Variance and shift of transition arrays for electric and magnetic multipole transitions

Menahem Krief*, Alexander Feigel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Generalized analytical expressions for the two-electron relativistic Unresolved-Transition-Array (UTA) energy variance and shift for electric and magnetic transitions of general multipole order are presented. The revised expressions are shown to agree with the exact moments calculated directly from the energy levels of two-electron configurations. We show that for electric transitions of even multipole order and for magnetic transitions, the available expressions in the literature, which are implemented in widely used atomic codes, are incorrect. We suggest an alternative method for the calculation of the UTA energy variance and shift by using the analytical expressions for the two-electron energy levels and line-strengths. The method is much more efficient and simple than the use of the traditional lengthy analytic expressions. Finally, the effect of UTA widths on Super-Transition-Array (STA) spectral opacity is shown for several examples.

Original languageAmerican English
Pages (from-to)254-262
Number of pages9
JournalHigh Energy Density Physics
StatePublished - 1 Dec 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.


  • Atomic spectra
  • Magnetic transitions
  • Multipole transitions
  • Super transition array
  • UTA
  • Unresolved transition array


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