^{1,a)}and L. I. Podobedova

^{1,b)}

### Abstract

This compilation is the first in a series of updates to a critical compilation published in 1969 [W. L. Wiese, M. W. Smith, and B. M. Miles, Atomic Transition Probabilities, Vol. II: Sodium through Calcium, NSRDS-NBS Vol. 2 (U.S. GPO, Washington, D.C., 1969)]. Atomic transition probabilities have been critically evaluated and compiled for about 11 400 spectral lines of sodium and magnesium (nuclear charge , respectively). The cited values and their estimated uncertainties are based on our consideration of all available theoretical and experimental literature sources. All ionization stages (except for hydrogenic) are covered, and the data are presented in separate tables for each atom and ion. Separate listings are given for “allowed” (electric dipole) transitions, on the one hand, and for “forbidden” (magnetic dipole plus electric and magnetic quadrupole) transitions, on the other. In each spectrum, lines are grouped into multiplets which are arranged in order of ascending lower and upper-level energies, respectively. For each line, the emission transition probability , the line strength , and (for allowed lines) the absorption oscillator strength are given, together with the spectroscopic designation, the wavelength, the statistical weights, and the energy levels of the lower and upper states. The estimated relative uncertainties of the line strength are also indicated, as are the source citations. We introduce a statistical method that we use to estimate these uncertainties for most of the cited transition rates. We only include those lines whose transition rates are deemed sufficiently accurate to qualify as reference values. Short introductions precede the tables for each ion. The general introduction contains a discussion of the principal criteria for our judgments and our method of data selection and evaluation.

1. Introduction

2. Data Assessment

2.1. Main Criteria

2.2. The Critical Factors for the Determination of Atomic Transition Probabilities

2.2.1. Theoretical Methods

2.2.2. Experimental Methods

2.3. Selection Procedure

3. Brief Discussion of the Principal Data Sources

3.1. General Remarks

3.2. The Opacity Project

3.3. Breit-Pauli MCHF

3.4. Configuration Interaction Methods

3.5. Many-Body Perturbation Theory

3.6. Other Multiconfiguration Calculations

3.7. Related Atomic Physics Data in Tables

4. Estimating Relative Uncertainties of Line Strengths

4.1. Pooling of Relative Uncertainties of the Different Lines in a Spectrum

4.2. Restriction to Data from Certain Authors

4.3. Evaluation Procedure

5. Arrangement of the Tables

6. Acknowledgments and Future Plans

7. Appendix A: Classical Statistical Considerations

8. Appendix B: Computing the Error Function

9. References for the Introductory Material—Sections 1–8

10. Na

10.1.

10.1.1. Allowed Transitions for

10.1.2. References for Allowed Transitions for

10.1.3. Forbidden Transitions for

10.1.4. References for Forbidden Transitions for

10.2.

10.2.1. Allowed Transitions for

10.2.2. References for Allowed Transitions for

10.2.3. Forbidden Transitions for

10.2.4. References for Forbidden Transitions for

10.3.

10.3.1. Allowed Transitions for

10.3.2. References for Allowed Transitions for

10.3.3. Forbidden Transitions for

10.3.4. References for Forbidden Transitions for

10.4.

10.4.1. Allowed Transitions for

10.4.2. References for Allowed Transitions for

10.4.3. Forbidden Transitions for

10.4.4. References for Forbidden Transitions for

10.5.

10.5.1. Allowed Transitions for

10.5.2. References for Allowed Transitions for

10.5.3. Forbidden Transitions for

10.5.4. References for Forbidden Transitions for

10.6.

10.6.1. Allowed Transitions for

10.6.2. References for Allowed Transitions for

10.6.3. Forbidden Transitions for

10.6.4. References for Forbidden Transitions for

10.7.

10.7.1. Allowed Transitions for

10.7.2. References for Allowed Transitions for

10.7.3. Forbidden Transitions for

10.7.4. References for Forbidden Transitions for

10.8.

