English

Synthetic Program:
• The nuclear potential
• The infinite nuclear-matter system
• Microscopic models for finite nuclear systems
• Many-body perturbation theory for finite nuclear systems
• The Similarity Renormalization Group (SRG)
• The In-Medium SRG

General reference books
- Nuclear Forces - Author: R. Machleidt, doi:10.4249/scholarpedia.30710
- An Advanced Course in Computational Nuclear Physics - Editors M. Hjorth-Jensen, M. P. Lombardo, U. van Kolck, Springer.
- A Shell Model Description of Light Nuclei - Author: I. S. Towner, Clarendon Press, Oxford.

LEARNING OUTCOMES:
Students should acquire a general understanding of modern approaches to the nuclear structure problem. In particular, at the end of the course, they should be familiar with 1) the understanding of nuclear forces based on their link with quantum chromodynamics (QCD), 2) the description of nuclear systems in terms of microscopic degrees of freedom, and 3) present status of nuclear structure theory.

KNOWLEDGE AND UNDERSTANDING:
Students will also need to understand how the covered topics come out from the basic principles of QCD and within a picture of nuclei in terms of the degrees of freedom of their constituent nucleons. The verification of knowledge and understanding is done with written and oral tests.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Students should acquire the ability the skills to solve quantum mechanical problems related to the topics listed in the learning outcomes.

MAKING JUDGEMENTS:
It is required the ability to select the best approach to solve the many-body nuclear problem.

COMMUNICATION SKILLS:
It is required the ability to communicate and explain the knowledge acquired to an audience with the prerequisites of present course.

LEARNING SKILLS:
The possibility will be given to deepen some topics covered by means of textbooks and monographs and scientific articles, if required by the interest and understanding. The ability to manage existing scientific literature on the topics covered is required.

Knowledge of Quantum Mechanics and fundamentals of Nuclear Physics

The course is structured in 40 hours of frontal lectures and 12 hours for classroom exercises.
It is highly recommended to attend the classes, but not compulsory, and interact with the teacher.
The course includes classes using the blackboard. Educational material will also be provided for further study after the classes.

During the course the students’ assessment will be performed by written tests that includes one or two problems about topics that have been covered during a specific segment of the course. Students will be allowed consulting one specific text during the written tests.
If the outcome of these tests will not be overall satisfactory, it is mandatory to pass a written test including problems about all topics covered during the course.
Finally, students will take an oral test. The final grade will be expressed in thirtieths.

None

• The nuclear potential: historical overview, theoretical foundations of Effective Field Theory (EFT), nonrelativistic EFT, symmetries and power counting, EFT for nuclear systems, pionless EFT, the two-nucleon s-wave system, the three-nucleon system.
• The infinite nuclear-matter system: basic properties of the nuclear matter, the Fermi gas model, the Brueckner-Hartree-Fock approach, the lowest order Brueckner-Hartree-Fock theory, the equation of state of the infinite nuclear matter.
• Microscopic models for finite nuclear systems: the Hartree-Fock theory, the full configuration interaction theory, the nuclear shell model, the coupled cluster theory.

• Many-body perturbation theory for finite nuclear systems: the Goldstone expansion, the calculation of the Brueckner reaction matrix.
• The Similarity Renormalization Group (SRG): concept, a two-dimensional toy problem, the pairing model, evolution of nuclear interactions.
• The In-Medium SRG: normal ordering and Wick’s theorem, the In-Medium SRG flow equations, decoupling, choice of the generator, In-Medium SRG solution of the pairing Hamiltonian.