ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
A qualitative study of the three-dimensional Percus–Yevick (PY) equation by means of Baxter's relations is considered for an arbitrary potential of finite range l by a perturbation method. It is shown that the PY equation has a unique solution Y(r,η,β§) and a unique solution Q(r,η,β§) if the following conditions are satisfied: (i) 0〈η〈0.175, (ii) 0〈β§〈(β§)0, (iii) Supr∈[0,l]||Qn||〈n! and Supr〉0||Yn(r)||〈n!, where both Q and Y are continuous functions of the reduced density η, and can expressed as absolutely and uniformly convergent series Y=∑∞n=0(1/n!)(β§)nYn(r,η), Q=∑∞n=0(1/n!)(β§)nQn(r,η) within the radius of convergence of the inverse reduced temperature (β§)0. As functions of r, Q∈C(0)[0,l] with Q(l)=0, whereas Y is continuous for r≥0 except for a possible finite discontinuity at r=1, and Y−r→0 exponentially as r→∞. Based on the solution of Y and Q, the isothermal compressibility KT =KT(∂ρ/∂P)T is a continuous and bounded function of η. As η→ηc =0.175, KT becomes divergent. The critical density ηc (or ρc) is independent of the range of the attractive potential l. On the other hand, the critical temperature (β§)c is determined by the positive root of F(β§)=12η∫l0Q(r)dr =1, which depends explicitly on the value of l.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527385
Permalink