10.8.1. Allowed Transitions for

10.8.2. References for Allowed Transitions for

10.8.3. Forbidden Transitions for

10.8.4. References for Forbidden Transitions for

10.9.

10.9.1. Allowed Transitions for

10.9.2. References for Allowed Transitions for

10.10.

10.10.1. Allowed Transitions for

10.10.2. References for Allowed Transitions for

11. Mg

11.1.

11.1.1. Allowed Transitions for

11.1.2. References for Allowed Transitions for

11.1.3. Forbidden Transitions for

11.1.4. References for Forbidden Transitions for

11.2.

11.2.1. Allowed Transitions for

11.2.2. References for Allowed Transitions for

11.2.3. Forbidden Transitions for

11.2.4. References for Forbidden Transitions for

11.3.

11.3.1. Allowed Transitions for

11.3.2. References for Allowed Transitions for

11.3.3. Forbidden Transitions for

11.3.4. References for Forbidden Transitions for

11.4.

11.4.1. Allowed Transitions for

11.4.2. References for Allowed Transitions for

11.4.3. Forbidden Transitions for

11.4.4. References for Forbidden Transitions for

11.5.

11.5.1. Allowed Transitions for

11.5.2. References for Allowed Transitions for

11.5.3. Forbidden Transitions for

11.5.4. References for Forbidden Transitions for

11.6.

11.6.1. Allowed Transitions for

11.6.2. References for Allowed Transitions for

11.6.3. Forbidden Transitions for

11.6.4. References for Forbidden Transitions for

11.7.

11.7.1. Allowed Transitions for

11.7.2. References for Allowed Transitions for

11.7.3. Forbidden Transitions for

11.7.4. References for Forbidden Transitions for

11.8.

11.8.1. Allowed Transitions for

11.8.2. References for Allowed Transitions for

11.8.3. Forbidden Transitions for

11.8.4. References for Forbidden Transitions for

11.9.

11.9.1. Allowed Transitions for

11.9.2. References for Allowed Transitions for

11.9.3. Forbidden Transitions for

11.9.4. References for Forbidden Transitions for

11.10.

11.10.1. Allowed Transitions for

11.10.2. References for Allowed Transitions for

11.11.

11.11.1. Allowed Transitions for

11.11.2. References for Allowed Transitions for

### Key Topics

- Sodium
- 85.0
- Magnesium
- 83.0
- Ab initio calculations
- 35.0
- Ionization
- 25.0
- Opacity
- 24.0

## Figures

Relative standard deviation of the mean (RSDM) vs the line strength for the transitions in for which the energy of the upper level is *less* than and which have values listed in both Refs. 90 (MCHF) and 57 (CI). Because there are two data sources, the RSDM for each transition is given by Eq. (4). The curve corresponds to fit values for the parameters in Eq. (5); 90% of the points lie under it. Using the method described in the text, the parameters were empirically found to be (“slope” of the curve) and (“intercept”), and (asymptotic background of the curve). In actual practice, for these data we would extend the ordinate of the graph only to 0.05, but here we extend it up to the maximum value of 1.0 to facilitate comparisons with Figs. 2 and 3. The quality of these data is much higher than in those higher energy level cases, which are plotted in Figs. 2 and 3. Below energies of , same J and parity energy levels are not closely spaced and level “mixing” is not generally important.

Relative standard deviation of the mean (RSDM) vs the line strength for the transitions in for which the energy of the upper level is *less* than and which have values listed in both Refs. 90 (MCHF) and 57 (CI). Because there are two data sources, the RSDM for each transition is given by Eq. (4). The curve corresponds to fit values for the parameters in Eq. (5); 90% of the points lie under it. Using the method described in the text, the parameters were empirically found to be (“slope” of the curve) and (“intercept”), and (asymptotic background of the curve). In actual practice, for these data we would extend the ordinate of the graph only to 0.05, but here we extend it up to the maximum value of 1.0 to facilitate comparisons with Figs. 2 and 3. The quality of these data is much higher than in those higher energy level cases, which are plotted in Figs. 2 and 3. Below energies of , same J and parity energy levels are not closely spaced and level “mixing” is not generally important.

