# NUCLEAR STRUCTURE

**Academic Year 2022/2023**- Teacher:

**FRANCESCO CAPPUZZELLO**

## Expected Learning Outcomes

**Learning ability**

The course aims at two specific objectives of knowledge achievements and learning abilities

1. To deepen some basic questions concerning the structure of the atomic nucleus, as an object of fundamental research. In this sense, the nucleus is represented, during the classes, as a particular form of aggregation of matter that we are presently not in condition to describe, starting from the elementary constituents of matter (quarks, gluons, etc.). Rather, the nucleons represent the effective "elementary" constituents through which a description, albeit partial, of the rich known phenomenology is possible. Students learn that the relatively large number of nucleons and the non-existence of a "universal" analytical form of the nucleon-nucleon potential in the nuclear medium limit the possibility of a microscopic description of the nuclear structure. For the opposite reason, the techniques of statistical mechanics find a difficult place in this research landscape. Therefore specific treatments of the many-body system with hypothetical-deductive approaches, based on models, represent the most important cultural figure of this discipline, and as such they are discussed in class. Particular emphasis is also given to collective models, particularly effective in the description of rotations and vibrations of the nuclei. The cultural project of the course focuses in particular on:

Critical acquisition of the model concept in the problem of nuclear structure

Concept of mean field and physical significance of single nucleon orbital

Concept of residual interaction for the study of excited states

Concept of collective motion and collective degrees of freedom

2. Provide the necessary tools and updates for a subsequent and possible in-depth work on issues related to both experimentation and the theory of modern research in the field of nuclear structure. This aspect is taken care of by proposing different links and

similarities between the concepts developed in class and the most modern research themes in this field. In particular, the course includes

A panoramic description of the main ideas characterizing the historical evolution of the physics of the nuclear structure

A description of the most effective experimental techniques, with guided visits to the "INFN - Laboratori Nazionali del Sud" and contextual familiarization with the complex instrumentation present therein

Indication of the main unresolved problems and current research trends

**Ability to apply the achieved knowledge**

The description of the structure of the atomic nucleus as a highly complex system of strongly interacting nucleons is particularly adequate to stimulate the student's ability to identify the most relevant aspects of a problem. Furthermore, the peculiar relevance of approximations in this field of physics, the reduction of theories in models, the need for increasingly complex experimental approaches, allows the student a deeper understanding of the sense of approximation. The continuous comparison between the concept of nuclear and atomic nuclear fields and the relevance of certain nuclear quantities in the processes of stellar evolution allow a fruitful connection between apparently distant fields of research. The mathematical tools required and preparatory are essential for the demonstrations that are proposed in class and that are required for the exams.

**Communication skills**

Most of the texts and articles proposed as educational material are in English and this provides a useful stimulus for the student's understanding of scientific language. Moreover, the powerful graphical representation of correlations between physical quantities present in the didactic material increases the student's ability to search for the best possible form in the description of a phenomenon.

## Course Structure

Frontal lectures on blackboard in english language. (5 CFU total of 35 hours + 1 CFU laboratory activity (15 hours). A visit at the INFN-LNS laboratory is also foreseen.

Should the circumstances require online or blended teaching, appropriate modifications to what is hereby stated may be introduced, in order to achieve the main objectives of the course.

## Required Prerequisites

**Required preparatory learning in Physics**

###### · Quantum mechanics (necessary)

###### · Elettro-magnetism (necessary)

###### - Nuclear reactions (suggsted)

###### · Perturbation theory and varational methods (necessary)

###### · Working principles for radiation detectors (suggested)

**Required preparatory learning in Mathematics**

###### · Mathematical methods for quantum physics (necessary)

###### · Second quantization methodology (necessary)

## Attendance of Lessons

The participation to the lectures is obligatory as a rule (please read the "Regolamento Didattico del Corso di Studi")

## Detailed Course Content

Structure of nuclei

The use of models in nuclear physics. Degrees of freedom and nuclear structure. Fermi gas model. Magic numbers. Hypothesis of mean field and concept of orbits of nucleons. The nuclear spin-orbit interaction. Model of Meyer, Haxel, Jensen. Magnetic dipole moment. Schmidt lines. Electric quadrupole moment. Static deformations. Excited states. Microscopic foundation of the shell model. Hartree-Fock theory. Direct and exchange forces. Particle-hole interaction. Mixing of configurations. Spectroscopic factor. Deep-hole states. Shell model with many particles. Shell model calculation methods. Cavedon experiment. Deformed potential model. Nilsson diagrams. Rotational motions. Rotational bands. Backbending. Vibrational motions. Bohr Hamiltonian. Dynamic deformations of the nuclear surface. Giant resonances. Sum rules. Macroscopic models. Hydrodynamic model of Steinwedel-Jensen. Microscopic models. Tamm-Dancoff theory. RPA approximation. Pairing vibrations. Giant pairing resonance. Nuclear response to isospin operators. Isobaric Analogue State and Gamow-Teller giant resonance. Clustered structures. Clusters in self-contained light nuclei. Hoyle state. Branching ratio α of nuclear states. Non-autoconjugated nuclei. Model of Hafstad and Teller. Validity of the clusters model. The role of symmetries in nuclei. Continuous and discrete symmetries. The interacting boson model.

## Textbook Information

**Suggested books:**

Suitable material prepared by the professor will be available for the students.

1. K.S. Krane, Introductory Nuclear Physics, Wiley and Sons Ltd.

2. W.S.C. Williams, Nuclear and Particle Physics, Oxford University Press.

3. K.L.G. Heyde, Basic Ideas and Concepts in Nuclear Physics, Institute Of Physics Publishing, series Editor D.F. Brewer.

4. W. Greiner, J.A. Maruhn, Nuclear Models, Springer Verlag.

5. A. Bohr, B.R. Mottelson, Nuclear Structure, World Scientific.

6. P. Ring, P. Schuck, The Nuclear Many-Body Problem, Springer.

7. M.A. Preston, R.K. Bhaduri, Structure of the Nucleus, Westview Press.

## Course Planning

Subjects | Text References | |

1 | All the items of the program are considered fundamental | Notes of the professor |

2 | Shell model | Heyde: chapters 9-10-11; Krane: chapter 5 |

3 | Collective models | Heyde: chapters 12; Krane: chapter 5 |

4 | Giant Resonances | Greiner: Chapters 6-8 |

## Learning Assessment Procedures

The assessment of learning is based on an oral examination. On this occasion the student's ability to express the concepts developed during the classes and the completeness of the preparation with respect to the program carried out is evaluated. It is examined in particular

* the ability to demonstrate concepts that can be expressed mathematically (demonstrations of theorems and formalization of relationships between physical quantities);

* the critical capacity in the comparison between models and experimental data;

* the knowledge of the orders of magnitude of the main physical quantities characteristic of the nuclear structure;

* the knowledge of the most relevant correlations between quantities through the graphical representation as discussed in class.

Exams may take place online, depending on circumstances.

The exam consists of a dozen questions distributed throughout the program, of which at least three provide for the full demonstration of theorems to highlight relationships between physical quantities, at least three provide the commentary on the comparison between theoretical models and experimental data, at least three the description of experimental techniques or measures of physical quantities, at least one knowledge of the approximate value of relevant physical quantities.