Variational calculations of the ground-state energy of hard-sphere, helium-4, Coulomb, and nuclear Yukawa fluids are carried out. The long-range part v(r>d) and a constant part λ at r<d of the bare interaction are assumed to contribute to the average field. The correlation function f(r) is obtained by minimizing the two-body cluster contribution due to the remainder interaction, and the distance d is determined by minimizing the energy as calculated with the hierarchy of hypernetted-chain-type equations. The convergence of two- and three-particle distribution functions given by these equations is discussed. The method is shown to be exact in the low-density limit, and the comparison of the present results with the available exact (standard) results in the high-density limit (region) verifies its accuracy over the entire density range. It is shown that the variationally obtained value of d in the high-density Coulomb fluid can be understood with conventional meanfield theory. A solidification criterion is obtained by studying the energies in liquid and solid phases with the present f(r). This criterion explains the solidification of the Coulomb, hard-sphere, and helium systems, and the inability of the nuclear Yukawa system to solidify. The variational method in the form presented here could be very useful for studying complicated quantum systems.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics