Credit: Alan Stonebraker; Data shown in (c) are courtesy of K. M. Daily, Washington State University

Figure 1:
(a),(b) Schematic illustrations of one of many possible configurations of the three-body cluster at low and high temperature, respectively. At low T, only a few configurations with small energy contribute to a given virial coefficient b_{n}. At high temperature, many configurations with small and large energy contribute. (c) Shows the cluster expansion parameter, or fugacity, z=exp[μ/(k_{B}T)], where μ denotes the chemical potential and k_{B} the Boltzmann constant, as a function of T/T_{F} for the example of infinitely strong interactions. The thermodynamic potential Ω, which determines the energy and entropy, can be written as Ω∝Σ_{n}b_{n}z^{n}, where b_{n} is determined by the energy spectrum of the nth cluster. The contribution of the nth cluster is suppressed by a factor of z compared to that of the (n-1)th cluster. The suppression is very effective for T/T_{F}>1 (i.e., only terms with n=1,2, and 3 are needed), but higher-order clusters are needed for T/T_{F}≤0.75.