008B
1.00 × 108 B
4f2Fo5/2
10g2G7/2
729.02A
0.013A,B
1.57 × 108 A
727.97B
1.67 × 108 B
4f2Fo7/2
10g2G7/2
737.09A
0.001A,B
5.70 × 106A
736.01B
5.97 × 106 B
4f2Fo7/2
10g2G9/2
737.09A
0.016A
1.97 × 108 A
736.01B
0.017B
2.09 × 108 B
4f2Fo5/2
9g2G7/2
742.58A
0.017A
2.06 × 108 A
740.62B
0.018B
2.15 × 108 B
5d2D3/2
10p2Po3/2
740.94A
0.001A,B
1.60 × 107 A
740.93B
1.70 × 107 B
5d2D3/2
10p2Po1/2
742.00A
0.007A,B
7.99 × 107 A
741.97B
8.44 × 107 B
4f2Fo7/2
9g2G7/2
750.95A
0.001A,B
7.44 × 106 A
748.94B
7.72 × 106 B
4f2Fo7/2
9g2G9/2
750.95A
0.022A
2.58 × 108 A
748.94B
0.023B
2.70 × 108 B
5d2D5/2
10p2Po3/2
749.86A
0.012A,B
1.39 × 108 A
749.84B
1.47 × 108 B
6p2Po1/2
12d2D3/2
978.38B
0.006B
4.54 × 107 B
6p2Po1/2
11d2D3/2
1002.77B
0.010B
6.50 × 107 B
6p2Po3/2
12d2D5/2
1008.75B
0.011B
7.46 × 107 B
6p2Po3/2
12d2D3/2
1008.94B
0.001B
8.29 × 106 B
6p2Po3/2
11d2D5/2
1034.62B
0.017B
1.06 × 108 B
6p2Po3/2
11d2D3/2
1034.89B
0.002B
1.18 × 107 B
6p2Po1/2
10d2D3/2
1061.80A
0.008A
4.59 × 107 A
1039.29B
0.016B
9.83 × 107 B
6p2Po3/2
10d2D5/2
1097.43A
0.014A
7.83 × 107 A
1073.42B
0.028B
1.61 × 108 B
6p2Po3/2
10d2D3/2
1097.89A
0.002A
8.55 × 106A
1073.84B
0.003B
1.78 × 107 B
6d2D3/2
12f2Fo5/2
1561.65B
0.036B
9.96 × 107 B
6d2D5/2
12f2Fo7/2
1572.18B
0.052B
1.39 × 108 B
6d2D5/2
12f2Fo5/2
1572.29B
0.002B
6.97 × 106B
6d2D3/2
11f2Fo5/2
1604.09B
0.050B
1.31 × 108 B
6d2D5/2
11f2Fo7/2
1615.16B
0.072B
1.83 × 108 B
6d2D5/2
11f2Fo5/2
1615.32B
0.004B
9.15 × 106 B
6d2D3/2
12p2Po1/2
1662.51B
0.002B
5.62 × 106 B
6d2D3/2
10f2Fo5/2
1665.31A
0.080A
1.93 × 108 A
1665.37B
0.073B
1.76 × 108 B
6d2D5/2
12p2Po3/2
1672.06B
0.004B
9.94 × 106B
6d2D5/2
10f2Fo7/2
1677.17A,B
0.114A
2.70 × 108 A
0.104B
2.46 × 108 B
6d2D5/2
10f2Fo5/2
1677.42A,B
0.006A
1.35 × 107 A
0.005B
1.23 × 107 B
6d2D3/2
11p2Po1/2
1754.58B
0.004B
7.85 × 106 B
6d2D5/2
11p2Po3/2
1764.04B
0.006B
1.39 × 107 B
6d2D3/2
10p2Po3/2
1901.87A
0.002A
2.94 × 106A
1901.69B
0.001B
2.31 × 106 B
6d2D3/2
10p2Po1/2
1908.76A
0.008A
1.45 × 107 A
1908.57B
0.006B
1.14 × 107 B
6d2D5/2
10p2Po3/2
1917.68A
0.014A
2.57 × 107 A
1917.49B
0.011B
2.03 × 107 B
5f2Fo5/2
10g2G7/2
1926.41A
0.025A,B
4.50 × 107 A
1919.09B
4.53 × 107 B
5f2Fo7/2
10g2G7/2
1929.39A
0.001A,B
1.66 × 106 A
1922.05B
1.67 × 106 B
5f2Fo7/2
10g2G9/2
1922.05A
0.032A,B
5.85 × 107 A
1929.39B
5.80 × 107 B
5f2Fo5/2
12d2D3/2
1931.60B
0.003B
5.03 × 106 B
5f2Fo7/2
12d2D5/2
1933.92B
0.004B
7.16 × 106 B
