ATOMIC TRANSITION PROBABILITIES

J. R. Fuhr, W. L. Wiese, L. I. Podobedova, and D. E. Kelleher

This table contains critically evaluated atomic transition probabilities for about 12,000 selected lines of all elements for which reliable data are available on an absolute scale. The values are largely for neutral and singly ionized spectra, but also include some prominent lines of doubly and more highly charged ions of important elements.

Most of the data are obtained from comprehensive compilations of the Data Center on Atomic Transition Probabilities at the National Institute of Standards and Technology. Specifically, data have been taken from critical compilations on H, He, and Li (Ref. 1); on Be and B (Ref. 2); on neutral and singly-ionized C and N (Ref. 3);and on Na (Ref. 4), Mg (Ref. 4), Al (Ref. 5), and Si (Ref. 6). Material from earlier compilations for the elements H through Ne (Refs. 7 and 8) and Na through Ca (Ref. 9) was supplemented by some more recent material taken directly from the original literature. Most of the original literature is cited in the above tables and in recent bibliographies (Refs. 10 and 11); for lack of space, individual literature references are not cited here.

The wavelength range for the neutral species is normally the visible spectrum or shorter wavelengths; only the very prominent near infrared lines are included. For the higher ions, most of the strong lines are located in the far UV. The tabulation is limited to electric dipole - including intercombination - lines and comprises essentially the fairly strong transitions with estimated uncertainties in the 10 % to 50 % range. With the exception of hydrogen, helium, and the alkali metals, most transitions are between states with low principal quantum numbers. Column definitions for the table are as follows.

Generally, the estimated uncertainties of the A-values are in the range from 25% to 50% for two-digit numbers, 10% to 25% for three-digit numbers and 1% or better for four- and five-digit numbers.

Each transition is identified by the wavelength λ in angstroms and the statistical weights, g_i and g_k , of the lower (i) and upper (k) states [the product g_kA (or g_if ) is needed for many applications]. Whenever the wavelengths of individual lines within a multiplet are extremely close, only an average wavelength for the multiplet as well as the multiplet A-value are given, and this is indicated by a footnote ^a on the wavelength. This also has been done when the transition probability for an entire multiplet has been taken from the literature and values for individual lines cannot be determined because of insufficient knowledge of the coupling of electrons. The wavelength data have been taken either from recent compilations or from the original literature cited in bibliographies published by the Atomic Energy Levels Data Center (Refs. 12 and 13) at the National Institute of Standards and Technology. Wavelength values are consistent with those given in the table “Line Spectra of the Elements,” which appears elsewhere in this Handbook.

In addition to the transition probability A, the atomic oscillator strength f and the line strength S are often used in the literature. The conversion factors between these quantities are (for electric-dipole transitions):

g_if = 1.499∙10^–8 λ²g_kA = 303.8 λ^–1S

where λ is in Å, A is in 10⁸s^–1, and S is in atomic units, which are a₀²e² = 7.188∙10^–59 m²C².

The transition probabilities for hydrogen and hydrogen-like ions are known precisely. Because of the hydrogen degeneracy, a “transition” is actually the sum of all fine-structure transitions between the principal quantum numbers; therefore, the hydrogen table gives weighted average A-values. For hydrogen-like ions of nuclear charge Z, the following scaling laws hold:

A_Z = Z⁴A_Hydrogenf_Z = f_HydrogenS_Z = Z^–2S_Hydrogenλ_Z = Z^–2λ_Hydrogen

For very highly-charged hydrogen-like ions, starting at about Z > 25, relativistic values must be used.

Further information on the atomic levels involved in the transitions may be found in Ref. 15.

References

1. Wiese, W. L., and Fuhr, J. R., J. Phys. Chem. Ref. Data 38, 565, 2009. [https://doi.org/10.1063/1.3077727]
2. Fuhr, J. R., and Wiese, W. L., J. Phys. Chem. Ref. Data 39, 013101, 2010. [https://doi.org/10.1063/1.3286088]
3. Wiese, W. L., and Fuhr, J. R., J. Phys. Chem. Ref. Data 36, 1287, 2007. [https://doi.org/10.1063/1.2740642]
4. Kelleher, D. E., and Podobedova, L. I., J. Phys. Chem. Ref. Data 37, 267, 2008. [https://doi.org/10.1063/1.2735328]
5. Kelleher, D. E., and Podobedova, L. I., J. Phys. Chem. Ref. Data 37, 709, 2008. [https://doi.org/10.1063/1.2734564]
6. Kelleher, D. E., and Podobedova, L. I., J. Phys. Chem. Ref. Data 37, 1285, 2008. [https://doi.org/10.1063/1.2734566]
7. Wiese, W. L., Smith, M. W., and Glennon, B. M., Atomic Transition Probabilities (H through Ne - A Critical Data Compilation), National Standard Reference Data Series, National Bureau of Standards 4, Vol. I, U.S. Government Printing Office, Washington, D.C., 1966. [https://doi.org/10.6028/NBS.NSRDS.4]
8. Wiese, W. L., Fuhr, J. R., and Deters, T. M., Atomic Transition Probabilities of Carbon, Nitrogen, and Oxygen, J. Phys. Chem. Ref. Data, Monograph 7, 1996.
9. Wiese, W. L., Smith, M. W., and Miles, B. M., Atomic Transition Probabilities (Na through Ca - A Critical Data Compilation), National Standard Reference Data Series, National Bureau of Standards 22, Vol. II, U. S. Government Printing Office, Washington, D.C., 1969.
10. Fuhr, J. R., Miller, B. J., and Martin, G. A., Bibliography on Atomic Transition Probabilities (1914 through October 1997), National Bureau of Standards Special Publication 505, 1978; Miller, B. J., Fuhr, J. R., and Martin, G. A., Bibliography on Atomic Transition Probabilities (November 1977 through February 1980), National Bureau of Standards Special Publication 505, Supplement 1, 1980. [https://doi.org/10.6028/NBS.SP.505]
11. Wiese, W. L., Reports on Astronomy, Trans. Int. Astron. Union 18A, 116, 1982; 19A, 122, 1985; 20A, 117, 1988, Reidel, D., Ed., Kluwer, Dordrecht, The Netherlands.
12. Moore, C. E., Bibliography on the Analyses of Optical Atomic Spectra, National Bureau of Standards Special Publication 306 - Section 1, 1968; Sections 2-4, 1969.
13. Hagan, L., and Martin, W. C., Bibliography on Atomic Energy Levels and Spectra (July 1968 through June 1971), National Bureau of Standards Special Publication 363, 1972; Hagan, L., Bibliography on Atomic Energy Levels and Spectra (July 1971 through June 1975), National Bureau of Standards Special Publication 363, Supplement 1, 1977; Zalubas, R., and Albright, A., Bibliography on Atomic Energy Levels and Spectra (July 1975 through June 1979), National Bureau of Standards Special Publication 363, Supplement 2, 1980; Musgrove, A., and Zalubas, R., Bibliography on Atomic Energy Levels and Spectra (July 1979 through December 1983), National Bureau of Standards Special Publication 363, Supplement 3, 1985. [https://doi.org/10.6028/NBS.SP.363]
14.   Kramida, A., Ralchenko, Yu., Reader, J. and NIST ASD Team (2013). NIST Atomic Spectra Database (version 5.1), National Institute of Standards and Technology, Gaithersburg, MD, <www.nist.gov/pml/data/asd.cfm>. 
15. <https://www.nist.gov/pml/basic-atomic-spectroscopic-data-handbook#II>

Wavelengths, Statistical Weights, and Transition Probabilities of Atomic Spectral Lines