A Static Model for the Continuum-Lowering of a Hydrogen-Like Ion as an Ultra-Dense Plasma Diagnostics

A simple formula for the density diagnostics of a plasma is proposed in the present work. The idea comes from the level-crossing feature of a hydrogen-like ion immersed in the plasma. Viewing the lowest electronic states to which the crossing between all neighboring levels takes place, the density is shown to be expressed in a tractable form as a function of the ionization-potential lowering of the emitter. The calculation performed for the ion-sphere model with the Hartree-potential turns out to be as accurate as those for the Stewart-Pyatt model. The edge-shift is discussed in connection with the ionization-potential lowering which is caused from the screening effect in the plasma.