Microscopic theory of elememtary excitations of nuclei

The theory of the elementary excitations of the nuclei in a formalism particularly adapted to the uses of the forces depending on density is presented. It is shown how the total energy of the nucleus is calculated from the effective interaction. This energy is considered as being a functional of the one body density matrix; from this is derived the mean field and the particle hole interaction which enable the Hamiltonian to be constructed for the elementary excitations. Green's functions with one or two particles are used for comparing this theory with Migdal's, to give a consistant framework to the calculation of processes bringing in the particle-vibration coupling, and to understand the nature of the particle-hole interaction in relation with the particle-particle interaction. As an illustration, two solvable models are presented. In the first one the particle-hole interaction is separable and the second one studies the response function in the nuclear matter at the boundary of weak transfer moments (damping of the collective mode, collective modes in infinite systems)