7p2Po1/2
12d2D3/2
1961.07B
0.014B
2.38 × 107 B
7p2Po3/2
12d2D5/2
2008.77B
0.024B
3.99 × 107 B
7p2Po3/2
12d2D3/2
2009.50B
0.003B
4.43 × 106 B
5f2Fo5/2
9g2G7/2
2024.06A
0.044A,B
7.09 × 107 A
2009.57B
7.26 × 107 B
5f2Fo7/2
9g2G7/2
2027.35A
0.002A,B
2.61 × 106 A
2012.81B
2.67 × 106 B
5f2Fo7/2
9g2G9/2
2027.34A
0.056A
9.15 × 107 A
2012.81B
0.057B
9.36 × 107 B
5f2Fo5/2
11d2D3/2
2029.02B
0.004B
7.36 × 106 B
5f2Fo7/2
11d2D5/2
2031.29B
0.006B
1.05 × 107 B
7p2Po1/2
11d2D3/2
2061.56B
0.022B
3.47 × 107 B
7p2Po3/2
11d2D5/2
2114.03B
0.039B
5.80 × 107 B
7p2Po3/2
11d2D3/2
2115.16B
0.004B
6.43 × 106 B
5f2Fo5/2
10d2D5/2
2284.24A
0.001A,B
7.40 × 105 A
2182.60B
8.22 × 105 B
5f2Fo5/2
10d2D3/2
2286.23A
0.008A,B
1.03 × 107 A
2184.34B
1.15 × 107 B
5f2Fo7/2
10d2D5/2
2288.43A
0.012A,B
1.47 × 107 A
2186.43B
1.63 × 107 B
7p2Po1/2
10d2D3/2
2327.62A
0.034A
4.21 × 107 A
2222.09B
0.040B
5.41 × 107 B
7p2Po3/2
10d2D5/2
2393.98A
0.060A
7.01 × 107 A
2282.58B
0.070B
8.98 × 107 B
7p2Po3/2
10d2D3/2
2396.17A
0.007A
7.73 × 106 A
2284.49B
0.008B
9.95 × 106 B
7d2D3/2
12f2Fo5/2
2786.97B
0.045B
3.86 × 107 B
7d2D5/2
12f2Fo7/2
2802.54B
0.064B
5.42 × 107 B
7d2D5/2
12f2Fo5/2
2802.90B
0.003B
2.71 × 106 B
7d2D3/2
11f2Fo5/2
2925.08B
0.064B
4.98 × 107 B
7d2D5/2
11f2Fo7/2
2942.09B
0.091B
7.00 × 107 B
7d2D5/2
11f2Fo5/2
2942.64B
0.004B
3.50 × 106 B
7d2D3/2
12p2Po3/2
3116.57B
0.001B
4.10 × 105 B
7d2D3/2
12p2Po1/2
3125.35B
0.003B
2.03 × 106 B
7d2D3/2
10f2Fo5/2
3135.24A,B
0.103A
6.99 × 107 A
0.096B
6.53 × 107 B
7d2D5/2
12p2Po3/2
3136.51B
0.005B
3.62 × 106B
7d2D5/2
10f2Fo7/2
3154.57A
0.146A
9.78 × 107 A
3154.55B
0.137B
9.16 × 107 B
7d2D5/2
10f2Fo5/2
3155.45A
0.007A,B
4.89 × 106 A
3155.42B
4.58 × 106 B
6f2Fo5/2
10g2G7/2
3392.75A
0.098A
5.70 × 107 A
3370.11B
0.099B
5.82 × 107 B
6f2Fo7/2
10g2G7/2
3398.40A
0.004A,B
2.10 × 106 A
3375.69B
2.14 × 106 B
6f2Fo7/2
10g2G9/2
3398.41A
0.127A
7.35 × 107 A
3375.69B
0.128B
7.50 × 107 B
6f2Fo5/2
12d2D5/2
3406.76B
0.001B
4.58 × 105 B
6f2Fo5/2
12d2D3/2
3408.88B
0.011B
6.40 × 106 B
6f2Fo7/2
12d2D5/2
3412.46B
0.016B
9.11 × 106 B
7d2D3/2
11p2Po3/2
3452.08B
0.001B
5.78 × 105 B
7d2D3/2
11p2Po1/2
3467.38B
0.005B
2.85 × 106 B
7d2D5/2
11p2Po3/2
3476.57B
0.009B
5.09 × 106 B
8p2Po1/2
12d2D3/2
3493.71B
0.028B
1.54 × 107 B
8p2Po3/2
12d2D5/2
3569.21B
0.050B
2.60 × 107 B
8p2Po3/2
12d2D3/2
3571.54B
0.005B
2.88 × 106 B
6f2Fo5/2
9g2G7/2
3707.80A
0.181A
8.76 × 107 A
3659.44B
