Long-Distance Behaviors of the Pair Distribution Function of Degenerate and Non-Degenerate Bose Fluids

概要

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The formalism proposed for degenerate Bose fluids by one of the present authors [T. Morita, Prog. Theor. Phys. 39 (1968), 1100] is extended for the calculation of the one- and two-particle distribution functions. With the aid of the diagram expansion, it is shown that the long-distance 1/r and 1/r^2 behaviors of the pair distribution function of the degenerate ideal Bose gas are exactly canceled in degenerate interacting Bose fluids in general. In the proof, it is assumed that vk/k→∞ as k→0 for the weakly interacting case andΣ_d(k,0)/k→∞ as k→0 for the general case, where vk and Σ_d(k,0) are the Fourier transforms of interacting potential and of a generalized binary collision kernel, respectively. It is stressed that the Hartree-Fock approximation is insufficient in showing the cancellation of the 1/r^2 term. In fact, the cancellation is attained by taking account of the averages of the type: <a^^~^*_p+k a^^~k a^^~p> and <a^^~_p^* a^^~_k^* a^^~p+k>. For non-degenerate case, the 1/r^2behavior, which appears just above the λ-point of the ideal Bose gas, is also shown to be canceled in interacting Bose fluids.
1969-01-25