SURFACE AND VOLUME PROPERTIES OF GROUND STATE NUCLEAR MATTER IN THE HARTREE- FOCK AND PUFF-MARTIN APPROXIMATIONS

Reynolds, J. C.

doi:10.2172/4742934

Title: SURFACE AND VOLUME PROPERTIES OF GROUND STATE NUCLEAR MATTER IN THE HARTREE- FOCK AND PUFF-MARTIN APPROXIMATIONS

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Abstract

ABS>A method was derived for computing the ground state properties of a spatially inhomogeneous self-bound system of many particles. This method was used to compute the density and effective potential across a plane surface of nuclear matter in the Hartree-Fock approximation and in an approximation developed by R. D. Puff and P. C. Martin which takes into account certain two- body correlation effects. A general theory of many-particle systems was developed in terms of the n-particle field correlation or Green's functions. It is shown that, for zero temperature and pressure, this treatment may be extended to inhomogeneous systems by repiacing the condition of spatial homogeneity on the Green's functions by appropriate asymptotic boundary conditions. Such conditions were derived for a semi-infinite volume of material with a single plane surface. This development was then applied to nuclear matter in the Hartree-Fock approximation. A solution for homogeneous matter was first obtained. A Gaussian interparticle potential was used, with depth and range fitted to low-energy scattering data. Nuclear saturation was produced by using an admixture of exchange forces. The resulting binding energy per particle was -3.63 Mev, and the interparticle spacing was 1.25 fermi. These may be compared with experimental values of -15.75more »« less

Authors:: Reynolds, J. C.

Publication Date:: Mon Oct 01 00:00:00 EDT 1962

Research Org.:: Argonne National Lab., Ill.

OSTI Identifier:: 4742934

Report Number(s):: ANL-6623

NSA Number:: NSA-17-009499

DOE Contract Number:: W-31-109-ENG-38

Resource Type:: Technical Report

Resource Relation:: Other Information: Orig. Receipt Date: 31-DEC-63

Country of Publication:: United States

Language:: English

Subject:: PHYSICS; ATOMS; BINDING ENERGY; CONFIGURATION; DIFFERENTIAL EQUATIONS; ENERGY; ENERGY LEVELS; FIELD THEORY; GAUSS POTENTIAL; GREEN FUNCTION; HARTREE-FOCK METHOD; INTERACTIONS; MANY BODY PROBLEM; MASS; MATHEMATICS; MATRICES; MOMENTUM; NUCLEAR MODELS; NUCLEI; NUMERICALS; OSCILLATIONS; PRESSURE; QUANTUM MECHANICS; S-STATES; SCATTERING; TEMPERATURE; THICKNESS; THOMAS-FERMI MODEL; TRANSPORT THEORY; YAMAGUCHI POTENTIAL

Citation Formats


                    Reynolds, J. C. SURFACE AND VOLUME PROPERTIES OF GROUND STATE NUCLEAR MATTER IN THE HARTREE- FOCK AND PUFF-MARTIN APPROXIMATIONS.  United States: N. p., 1962. 
        Web.  doi:10.2172/4742934.

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                    Reynolds, J. C. SURFACE AND VOLUME PROPERTIES OF GROUND STATE NUCLEAR MATTER IN THE HARTREE- FOCK AND PUFF-MARTIN APPROXIMATIONS.  United States.  https://doi.org/10.2172/4742934

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                    Reynolds, J. C. 1962.  
        "SURFACE AND VOLUME PROPERTIES OF GROUND STATE NUCLEAR MATTER IN THE HARTREE- FOCK AND PUFF-MARTIN APPROXIMATIONS".  United States.  https://doi.org/10.2172/4742934.  https://www.osti.gov/servlets/purl/4742934.

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@article{osti_4742934,

  title        = {SURFACE AND VOLUME PROPERTIES OF GROUND STATE NUCLEAR MATTER IN THE HARTREE- FOCK AND PUFF-MARTIN APPROXIMATIONS},

  author       = {Reynolds, J. C.},

  abstractNote = {ABS>A method was derived for computing the ground state properties of a spatially inhomogeneous self-bound system of many particles. This method was used to compute the density and effective potential across a plane surface of nuclear matter in the Hartree-Fock approximation and in an approximation developed by R. D. Puff and P. C. Martin which takes into account certain two- body correlation effects. A general theory of many-particle systems was developed in terms of the n-particle field correlation or Green's functions. It is shown that, for zero temperature and pressure, this treatment may be extended to inhomogeneous systems by repiacing the condition of spatial homogeneity on the Green's functions by appropriate asymptotic boundary conditions. Such conditions were derived for a semi-infinite volume of material with a single plane surface. This development was then applied to nuclear matter in the Hartree-Fock approximation. A solution for homogeneous matter was first obtained. A Gaussian interparticle potential was used, with depth and range fitted to low-energy scattering data. Nuclear saturation was produced by using an admixture of exchange forces. The resulting binding energy per particle was -3.63 Mev, and the interparticle spacing was 1.25 fermi. These may be compared with experimental values of -15.75 Mev and 1.1 to 1.2 fermi. The inhomogeneous geometry was then considered. A short development was made of an approximation analogous to the Thomas-Fermi approximation in atomic physics, but it is shown that this approach breaks down for nuclear matter and leads to inconsistencies because of the exchange nature of the forces. A numerical solution for the inhomogeneous geometry was then obtained by an iterative self-consistent procedure, using an effective mass approximation. The thickness of the resulting surface (the distance over which the density drops from 90 to 10% of its asymptotic value in the interior) was 2.01 compared with experimental value of 2.5 plus or minus 0.2 fermi, and the density function exhibited oscillations near the surface due to the sharpness of the edge. The effective potential was strongly momentum-dependent but is nearly isotropic. A similar treatment was carried out for the Puff-Martin approximation. In this approximation the effective potential becomes an energy dependent function which is expressed as a folding integral of the spectral function of the system and a two-body scattering matrix. An ambiguity in the definition of the pressure appeared in the approximation; it was resolved by showing that a pressure expression derived from local-transport considerations must be used to insure the existence of time- independent solutions for the inhomogeneous case. Puff was followed in using an interparticle potential consisting of a separable Yamaguchi potential plus an S- state repulsive hard shell. In the homogeneous case the approximation led to a binding energy per particle of -14.4 to -17.5 Mev and an interparticle spacing of 0.871 to 1.01 fermi (depending on which expression for the pressure is set equal to zero to obtain an uncompressed system). A computation of the density correlation function is given. The inhomogeneous case was again treated by an iterative self-consistent procedure with an effective-mass approximation. The results gave a surface thickness of 2.33 fermi and a surface energy of 18.79 Mev, which may be compared with experimental values of 2.5 plus or minus 0.2 fermi and 17.804 Mev. As in the Hartree case, the effective potential was nearly isotropic, but there was no significant oscillations inside the surface. (auth)},

  doi          = {10.2172/4742934},

  url          = {https://www.osti.gov/biblio/4742934},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Mon Oct 01 00:00:00 EDT 1962},

  month        = {Mon Oct 01 00:00:00 EDT 1962}

}

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