Condensation Phenomena in a Clustering Bose-Einstein Gas

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Abstract
It has been shown that Mayer's theory of imperfect gases can be handled approximately as a problem in association in which the actual gas is replaced by a mixture of ideal gases consisting of clusters of all sizes and between which dissociative equilibrium exists. Kahn and Uhlenbeck have shown how Mayer's theory can be generalized to apply to quantum degenerate gases. The purpose of the present paper is to examine the clustering approximation to such a theory of the quantum degenerate Bose-Einstein gas. The symmetrized wave functions for the clustering assembly are set up and the partition function evaluated for all ways of clustering. Equations of state are deduced that include condensation into the liquid phase as a clustering avalanche at the saturation pressure. It is found that clustering has the effect of lowering the lambda-temperature due to statistical degeneracy right down to the saturated vapor line, so that the lambda-transition is entirely inhibited from the gas phase.

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