The Thomas-Kuhn-Reiche sum rule for bound electrons of ions in warm dense plasmas

Abstract

The Thomas-Kuhn-Reiche oscillator strength sum rule is analyzed for the case of ionized atoms in warm dense plasmas: The statistical summation of the bound-bound and the bound-free oscillator strength is proportional to the average bound electrons. This sum rule is checked for approximated absorption spectra like the detailed line accounting, detailed configurations accounting, the super transition arrays and the average atom using the CRSTA code. We show that the sum rule is properly satisfied for various elements in ranges of temperature-density that have sufficient bound orbitals. On the other hand, for the cases of few bound orbitals, the sum-rule is poorly satisfied, like in the case of high density and low temperature.