Simple expression of occupation probability in the "chemical picture"

We propose a simple analytical expression for the occupation probability of highly excited states in low-density hydrogenic plasmas. This expression is based on the "chemical picture" and is derived by using the Holtsmark field and the saddle-point estimates. We believe that this expression would be a basic model in the chemical picture since ion-ion correlation is neglected and the simple saddle-point estimates are used. If the density of the plasma is low enough and the temperature is high enough, this expression would be a good approximation. If not, this model gives roughly the critical principal quantum number at which bound states disappear and the basic reference numerical values of the occupation probability for quantitative comparison study with numerical results by detailed modeling.