Abstract
Abstract : This document investigates the so-called Hartree-Fock theory arising in the study of the structure of nuclii. The Hartree-Fock theory is an approximation method of many-body problems modelling the interaction of nucleons (netrons and protrons), which lead to nonlinear variational systems fo elliptic equations (the Hartree-Fock equations). These equations pertain to questions related to Spin dependence and Spin orbit forces, Symmetries of the nucleus and symmetry breakings and time dependent Hartree Fock equations. One of the main features of these problems is the tranlation invariance which creates compactness difficulties which are overcome by the use of the concentration-compactness method. Keywords: Nonlinear Schrodinger equations; and Nuclear physics.
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