Ordering principle for cluster expansions in the theory of quantum fluids, dense gases, and simple classical liquids

Journal Article · Mon Mar 01 04:00:00 EST 1982 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.25.1710· OSTI ID:5525341

Feenberg, E; Lee, D K

A study is made of a series-expansion procedure which gives the leading terms of the n-particle distribution function p/sup( n/)(1,2,...,n) as explicit functionals in the radial distribution function g(r). The development of the series is based on the cluster-expansion formalism applied to the Abe form for p/sup( n/) expressed as a product of the generalized Kirkwood superposition approximation P/sup( n/)/sub K/ and a correction factor exp(A/sup( n/)(1,2,...,n)). An ordering parameter ..mu.. is introduced to determine A/sup( n/) and p/sup( n/) in the form of infinite power series in ..mu.., and the postulate of minimal complexity is employed to eliminate an infinite number of possible classes of solutions in a sequential relation connecting A/sup( n/-1) and A/sup( n/). Derivation of the series for p/sup( n/) and many other algebraic manipulations involving a large number of cluster integrals are greatly simplified by the use of a scheme which groups together all cluster terms having, in a certain way, the same source term. In particular, the scheme is useful in demonstrating that the nature of the series structure of p/sup(/sup 3/) is such that its three-point Fourier transform S/sup(/sup 3/)(k/sub 1/,k/sub 2/,k/sub 3/) has as a factor the product of the three liquid-structure functions S(k/sub 1/)S(k/sub 2/)S(k/sub 3/). The results obtained to order ..mu../sup 4/ for A/sup(/sup 3/), p/sup(/sup 3/), and S/sup(/sup 3/) agree with those derived earlier in a more straightforward but tedious approach. The result for p/sup(/sup 4/) shows that the convolution approximation p/sup(/sup 4/)/sub c/, which contains ..mu../sup 3/ terms, must be supplemented by a correction of O(..mu../sup 3/) in order to be accurate through third order. The ..mu..-expansion approach is also examined for the cluster expansion of the correlation function in the Bijl-Dingle-Jastrow description of a many-boson system, and then compared with the number-density expansion formula by using the Gaussian model for g(r)-1 to evaluate cluster integrals.

• Research Organization: Arthur Holly Compton Laboratory of Physics, Washington University, St. Louis, Missouri 63130
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 5525341
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 25:3; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640420* -- Fluid Physics-- Properties & Structure of Fluids-- (-1987)
640460 -- Fluid Physics-- Other Quantum Fluids
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOSONS
CLUSTER EXPANSION
CORRELATION FUNCTIONS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ENERGY LEVELS
EQUATIONS
EVEN-EVEN NUCLEI
FLUIDS
FOURIER TRANSFORMATION
FUNCTIONALS
FUNCTIONS
GASES
GROUND STATES
HELIUM 4
HELIUM ISOTOPES
INTEGRAL TRANSFORMATIONS
ISOTOPES
LIGHT NUCLEI
LIQUIDS
MECHANICS
NUCLEI
ORDER PARAMETERS
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTUM FLUIDS
SCHROEDINGER EQUATION
SERIES EXPANSION
STABLE ISOTOPES
STATISTICAL MECHANICS
STRUCTURE FUNCTIONS
TRANSFORMATIONS
WAVE EQUATIONS