It is pointed out that scaling relations suggested previously between the critical and ground-state properties of electron-hole droplets lack theoretical justification; by detailed calculations for model systems with widely varying band structure, these relations are shown not to be satisfied. New scaling relations are proposed, and their existence is traced to systematic trends in the band structure and the exchange-correlation energy of the electron-hole system.

• Received 27 April 1979

DOI:https://doi.org/10.1103/PhysRevLett.43.1054