Relative standard deviation of the mean (RSDM) vs the line strength for the transitions in for which the energy of the upper level is *greater* than and which have values listed in both Refs. 90 (MCHF) and 57 [configuration interaction (CI)]. Because there are two data sources, the RSDM for each transition is given by Eq. (4). The two curves correspond to different values of the and parameters in Eq. (5); 50% of the points in the figure lie under the lower curve, and 90% lie under the upper curve. For these curves, the parameters in Eq. (5) were empirically found to be (both curves) and , and for the (upper) 90% envelope curve. Above energies of , same J and parity energy levels are more closely spaced and level “mixing” becomes increasingly significant. Still, the agreement of the MCHF data with the CI data is considerably better than it is with the OP, as seen in Fig. 3.

Relative standard deviation of the mean (RSDM) vs the line strength for the transitions in for which the energy of the upper level is *greater* than and which have values listed in both Refs. 90 (MCHF) and 57 [configuration interaction (CI)]. Because there are two data sources, the RSDM for each transition is given by Eq. (4). The two curves correspond to different values of the and parameters in Eq. (5); 50% of the points in the figure lie under the lower curve, and 90% lie under the upper curve. For these curves, the parameters in Eq. (5) were empirically found to be (both curves) and , and for the (upper) 90% envelope curve. Above energies of , same J and parity energy levels are more closely spaced and level “mixing” becomes increasingly significant. Still, the agreement of the MCHF data with the CI data is considerably better than it is with the OP, as seen in Fig. 3.

Relative standard deviation of the mean (RSDM) vs the line strength for the transitions in for which the energy of the upper level is *greater* than . Opacity Project data is included. and which have values listed in both Refs. 90 (MCHF) and 16 [Opacity Project (OP)]. Because there are two data sources, the RSDM for each transition is given by Eq. (4). The two curves correspond to different values of the and parameters in Eq. (5); 50% of the points in the figure lie under the lower curve, and 90% lie under the upper curve. For these curves, the parameters in Eq. (5) were empirically found to be (both curves) and , and for the (upper) 90% envelope curve. The agreement of the OP data with the MCHF data is considerably poorer than is the configuration interaction data seen in Fig. 2.

Relative standard deviation of the mean (RSDM) vs the line strength for the transitions in for which the energy of the upper level is *greater* than . Opacity Project data is included. and which have values listed in both Refs. 90 (MCHF) and 16 [Opacity Project (OP)]. Because there are two data sources, the RSDM for each transition is given by Eq. (4). The two curves correspond to different values of the and parameters in Eq. (5); 50% of the points in the figure lie under the lower curve, and 90% lie under the upper curve. For these curves, the parameters in Eq. (5) were empirically found to be (both curves) and , and for the (upper) 90% envelope curve. The agreement of the OP data with the MCHF data is considerably poorer than is the configuration interaction data seen in Fig. 2.

## Tables

Correspondence between accuracy and estimated relative uncertainty

Correspondence between accuracy and estimated relative uncertainty

Conversion factors for transition rates

Conversion factors for transition rates

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: ,^{104} Fischer,^{34} *et al.*,^{48} *et al.*,^{72} *et al.*,^{120} and Prokof’ev^{28})

Transition probabilities of allowed lines for (references for this table are as follows: ,^{104} Fischer,^{34} *et al.*,^{48} *et al.*,^{72} *et al.*,^{120} and Prokof’ev^{28})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: Fischer^{35})

Transition probabilities of forbidden lines for (references for this table are as follows: Fischer^{35})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Froese Fischer,^{98} and Froese Fischer,^{93} *et al.*,^{45} and ^{107})

