Low temperature expansions for the second and third cluster integrals of a two dimensional quantum system of hard discs

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Abstract
Low temperature series are derived for the second and third cluster integrals of a quantum mechanical, two dimensional gas of hard discs. The methods used are similar to those previously employed for the three dimensional, hard sphere gas, but the presence of logarithmic terms makes both the derivations and the results more complicated in the present case. The corresponding contributions to the density expansion of the specific heat are calculated. The three body contribution is large and negative, thus leading to a downturn in the specific heat at low temperature, in accordance with a prediction of Siddon and Schick.