Nuclear Shapes and Nuclear Structure at Low Excitation Energies: Theoretical Aspects

Abstract

In describing nuclear structure and observables that give information on the nuclear shape at low excitation energy, one has to outline the different approximation methods with which to describe the interacting A-nucleon system as close as possible. In the present discussion we shall describe three approximation schemes that contain most of the theoretical efforts carried out up to now. In a first approximation we start from a spherical Hartree-Fock field to which the effects of residual interactions amongst a number of valence nucleons are added. This method presents its limitations when the number of valence nucleons is increasing so that the residual interaction energy becomes a substantial part of the total nuclear binding energy. We shall discuss various “signals” indicating a breakdown of this spherical shell-model approach. In a second approximation, the concept of shape is introduced from the very beginning and the importance of various multipole field producing interactions in accentuated. Here, the importance of the proton-neutron interaction is illustrated from a more microscopic approach. We present some state-of-the-art studies in this field. In a third approximation, the importance of symmetries in outlining basic low-lying nuclear structure properties is discussed. In this respect, the role played by various group-theoretical methods (such as the interacting boson model (IBM)) will be presented.