SUR LA DÉTERMINATION DES PREMIERS ÉTATS D'UN SYSTÈME DE FERMIONS DANS LE CAS DÉGÉNÉRÉ

Abstract

Abstract The linked diagram expansion of the ground state energy and wave function of a system of fermions are extended to the case where the ground state of the unperturbed system is degenerate, as, for instance, in a nucleus with an incomplete shell. The state where all the complete shells are filled is taken as vacuum state. It is then shown, to all orders in the perturbation expansion, that the energy of the first levels is given by the sum of two terms. The first term, is the energy of the core alone and is given by a linked diagram expansion of the usual form. The second term is the energy of the particles outside the core. It is obtained by solving an eigenvalue problem in the space of the degenerate unperturbed wave functions. The corresponding eigen-functions are given by linked diagram expansions very similar with the usual ones. A few generalizations of the method, and its relation to the Brillouin-Wigner perturbation method are discussed.