Abstract
The three-body correlation function is evaluated for the ground state of a dilute boson gas with hard-sphere interaction and the validity of the superposition approximationD(r12,r13,r23)=D(r12)D(r13)D(r23) is discussed. The main result of this paper is that the superposition approximation holdsonly whenall the relative co-ordinates are much greater than the correlation lengthr0=(8παϱ)−1/2 (α and ϱ are the hard sphere radius and number density of the gas, respectively). One also finds that the system shows unexpected long-distance correlations since one hasD(r12, ∞, ∞) ≠D(r12).
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