87965 - Theoretical and Numerical Aspects of Nuclear Physics

Learning outcomes

At the end of the course the student will learn several theoretical many-body approaches for the description of finite nuclei. Further, he/she will have the ability to devise numerical algorithms implementing the theoretical models. Small student goups will be guided to the development of short projects with the goal of enhancing their teamwork abilities.

Course contents

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.

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 moments 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 potentials (Vlowk and Vsrg) and numerical implementation of the procedure. Bayes estimation of uncertainties

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. Coupled-cluster approach. Fermi hypernetted chains. Numerical implementation for nuclear matter.

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. Neural Networks.

Readings/Bibliography

All lectures and references can be found on the following website

https://virtuale.unibo.it/

https://github.com/paolofinelli/Theoretical-and-Numerical-Nuclear-Physics-Course

Teaching methods

Standard classroom classes.

Lectures will not be recorded

Assessment methods

For those students who regularly follow classes:

Oral examination on a single topic chosen by the student (around 20/30 minutes, at the blackboard) and development of an original numerical project connected to the topics of the course.

For students who do not attend regularly classes 

  Full oral examnination on two/three topics chosen by the teacher

Please fill the corresponding form through Almaesami.

Teaching tools

Slides, notes and reading materials (english and italian language) will be available on the website.

Links to further information

https://github.com/paolofinelli/Theoretical-and-Numerical-Nuclear-Physics-Course

Office hours

See the website of Paolo Finelli