Contents and bibliography (some additional bibliography can be found in the forked repositories)
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Basic notions of nuclear physics and its main theoretical aspects essential to the development of the course. Second quantization elements: creation and destruction operators of single particles for bosons and fermions. Representation of states and operators. Calculation of amplitudes and matrix elements. Field operators. Wick's theorem. Algebra of angular momentum.
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Nuclear potentials. Phenomenology of nuclear potentials (phase-shifts, scattering lengths, effective ranges). Non-relativistic formulation in the space of coordinates and relativistic in the space of momenta with particular attention to the most recent chiral approaches. Scattering theory. Lippmann-Schwinger equation (analytical treatment and numerical solution with Gauss integration). Comparison with experimental data. Theoretical description and numerical treatment of deuteron. Three-body forces. Faddeev equations for systems interacting for few-body systems. Application of the renormalization group to nuclear potential (Vlowk and Vsrg) and numerical implementation of the procedure.
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Many-body approaches to nuclear physics. The concept of the mean field: empirical evidence in atomic and nuclear systems. Shell model approach to the nuclear problem of many body: mean field and residual interaction. Hartree's method for the description of the fundamental state. Iterative method for self-consistent solutions. Introducing the Pauli principle and Hartree-Fock equations. The local and non-local mean field. Numerical implementation. Perturbation theory for many-body systems: time evolution operator, Gell Mann-Low theorem, Goldstone theorem, Feynman-Goldstone diagrams. Brueckner theory for infinite systems: correlation energy, correlated wave functions, Jastrow factors. Numerical implementation for nuclear matter.
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Monte Carlo methods. Introduction to stochastic methods: central limit theorem, Markov chains, error estimates. Metropolis method. Introduction to the Diffusion Monte Carlo and Variational Monte Carlo approaches also through numerical simulations and code development.