THE RELATIVISTIC MEAN-FIELD EQUATIONS OF THE ATOMIC NUCLEUS

摘要

In nuclear physics, the relativistic mean-field theory describes the nucleus as a systemnof Dirac nucleons which interact via meson fields. In a static case and without nonlinearnself-coupling of the σ meson, the relativistic mean-field equations become a system ofnDirac equations where the potential is given by the meson and photon fields. The aimnof this work is to prove the existence of solutions of these equations. We consider anminimization problem with constraints that involve negative spectral projectors andnwe apply the concentration-compactness lemma to find a minimizer of this problem. Wenshow that this minimizer is a solution of the relativistic mean-field equations considered