Abstract
The refined semiclassical method based on the Thomas-Fermi statistical model takes into account the shell effects by means of an additive correction. The method has been verified in the calculations of a plasma equation of state at high temperatures. To expand its application range to low temperatures some assumptions are revised that have been made to obtain the simple formula for a shell correction. The validity of the assumptions is discussed and the results of their refusal are analyzed. As examples, a number of single-particle states in the ideal plasma of a few elements with strongly differing atomic numbers is calculated.
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