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Title: More many-body perturbation theory for an electron-ion system

Abstract

From previous finite-temperature, quantum, many-body perturbation theory results for the grand partition function of an electron-ion fluid through order {epsilon}{sup 4}, we compute the electron and ion fugacities in terms of the volume per ion and the temperature to that same order in perturbation theory. From these results we also give the pressure, again to the same order in perturbation theory about the values for the non-interacting fluid.

Authors:
;
Publication Date:
Research Org.:
Los Alamos National Lab., NM (United States)
Sponsoring Org.:
USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)
OSTI Identifier:
539870
Report Number(s):
LA-UR-97-3442; CONF-970994-
ON: DE98000263; TRN: 97:005549
DOE Contract Number:
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: Condensed matter theories conference, Luso (Portugal), 22-27 Sep 1997; Other Information: PBD: 1997
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; PLASMA; PERTURBATION THEORY; MANY-BODY PROBLEM; PARTITION FUNCTIONS; HAMILTONIANS; PARTIAL DIFFERENTIAL EQUATIONS; SERIES EXPANSION; EQUATIONS OF STATE

Citation Formats

Baker, G.A. Jr., and Johnson, J.D.. More many-body perturbation theory for an electron-ion system. United States: N. p., 1997. Web.
Baker, G.A. Jr., & Johnson, J.D.. More many-body perturbation theory for an electron-ion system. United States.
Baker, G.A. Jr., and Johnson, J.D.. Wed . "More many-body perturbation theory for an electron-ion system". United States. doi:. https://www.osti.gov/servlets/purl/539870.
@article{osti_539870,
title = {More many-body perturbation theory for an electron-ion system},
author = {Baker, G.A. Jr. and Johnson, J.D.},
abstractNote = {From previous finite-temperature, quantum, many-body perturbation theory results for the grand partition function of an electron-ion fluid through order {epsilon}{sup 4}, we compute the electron and ion fugacities in terms of the volume per ion and the temperature to that same order in perturbation theory. From these results we also give the pressure, again to the same order in perturbation theory about the values for the non-interacting fluid.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Oct 01 00:00:00 EDT 1997},
month = {Wed Oct 01 00:00:00 EDT 1997}
}

Conference:
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  • The expansion in powers of the electron charge, e, for a neutral system of electrons (fermions) and ions (Maxwell-Boltzmann particles) is extended to order e{sup 4} for arbitrary values of temperature and density. The methods of calculation of the series terms will be illustrated, and some of the consequences of these results will be discussed. The ionization profile so derived, at least at high temperatures, will be contrasted with Saha theory. Some special features of hydrogen related to the possible plasma phase transition will be noted. (c) 2000 American Institute of Physics.
  • Diagrammatic many-body perturbation theory is used to calculate the electronic energy and the static electric dipole polarizability of the hydrogen molecule in its ground state. An amply extended discrete basis set of Gaussian orbitals is employed to minimize basis set errors and single-electron states are generated by the Hartree--Fock V/sup N/ potential. The correlation energy is evaluated through third order and with some higher-order corrections included by denominator shifts to recover about 95% of the total correlation energy. Dipole polarizabilities are calculated through second order in electron correlation with an accuracy of approx.2%. Also the energy-denominator decoupling theorem is explicitlymore » proved by invoking combinatorial analysis to implement extensive denominator shifts. Considering the values obtained, some comments are given on the application of partial summation techniques to molecular problems.« less
  • The region of validity of our previously derived series expansion for the pressure of an electron-ion system in powers of the electron charge is investigated. For the case of Hydrogen, we both assess the radius of convergence of the series, as a function of the de Broglie density, and cross-compare the results with those from the spherical cellular model. These methods more or less agree in an understandable way, and indicate that the region of validity lies well inside the one-phase region. We are then in a position to combine the series results with our experiential knowledge and thus extendmore » our assessment to general values of Z. Also, as is well known, there is a region of high density and low temperature where the pressure and the internal energy are almost independent of temperature. For this region we may, for each density, use the highest temperature for which that independence holds (to the desired accuracy) and thus extend the series results.« less
  • In previous work, we have calculated the expansion of the pressure P of an electron-ion system. This expansion is in powers of the electron charge e. We extended the expansion by adding the e{sup 4} term and gave results for general ion charge Z and general de Broglie density {zeta}. In our present work we now have obtained the expansions for the internal energy U, and the potential and kinetic energy. In addition we have obtained expansions for several, dimensionless, thermodynamic quantities which depend on derivatives of the aforementioned quantities. They are the Griineisen's parameter, {Lambda} = {Omega}({partial_derivative}p/{partial_derivative}U)|{sub {Omega}} wheremore » {Omega} is the volume, the adiabatic exponent {gamma} = {Lambda} = (T/P)({partial_derivative}P/{partial_derivative}T)|{sub {Omega}}-({Omega}/P)({partial_derivative}P/{partial_derivative}{Omega}){sub T} where T is the temperature, and the dimensionless specific heat g = P{Omega}/[T({partial_derivative}U/{partial_derivative}T)|{sub {Omega}}]. These quantities are of interest in the hydrodynamic behavior of fluids, and, in particular, shock and release wave features.« less