Nuclear physics

In atomic nuclei, the strong interaction binds protons and neutrons, turning them into complex systems. These systems are typically studied either as many-body systems (using methods such as the shell model or QRPA-type mean field) or as few-body systems. Few-body methods are useful not only for nuclei formed by a small number of particles but also for studying correlations in N-body systems. Furthermore, few-body mathematical models are valid not only for studying nuclei but also for molecules and atoms, and their potential is still far from being fully exploited. The theoretical investigations of such quantum systems are complex and simultaneously necessary for an adequate description of them. The type of systems we study, which are mostly weakly bound nuclei in the proton or neutron drip regions, or excited states of more bound nuclei, are also being investigated experimentally at facilities such as TRIUMF (Canada), GANIL (France), RIKEN (Japan), or the future FAIR (formerly GSI, Germany).

To describe three-body systems, we use the adiabatic expansion in hyperspherical harmonics, which involves describing the three-body wave function using the eigenvectors of the angular part of the Hamiltonian, which has been previously diagonalized for fixed values of the hyperradius. The appropriate coordinates to describe the system would be the Jacobi coordinates. If we also rotate the radial coordinates in the complex plane and allow the energies to be complex (complex scaling), we can study resonances as if they were bound states.

We have studied systems as interesting as ¹²C, which is of vital importance in stellar nucleosynthesis, ⁹Be, and ⁶Be, and there are still many potential candidates in the lower part of the nuclear chart, whether they are halo nuclei (¹¹Li, ²⁹F, etc.) or two-proton or two-neutron emitters (¹²Be, ¹²O, etc.).