# Nuclear structure and reactions

## Exactly solvable many-body problems

The investigation is focused on the exactly solvable many-body problems and the application of such solutions in the analyses of fundamental interactions and systems such as atomic nuclei and other complex many-body systems. A two-body interaction is often sufficient ingredient for the description of A-body systems since three- and more particles rarely come in close proximity simultaneously. However, based on the Chiral Perturbation theory approach to the effective nuclear interaction, it has been shown that three-nucleon interactions in the structure of light nuclei are important. Оur research projects aim at exploring the A-body interactions paradigm; in particular, the role of the three- and four- nucleon QCD derived effective interactions in nuclei; as well as charting the limits of applicability of the exactly solvable extended A-body pairing interaction to nuclei and other complex systems.

## Nucleon correlations beyond the nuclear mean field

Approximating the correlated ground state of a many-body quantum system has been receiving considerable attention since the early days of nuclear structure physics and degenerate electron gas theory and still represents a formidable challenge. This is an arduous task within the “beyond the mean-field” theories because of the action of the residual interaction which brings particle-hole admixtures into the ground states. This problem constitutes a major challenge to nuclear theory as it lends hope to establish a link between the smoothly varying quantities predicted by the fluid dynamics inspired nuclear models and the abrupt behavior prescribed by the mean field. We mainly focus on the effects of **long-range** part of this interaction. The short-range residual forces, on the other hand, compete with the long-range ones in dominating the ground-state shapes formation. As a result of this competition, in the beginning and the end of major shells the nucleons are paired, giving rise to spherical shape, while in the middle of the shell the nucleons are paired off and they align to the field generating forces thus contributing to deformation. We are trying to lay the foundations of a novel approach to investigate the mechanism of the transition between these two regimes and in particular on the pairs decoupling process.

The timeliness of this research topic is very high due to the start of operation of several facilities for rare isotope beams which permit to explore new patterns in nuclear structure in areas where the many-body correlations, rather than the nuclear mean field, dominate.

### Group members

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### References

- Petr Navratil, V. G. Gueorguiev, J. P. Vary, W. E. Ormand, and A. Nogga, “Structure of A = 10 -13 nuclei with two- plus three-nucleon interactions from chiral effective field theory,” Phys. Rev. Lett. 99, 042501 (2007)
- J. Dukelsky, V. G. Gueorguiev, P. Van Isacker, S. Dimitrova, B. Errea, and S. Lerma H., “Exact Solution of the Isovector Neutron-Proton Pairing Hamiltonian,” Phys. Rev. Lett. 96, 072503 (2006)
- F. Pan, V. G. Gueorguiev, and J. P. Draayer, “Algebraic Solutions of an Extended Pairing Model for Well-Deformed Nuclei,” Phys. Rev. Lett. 92, 112503 (2004)
- S. Mishev, Structure of the phonon vacuum state, Phys. Rev. C 87, 064310 (2013)
- S. Mishev and V. V. Voronov, Effects of ground state correlations on the structure of odd-mass spherical nuclei, Phys. Rev. C 78, 024310 (2008)
- S. Mishev and V. V. Voronov, Extended approximation for the lowest-lying states in odd-mass nuclei, Phys. Rev. C 82, 064312 (2010)