Effects of mass operator energy dependence in atomic nuclei: Quasiparticle lagrangian versus quasiparticle hamiltonian

Different effects of the mass operator energy dependence are discussed. They are calculated within the framework of the Hartree-Fock (HF) method with effective forces as RPA corrections to the HF ground state. In the quasiparticle Lagrange method (QLM) they arise naturally and are taken into account in the self-consistent procedure itself. Approaches with the quasiparticle lagrangian and quasiparticle hamiltonian are compared. It is shown that the QLM can also be formulated with the help of the hamiltonian, but a simple lagrangian corresponds to a very complicated hamiltonian. Arguments in favour of the simple lagrangian are presented.