Long-Distance Behavior of the Pair Distribution Fnction of Hard-Sphere Fermi Gases
Hiroaki Hara, Tohru Morita
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)∼k0-2r-4[C1+C2 cos2k0r]. where k0 is the Fermi wave number and Ci's are constants. Corrections arise from the temperature dependence of the chemical potential and from the deformation of the Fermi distribution function fp. The temperature dependence of the terms due to these corrections is estimated to be of the order O(T2), while the distance behavior is found to be O(1/r3) and O(1/r2), 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.
Progress of Theoretical Physics•May 1, 1971•0 citations