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We consider scattering state contributions to the partition function of atwo-dimensional (2D) plasma in addition to the bound-state sum. A partitionfunction continuity requirement is used to provide a statistical mechanicalheuristic proof of Levinson's theorem in two dimensions. We show that a properaccount of scattering eliminates singularities in thermodynamic properties ofthe nonideal 2D gas caused by the emergence of additional bound states as thestrength of an attractive potential is increased. The bound-state contributionto the partition function of the 2D gas, with a weak short-range attractionbetween its particles, is found to vanish logarithmically as the binding energydecreases. A consistent treatment of bound and scattering states in a screenedCoulomb potential allowed us to calculate the quantum-mechanical second virialcoefficient of the dilute 2D electron-hole plasma and to establish thedifference between the nearly ideal electron-hole gas in GaAs and the stronglycorrelated exciton/free-carrier plasma in wide-gap semiconductors such as ZnSeor GaN.Comment: 10 pages, 3 figures; new version corrects some minor typo

Levinson’s theorem and scattering phase-shift contributions to the partition function of interacting gases in two dimensions