On the Li-Rosmej analytical formula for energy level shifts in dense plasmas

Li and Rosmej derived analytical fits for the energy level shifts due to plasma screening on the basis of a free-electron potential published by Rosmej et al. one year earlier. The derivation of the fits, which were shown by Iglesias to be inconsistent with the fundamental premise of the ion-sphere model, was motivated by the belief that no analytical expression exists for the expectation value $⟨r^{3\mathrm{/}2}⟩$, an assertion that was also contradicted by Iglesias. In this short note, I point out that a simple expression for the latter quantity can be obtained as a particular case of a formula published by Shertzer, and I provide a corresponding compact analytical expression for the level shifts in the framework of Rosmej’s formalism.