0.183B
9.13 × 107 B
6f2Fo7/2
9g2G7/2
3714.55A
0.007A,B
3.23 × 106 A
3666.01B
3.36 × 106 B
6f2Fo7/2
9g2G9/2
3714.49A
0.234A
1.13 × 108 A
3666.01B
0.237B
1.18 × 108 B
6f2Fo5/2
11d2D5/2
3720.97B
0.001B
6.83 × 105 B
6f2Fo5/2
11d2D3/2
3724.47B
0.020B
9.54 × 106 B
6f2Fo7/2
11d2D5/2
3727.77B
0.028B
1.36 × 107 B
8p2Po1/2
11d2D3/2
3825.97B
0.050B
2.30 × 107 B
8p2Po3/2
11d2D5/2
3915.63B
0.089B
3.86 × 107 B
8p2Po3/2
11d2D3/2
3919.50B
0.010B
4.28 × 106 B
7d2D3/2
10p2Po3/2
4093.95A
0.003A
1.05 × 106 A
4093.09B
0.002B
8.64 × 105 B
7d2D3/2
10p2Po1/2
4126.00A
0.013A
5.11 × 106 A
4125.12B
0.011B
4.22 × 106 B
7d2D5/2
10p2Po3/2
4128.47A
0.023A
9.13 × 106 A
4127.55B
0.019B
7.59 × 106 B
6f2Fo5/2
10d2D5/2
4685.40A
0.003A,B
8.22 × 105 A
4276.87B
1.10 × 106 B
6f2Fo5/2
10d2D3/2
4693.78A
0.038A
1.14 × 107 A
4283.55B
0.042B
1.54 × 107 B
6f2Fo7/2
10d2D5/2
4696.17A
0.054A
1.63 × 107 A
4285.85B
0.060B
2.19 × 107 B
8p2Po1/2
10d2D3/2
4856.14A
0.091A
2.57 × 107 A
4418.37B
0.110B
3.74 × 107 B
8p2Po3/2
10d2D5/2
4998.26A
0.160A
4.26 × 107 A
4536.05B
0.192B
6.22 × 107 B
8p2Po3/2
10d2D3/2
5007.81A
0.018A
4.69 × 106 A
4543.57B
0.021B
6.88 × 106 B
8d2D3/2
12f2Fo5/2
4613.96B
0.058B
1.82 × 107 B
8d2D5/2
12f2Fo7/2
4637.33B
0.083B
2.57 × 107 B
8d2D5/2
12f2Fo5/2
4638.30B
0.004B
1.28 × 106 B
8d2D3/2
11f2Fo5/2
5005.22B
0.086B
2.30 × 107 B
8d2D5/2
11f2Fo7/2
5032.28B
0.123B
3.23 × 107 B
8d2D5/2
11f2Fo5/2
5033.88B
0.006B
1.61 × 106 B
6g2G9/2
12f2Fo7/2
5136.94B
0.001B
1.75 × 105 B
6g2G7/2
12f2Fo5/2
5137.90B
0.001B
1.35 × 105 B
8d2D3/2
12p2Po3/2
5593.28B
0.001B
1.96 × 105 B
8d2D3/2
12p2Po1/2
5621.62B
0.005B
9.65 × 105 B
6g2G9/2
11f2Fo7/2
5626.07B
0.001B
2.71 × 105 B
6g2G7/2
11f2Fo5/2
5627.78B
0.001B
2.09 × 105 B
8d2D5/2
12p2Po3/2
5629.09B
0.008B
1.73 × 106 B
8d2D3/2
10f2Fo5/2
5653.76A
0.144A
3.02 × 107 A
5653.69B
0.138B
2.87 × 107 B
8d2D5/2
10f2Fo7/2
5687.53A
0.203A
4.23 × 107 A
5687.46B
0.196B
4.03 × 107 B
8d2D5/2
10f2Fo5/2
5690.36A
0.010A,B
2.11 × 106 A
5690.29B
2.01 × 106 B
7f2Fo5/2
10g2G7/2
5773.05A
0.247A
4.95 × 107 A
5707.79B
0.250B
5.13 × 107 B
7f2Fo7/2
10g2G7/2
5784.03A
0.009A,B
1.82 × 106 A
5718.53B
1.89 × 106 B
7f2Fo7/2
10g2G9/2
5784.05A
0.320A
6.38 × 107 A
5718.53B
0.324B
6.61 × 107 B
7f2Fo5/2
12d2D5/2
5813.72B
0.002B
4.69 × 105 B
7f2Fo5/2
12d2D3/2
5819.89B
0.033B
6.55 × 106 B
7f2Fo7/2
12d2D5/2
5824.86B
0.047B
9.33 × 106 B
9p2Po1/2
12d2D3/2
5996.59B
0.061B
1.12 × 107 B