Transition probabilities of allowed lines for (references for this table are as follows: and Froese Fischer,^{98} and Froese Fischer,^{93} *et al.*,^{45} and ^{107})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{98} and ^{53})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{98} and ^{53})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{15} and Froese Fischer,^{97} and and Hibbert^{57})

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{15} and Froese Fischer,^{97} and and Hibbert^{57})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (reference for this table is as follows: and Froese^{97})

Transition probabilities of forbidden lines for (reference for this table is as follows: and Froese^{97})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{15} and Froese Fischer,^{94} and *et al.* ^{119})

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{15} and Froese Fischer,^{94} and *et al.* ^{119})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{94} *et al.*,^{39} and *et al.* ^{40})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{94} *et al.*,^{39} and *et al.* ^{40})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Lennon,^{12} and Froese Fischer,^{94} and *et al.* ^{65})

Transition probabilities of allowed lines for (references for this table are as follows: and Lennon,^{12} and Froese Fischer,^{94} and *et al.* ^{65})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{94} and *et al.* ^{63})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{94} and *et al.* ^{63})

Wavelengths finding list for allowed lines for

Wavelengths finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Pradhan,^{56} and Froese Fischer,^{94} *et al.*,^{4} 4=Fawcett,^{21} and *et al.* ^{62})

Transition probabilities of allowed lines for (references for this table are as follows: and Pradhan,^{56} and Froese Fischer,^{94} *et al.*,^{4} 4=Fawcett,^{21} and *et al.* ^{62})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{94} *et al.*,^{118} *et al.* ^{40} )

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{94} *et al.*,^{118} *et al.* ^{40} )

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{25} and Froese Fischer,^{94} *et al.*,^{64} *et al.*, ^{41}and *et al.* ^{81})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{25} and Froese Fischer,^{94} *et al.*,^{64} *et al.*, ^{41}and *et al.* ^{81})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{94} and *et al.*.^{41})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{94} and *et al.*.^{41})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{113} and Froese Fischer,^{94} *et al.*,^{19} *et al.*,^{80} and *et al.* ^{82})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{113} and Froese Fischer,^{94} *et al.*,^{19} *et al.*,^{80} and *et al.* ^{82})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{94} and *et al.* ^{82})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{94} and *et al.* ^{82})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{76} *et al.*,^{127} *et al.* ^{129} and Martin *et al.* ^{59})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{76} *et al.*,^{127} *et al.* ^{129} and Martin *et al.* ^{59})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (reference for this table are as follows: *et al.* ^{27} and *et al.* ^{50})

Transition probabilities of allowed lines for (reference for this table are as follows: *et al.* ^{27} and *et al.* ^{50})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{13} and Froese Fischer,^{99} *et al.*,^{114} , Tang^{17}, and ^{123})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{13} and Froese Fischer,^{99} *et al.*,^{114} , Tang^{17}, and ^{123})

Wavelength finding list for forbidden lines

Wavelength finding list for forbidden lines

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{95} and ^{42})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{95} and ^{42})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: ,^{103} Fischer,^{36} *et al.*,^{84} *et al.*,^{2} and Federman,^{106} *et al.*,^{47} and Fischer^{37})

Transition probabilities of allowed lines for (references for this table are as follows: ,^{103} Fischer,^{36} *et al.*,^{84} *et al.*,^{2} and Federman,^{106} *et al.*,^{47} and Fischer^{37})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: Fischer,^{32} and Mukherjee,^{52} *et al.*,^{42} and *et al.* ^{110})

Transition probabilities of forbidden lines for (references for this table are as follows: Fischer,^{32} and Mukherjee,^{52} *et al.*,^{42} and *et al.* ^{110})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Froese Fischer,^{96} and Froese Fischer,^{92} *et al.*,^{45} ,^{107} and *et al.* ^{10})

Transition probabilities of allowed lines for (references for this table are as follows: and Froese Fischer,^{96} and Froese Fischer,^{92} *et al.*,^{45} ,^{107} and *et al.* ^{10})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{96} and ^{53})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{96} and ^{53})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{14} and Froese Fischer,^{96} and Froese Fischer,^{92} and ^{7})

