Radial Distribution Function for Hard-Sphere Fermions at Zero and Finite Temperatures

概要

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A quantal version of the Percus-Yevick (PY) equation proposed previously is numerically solved for hard-sphere Fermions, as a model for liquid ^3He, for a wide range of temperatures including two limits: zero and infinity. In the first place the density distributions n(r|v) around a fixed atom in the fluid, for which the integral equation is set up, are calculated at various temperatures, and the static density-density response functions χ_Q are obtained from the Fourier transforms of n(r|v)-n_0,n_0 being the average density of the system. Next, the structure factors S(Q) are computed by the use of the sum rule, that is, by the integration, over frequency ω, of the dynamic structure factors S(Q,ω), which are obtained in a generalized Hartree approximation in conjunction with the quantal direct correlation function determined by the quantal PY equation. Finally, the radial distribution functions g(r) at corresponding temperatures are obtained by their inverse Fourier transforms. Thus, the quantal PY equation is shown to give the reasonable results for n(r|v), χ_Q, g(r) and S(Q) of hard-sphere Fermions for a complete range of temperatures in a unified manner.
理論物理学刊行会の論文
1977-09-25