Structure of Finite Nuclei in the LocalDensity Approximation
Abstract
A new theory is presented for calculating the structure of finite nuclei from the nucleonnucleon interaction. The essential features of the reaction matrix in finite nuclei are obtained from nuclearmatter theory through the localdensity approximation. The resulting density and energydependent effective interaction is justified in detail, and it is shown that the tensor force plays an important role in saturation. The effective interaction is cast into two different forms, one convenient for use in calculating matrix elements and the other specialized for a HartreeFock calculation in position space. The densitydependent HartreeFock equations are derived by variation of the groundstate expectation value of the energy, and in addition to the usual HartreeFock terms, one obtains rearrangement terms arising from the variation of the density appearing in the densitydependent interaction. The appropriate angularmomentum reduction for closed jshell nuclei is performed. The need for modifying the effective interaction to account for higherorder corrections is discussed, and the constraints imposed on this modification by the properties of nuclear matter are examined. The results of this theory for O^{16}, Ca^{40}, Ca^{48}, Zr^{90}, and Pr^{208} are shown to yield very satisfactory agreement with experimental binding energies, singleparticle energies, and electron scattering cross sections. The rearrangement terms in the densitydependent theory are demonstrated to have two essential effects on nuclear structure: a significant reduction in the central density of the nucleus, and a modification of the usual HartreeFock relation between singleparticle energies and the binding energy. Equivalent local singleparticle potentials are calculated and are shown to have significant state dependence.
 Publication:

Physical Review C
 Pub Date:
 April 1970
 DOI:
 10.1103/PhysRevC.1.1260
 Bibcode:
 1970PhRvC...1.1260N