Friedel sum rule at finite temperature in hot dense plasmas

We study the notion of Friedel sum rule at finite temperature in hot dense plasmas. Using the average-atom model, we establish expressions for the Friedel sum rule at zero and finite temperature using non-relativistic or relativistic approaches. Formulas are also given using the Born approximation for the phase shifts. Numerical examples are provided. The Friedel sum rule is a stringent test of the internal consistency of a quantum average-atom model. The question of normalization of free wavefunctions is also discussed.