INDIRECT EXPONENTIAL COUPLING IN THE CLASSICAL MANY-BODY PROBLEMS

Journal Article · Tue May 01 00:00:00 EDT 1962 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.126.883· OSTI ID:4834081

Meeron, E

The usual coupling procedure consists of multiplying the interparticle potential, U/sub N/(r/sup N/), by a coupling parameter LAMBDA and expanding thermodynamic functions in powers of LAMBDA . The Kirkwood variation couples only one particle of the system, resulting in an integrodifferential equation for distribution functions, which also can be expanded in powers of the coupling parameter. These expansions converge and are valid only for weakly coupled systems. If the Ursell f bonds are coupled instead of the direct interaction potentials, thermodynamic fanctions can be expanded in powers of the exponential coupling parameters; for actual physical systems these expansions are practically finite low-order polynomials in the coupling parameters. Integrodifferential equations for distribution functions are derived, and distribution functions are given by ratios of two practically finite polynomials in the exponential coupling parameters. The coefficients in these polynomials are finite even for strongly singular (e.g., hard sphere) potentials. The method provides a well-defined expansion parameter for the KirkwoodSalzburg hierarchy and appears related to the f-bond chain summation and nodal expansion methods. Applications include: theory of fused salts and electrolytes, theory of ferroelectricity, ion pairing in semiconductors, equation of state of the high-temperature electron gas, and problems of phase transitions. The possibility of applying exponential coupling to quantum-mechanical systems is noted. (auth)

• Research Organization: Convair, San Diego, Calif.
• NSA Number: NSA-16-022907
• OSTI ID: 4834081
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Vol. Vol: 126; Other Information: Orig. Receipt Date: 31-DEC-62
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

PHYSICS
ALLOTROPY
DIFFERENTIAL EQUATIONS
DISTRIBUTION
ELECTROLYTES
ELECTRONS
ELEMENTARY PARTICLES
FERROELECTRIC MATERIALS
FERROMAGNETIC MATERIALS
FUSED SALTS
HIGH TEMPERATURE
INTERACTIONS
IONS
KIRKWOOD METHOD
LIQUIDS
MANY BODY PROBLEM
MATHEMATICS
MOLECULES
PHASE DIAGRAMS
PHASE TRANSFORMATION
PLASMA
QUANTUM MECHANICS
SEMICONDUCTORS
THERMODYNAMICS