Long-Distance Behavior of the Pair Distribution Function of Hard-Sphere Fermi Gases

概要

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The long-distance behavior of the pair distribution function of a hard-sphere Fermi gas, ρ^<(2)>(r) is investigated. It is shown that its distance dependence at zero temperature is the same as that of the ideal Fermi gas, though the amplitudes are different; namely ρ^<(2)>(r)~k_0^<-2>r^<-4>[C_1+C_2 cos2 k_0r], where k_0 is the Fermi wave number and C_i's are constants. Corrections arise from the temperature dependence of the chemical potential and from the deformation of the Fermi distribution function f_p. The temperature dependence of the terms due to these corrections is estimated to be of the order O(T^2), while the distance behavior is found to be O(1/r^3) and O(1/r^2), respectively. Comments are given on higher order contributions. It is argued that the exchange and the direct contribution to the interaction parts of ρ^<(2)>(r) have the same long-distance behavior for an electron gas as for a hard-sphere Fermi gas.
理論物理学刊行会の論文
1971-05-25