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{14} and Froese Fischer,^{96} and Froese Fischer,^{92} and ^{7})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{96} and and Froese Fischer^{92})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer^{96} and and Froese Fischer^{92})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{14} and Froese Fischer,^{100} and Froese Fischer,^{101} *et al.*,^{119} and *et al.* ^{9})

Transition probabilities of allowed lines for (references for this table are as follows: and Zeippen,^{14} and Froese Fischer,^{100} and Froese Fischer,^{101} *et al.*,^{119} and *et al.* ^{9})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (reference for this table are as follow: and Froese Fischer,^{96} and Froese Fischer,^{92} *et al.*,^{39} and *et al.* ^{40})

Transition probabilities of forbidden lines for (reference for this table are as follow: and Froese Fischer,^{96} and Froese Fischer,^{92} *et al.*,^{39} and *et al.* ^{40})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (reference for this table are as follows: and Lennon,^{11} and Froese Fischer,^{99} and Froese Fischer,^{95} *et al.* ^{65})

Transition probabilities of allowed lines for (reference for this table are as follows: and Lennon,^{11} and Froese Fischer,^{99} and Froese Fischer,^{95} *et al.* ^{65})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{99} and Froese Fischer,^{96} and *et al.* ^{63})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{99} and Froese Fischer,^{96} and *et al.* ^{63})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: and Pradhan,^{55} and Froese Fischer,^{91} ,^{3} ,^{21} and *et al.* ^{62})

Transition probabilities of allowed lines for (references for this table are as follows: and Pradhan,^{55} and Froese Fischer,^{91} ,^{3} ,^{21} and *et al.* ^{62})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as table follows: and Froese Fischer,^{91} *et al.*,^{118} and *et al.* ^{40})

Transition probabilities of forbidden lines for (references for this table are as table follows: and Froese Fischer,^{91} *et al.*,^{118} and *et al.* ^{40})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{24} and Froese Fischer,^{92} *et al.*,^{64} and *et al.* ^{41})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{24} and Froese Fischer,^{92} *et al.*,^{64} and *et al.* ^{41})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{92} *et al.*,^{41} and *et al.* ^{116})

Transition probabilities of forbidden lines for (references for this table are as follows: and Froese Fischer,^{92} *et al.*,^{41} and *et al.* ^{116})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transitions probabilities of allowed lines for (reference for this table are as follows: *et al.*,^{112} and Froese Fischer,^{92} *et al.*,^{19} *et al.*,^{80} *et al.*,^{82} *et al.*,^{109} and Grant,^{30} and Huang,^{46} and Vainshtein,^{79} and *et al.* ^{29})

Transitions probabilities of allowed lines for (reference for this table are as follows: *et al.*,^{112} and Froese Fischer,^{92} *et al.*,^{19} *et al.*,^{80} *et al.*,^{82} *et al.*,^{109} and Grant,^{30} and Huang,^{46} and Vainshtein,^{79} and *et al.* ^{29})

Wavelength finding list for forbidden lines for

Wavelength finding list for forbidden lines for

Transition probabilities of forbidden lines for (reference for this table are as follows: and Froese Fischer^{92} and and Hibbert^{51})

Transition probabilities of forbidden lines for (reference for this table are as follows: and Froese Fischer^{92} and and Hibbert^{51})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{75} and Froese Fischer,^{102} *et al.*,^{127} *et al.* ^{129})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.*,^{75} and Froese Fischer,^{102} *et al.*,^{127} *et al.* ^{129})

Wavelength finding list for allowed lines for

Wavelength finding list for allowed lines for

Transition probabilities of allowed lines for (references for this table are as follows: *et al.* ^{26} and *et al.* ^{50})

Transition probabilities of allowed lines for (references for this table are as follows: *et al.* ^{26} and *et al.* ^{50})

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