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'Classical' Self-Consistent Nuclear Model. II

Jul 1, 1963
10 pages
Published in:
  • Phys.Rev. 131 (1963) 355-365
DOI:
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Abstract: (APS)
The gross energetics and sizes of the stable nuclei are accurately reproduced by a simple model of nuclear structure using Thomas-Fermi approximation. Saturation is obtained by taking the (spatially Yukawa) two-body interaction to be (quadratically) momentum-dependent. Coulomb effects and neutron-proton mass difference are included. The two coupled nonlinear integral equations for neutron and proton spatial distributions are integrated. The system of equations is made unique by the choice of only four input parameters, and these parameters are optimized by requiring a best fit of the solution to the binding-energy-per-nucleon and neutron-proton-ratio curves as a function of A. The optimum parameter values are reasonable. The Yukawa force range is found to be about 40% of ℏ(mπc). A small but definite excess of neutron radius over proton radius is found, and also a slight depression of the central proton density for the heavier nuclei. Satisfactory agreement with measured radii and surface thicknesses is obtained.