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 websites: https://virtuale.unibo.it/

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

Reference text:

M. Hjorth-Jensen, "An Advanced Course in Computational Nuclear Physics," Springer Ed.

Teaching methods

Frontal lessons on the blackboard or with the use of slides.

Lectures will not be recorded.

Assessment methods

For students who attend classes regularly: Oral exam on a single topic of the student's choice (approximately 20-30 minutes, on the blackboard) and development of an original numerical project related to the course topics (the list of available projects and all project evaluation details are available at the following link).

Both exams contribute equally to the final grade.

For students who do not attend classes regularly: Full oral exam on two or three topics of the instructor's choice.

Failure to attend will not be considered a negative factor in the grade.

In both cases, the purpose of the oral exam is to assess the student's ability to apply their knowledge and make the necessary logical-deductive connections.

Oral grade grading:

Limited presentation and analytical ability that emerges only with the instructor's assistance; overall correct language expression → 18-24;

Ability to study and analyze independently on a sufficiently broad range of topics, ability to make independent critical analysis choices, mastery of specific terminology → 25-29;

Substantially comprehensive preparation on the topics covered in the course, ability to make independent critical analysis and connection choices, full mastery of specific terminology, and ability to argue and self-reflect → 30-30L.

Students with learning disabilities (LD) or temporary or permanent disabilities: Please contact the relevant University office in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/it). They will be responsible for suggesting any adaptations to the students concerned. However, these must be submitted to the instructor for approval 15 days in advance, who will evaluate their suitability also in relation to the course's learning objectives.

Please contact the instructor to schedule the exam.

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