Department of Physics

Methods

The FIDIPRO project will use and develop most advanced theoretical methods in nuclear structure.

The research plan of the project will focus on key directions of the present-day nuclear structure theory, namely, mean-field description of nuclei across the mass table based on the energy-density-functional methods and symmetry-restoration techniques, shell-model description of light nuclei including derivations of interactions for exotic systems, description of excited nuclear states within the RPA and GCM methods, description of quadrupole collective states including full rotation-vibration-pairing coupling, and description of states near drip-lines that are strongly coupled to open channels. Within these directions, the team will pursue specific investigations by using present and acquired competence of its members, attempting as large as possible covering of the field.

Spontaneous symmetry breaking effects are at the heart of the mean-field description of highly correlated many-body systems. A large part of those correlations can indeed be included by considering symmetry-breaking product states. Within the mean-field approach, one can understand many physical observables by directly employing broken-symmetry states, however, for finite systems quantitative description often does require symmetry restoration.

In the present project, we intend to develop methods that would allow for self-consistent variational calculations after restoring the particle number symmetry. In these way one can properly describe transitions between normal and superconducting phases in finite systems, which are inherent in (semi)magic nuclei, and also improve on uncertainties related to currently used approximate projection method of Lipkin-Nogami.

We also intend to study isospin-symmetry-breaking effects by carrying out the exact isospin-symmetry restoration. This problem has two aspects: (i) unphysical isospin-symmetry breaking caused by the mean-field approximation, and (ii) physical symmetry breaking (isospin mixing), mainly caused by the Coulomb force, which requires rediagonalization of the Hamiltonian within a basis of good-isospin states. A better understanding of isospin-symmetry-breaking effects is essential for a proper description of the so-called superallowed beta decay. We also intend to investigate the role of isospin symmetry in the study of the T=0 p-n pairing, where we plan to analyze the spatial point symmetries and the relation between the T=0 superconductivity and the spin-orbit forces.

We plan to investigate vibrational and rotational correlation effects by implementing corrections to the mean field based on the Gaussian overlap approximation to the generator coordinate method and on the adiabatic approximation. We intend to work out approximations that would allow avoiding full-scale collective calculations, but would be based on calculations performed on the top of self-consistent mean fields. These methods will be applied both to the ground-state masses and spontaneous fission. In a similar fashion, we plan to treat dynamical corrections related to pair vibration effects.