### Speaker

### Description

The nuclear shell model [1] is a well developed theory for the calculation of finite nuclei properties. Its main idea is simple: a non-relativistic A-nucleon Hamiltonian, containing nucleonic kinetic energies and inter-nucleon interactions, is diagonalized in a spherically-symmetric harmonic-oscillator basis. For light nuclei, the model treats all A nucleons as active particles occupying a large-dimensional model space comprised from many oscillator shells, representing thus a fully ab-initio many-body approach referred to as no-core shell model [2]. However, a rapid growth of the basis dimension with the number of nucleons prohibits such calculations for heavier nuclei. A common practice to limit the number of basis configurations is proposed by the interacting shell model which assumes an inert core (usually being a doubly-closed shell nuclei) and treats only valence nucleons as active particles moving in a model space comprised from one or two oscillator shells. Such severe truncation of the Hilbert space requires a consistent derivation of the so-called effective interaction for valence nucleons. Phenomenological effective interactions, obtained from a fit to experimental data [1,3], usually demonstrate a high descriptive and predictive power of the shell model. Construction of microscopic effective interactions from realistic nucleon-nucleon potentials has been a long-standing problem of nuclear theory which stays challenging up to present [4,5]. In this talk I will present novel developments within many-body perturbation theory which allows derivation of effective valence-space shell-model interactions from a nucleon-nucleon potential for the first time beyond the conventional 3rd order. Both harmonic-oscillator basis and self-consistent Hartree-Fock basis were implemented to investigate convergence properties of the theory with respect to the model-space parameters. As an example of application, we will consider in detail effective interactions for the p-shell obtained from the Daejeon16 nucleon-nucleon potential [6]. Calculated ground state energies and spectra of A=6 systems will be compared with those obtained from the phenomenological p-shell interaction [3] and with the results from the no-core shell model [6]. Finally, I will show ground-state energies and spectra of selected p-shell nuclei obtained from the derived effective interactions.

**[References]**

[1] E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker, The Shell Model as a Unified View of Nuclear Structure, Rev. Mod. Phys. 77, 2 (2005).

[2] B. R. Barrett, P. Navrátil, and J. P. Vary, ab initio No Core Shell Model, Progress in Particle and Nuclear Physics 69, 131 (2013).

[3] S. Cohen and D. Kurath, Effective Interactions for the 1p Shell, Nucl. Phys. 73, 1 (1965).

[4] M. Hjorth-Jensen, T. T. S. Kuo, and E. Osnes, Realistic Effective Interactions for Nuclear Systems, Physics Reports 261, 125 (1995).

[5] S. R. Stroberg, H. Hergert, S. K. Bogner and J. D. Holt, Non-empirical interactions for the nuclear shell model: an update, Ann. Rev. Nucl. Part. Sci. 69, 307 (2019).

[6] A. M. Shirokov, I. J. Shin, Y. Kim, M. Sosonkina, P. Maris, J. P. Vary, N3LO NN interaction adjusted to light nuclei in ab exitu approach, Phys. Lett. B 761, 87 (2016).