9p2Po3/2
12d2D5/2
6131.85B
0.107B
1.89 × 107 B
9p2Po3/2
12d2D3/2
6138.72B
0.012B
2.10 × 106 B
6g2G9/2
10f2Fo7/2
6457.77A
0.003A,B
4.51 × 105 A
6457.76B
4.59 × 105 B
6g2G7/2
10f2Fo5/2
6461.09A
0.002A,B
3.48 × 105 A
6461.03B
3.53 × 105 B
7f2Fo5/2
9g2G7/2
6748.79A
0.512A
7.50 × 107 A
6590.26B
0.525B
8.07 × 107 B
7f2Fo7/2
9g2G7/2
6763.80A
0.019A,B
2.76 × 106 A
6604.58B
2.97 × 106 B
7f2Fo7/2
9g2G9/2
6763.63A
0.663A
9.66 × 107 A
6604.58B
0.679B
1.04 × 108 B
8d2D3/2
11p2Po3/2
6775.04B
0.002B
2.86 × 105 B
7f2Fo5/2
11d2D5/2
6792.55B
0.005B
7.23 × 105 B
7f2Fo5/2
11d2D3/2
6804.23B
0.070B
1.01 × 107 B
7f2Fo7/2
11d2D5/2
6807.77B
0.100B
1.44 × 107 B
8d2D5/2
11p2Po3/2
6827.66B
0.017B
2.52 × 106 B
8d2D3/2
11p2Po1/2
6834.22B
0.010B
1.39 × 106 B
9p2Po1/2
11d2D3/2
7046.99B
0.130B
1.75 × 107 B
9p2Po3/2
11d2D5/2
7230.87B
0.228B
2.91 × 107 B
9p2Po3/2
11d2D3/2
7244.09B
0.025B
3.21 × 106 B
9d2D3/2
12f2Fo5/2
7457.70B
0.079B
9.47 × 106 B
9d2D5/2
12f2Fo7/2
7494.42B
0.112B
1.33 × 107 B
9d2D5/2
12f2Fo5/2
7496.98B
0.006B
6.66 × 105 B
7g2G9/2
12f2Fo7/2
8263.95B
0.003B
2.86 × 105 B
7g2G7/2
12f2Fo5/2
8266.14B
0.002B
2.21 × 105 B
9d2D3/2
11f2Fo5/2
8536.25B
0.124B
1.14 × 107 B
9d2D5/2
11f2Fo7/2
8583.10B
0.176B
1.60 × 107 B
9d2D5/2
11f2Fo5/2
8587.74B
0.009B
7.97 × 105 BElectron 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 (Fk and Gk) and of configuration interaction integrals (Rk), 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 possibleE1 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 gf and gAki have been found in the 0–10% range for the transitions np (n=6–8)–ns (n=6–10), nd (n=6–9), in the 0.5–9% range for the transitions nd (n=6,7)–nf (n=5–8), np (n=7–9), and in the 1.5–20% range for the transitions nf (n=5–8)–nd (n=7–9), ng (n=5–8). 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 2Po3/2–9d 2D3/2, 5d 2D3/2–9p 2Po1/2, 4f 2Fo7/2–5g 2G7/2, 4f 2Fo7/2–6g 2G7/2, and 4f 2Fo5/2–8g 2G7/2,9/2, we found the values 1.064 (in calculation A) and 1.078 (in calculation B) for the mean ratio gf (this work)/gf [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 gAki (this work)/gAki [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 gf and gAki 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 Table2 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.



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*Source: 246105-2012-09-27.xml*