# Nuclear and Subnuclear Physics Elements

Module MODULO 1

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

**Francesca RIZZO**

## Expected Learning Outcomes

The student will acquire knowledge of nuclear phenomena, nuclear structure, nuclear interactions, radioactive decays laws and basic concepts related to nuclear collisions. The issues are introduced by describing the phenomenology, the approach used in the measurements and a qualitative and, where possible, quantitative description of the described nuclear phenomena is given. In learning the main theoretical models through which the nuclear structure is studied, the student will also use many concepts acquired in previous courses or which run in parallel with the course in question.

With reference to the Dublin Descriptors, this course contributes to acquiring the following soft skills:

__Knowledge
and understanding__

At the end of the course students will have developed inductive and deductive reasoning skills.

They will have acquired the main notions underlying the experimentation and phenomenology that led to the description of nuclei and their interactions. They will know the laws and properties of radioactive decays, the structure of nuclei and will know the principles underlying the models that describe the nucleons organization inside the nucleo.

__Ability
to apply knowledge:__

With the knowledge acquired, students will be able to enrich their knowledge of the topics covered in more advanced courses of their study path.

__Autonomy
of judgment:__

Acquisition of critical reasoning skills

__Communication
skills__

Good skills in tools for the management of scientific information and bibliographic research.

Ability to present an argument orally, with properties of language and appropriate scientific terminology, explaining the motivations and results.

__Learning
ability__

Ability to know how to update their knowledges by reading scientific publications, in Italian or English, in the various fields of physical disciplines, even if not specifically studied during their University studies.

## Course Structure

The Course is structured in about 13 weeks, 4 hours of frontal lectures each week.

During the lesson period a guided tour is carried out at the Laboratori Nazionali del Sud-INFN Catania, during which the activities carried out by researchers in the field of Nuclear Physics are illustrated, also in connection with research in collaboration with Universities and Research Institutes Italian and Foreign.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the program planned and outlined in the Syllabus.

## Required Prerequisites

Essential knowledge: General Physics, Derivatives, Integrals, Differential Equations.

## Attendance of Lessons

Attendance to the course is usually obligatory (consult the Academic Regulations of the Course of Studies)## Detailed Course Content

The duration of the course is about 13 weeks. For each week there are 2 lectures, 2 hours each.

__Atoms and
nuclei__: Size and shape. Mass defect and Nuclear binding energy . Weisszacher formula.
Nuclear Instability
in alpha-decay, beta-decay and Spontaneous Fission. (1^{st}week)

__Decays__: The
radioactive decay law. Half-life. Multimodal decays. The production of
radioactive material.
Sequential decays. Transition rate. 14C dating method. ( 2^{nd}week)

__Alpha
decay: __Coulomb barrier penetration. Gamow factor. Angular momentum barrier.
Decay schemes involving
alpha-particle emission. Geiger-Nuttal formula. Schrodinger equation in polar
coordinates. Angular momentum conservation. (3^{rd} week)

__Nuclear
Model: __The nuclear binding energy. The liquid drop model. Fermi gas model. Shell model. Nuclear energy levels. Wood-Saxon
potential. Spin-orbit interaction. Magic numbers. Splitting of energy levels. (4^{th}week) . Bound and
virtual levels. Excited states. Spin and parity. Residual interaction in shell
model and pairing. (5^{th}week)

__Nuclear
spin and Moments__: Nuclear spin. Magnetic and electric Moments. Bohr magneton.
Nuclear magneton.
Schmidt lines. (6^{th}week). Multipole electric moment. Electric
Quadrupole moment and deformed Nuclei.
Rotational and vibrational bands. Nilsson levels. (7^{th}week)

__Beta decay:
__Energy release in beta decay. Golden Rule n.2. Fermi Theory. Angular momentum
and parity
selection rules. Fermi (F) and Gamow-Teller (G-T) allowed transitions.
Forbidden decays. (8^{th}week) . Beta spectrum, end-point. Kurie-plot. (9^{th}week)

__Gamma
decay: __Energetics of gamma decay. Classical electromagnetic radiation.
Transition to quantum
mechanics. Angular momentum and parity selection rules. (10^{th}week) . Internal conversion. Weisskopf estimation. Metastable
states. (11^{th}week)

__Nuclear
collisions: __Q-value. 2-body kinematics: study in the laboratory and in the C.M
reference frame. Threshold energy. Elastic, inelastic and reaction cross
section. Solid angle. (12^{th} week). Direct and Compound Nucleus
reaction mechanisms. Cross section resonances in C.N. mechanisms. Breit-Wigner formula. Measurement of the
experimental differential cross section. (13^{th} week)

## Textbook Information

- H.A.Enge: Introduction to Nuclear Physics (Addison Wesley Pub.Co.)
- J.S.Lilley: Nuclear Physics- Principles and Applications (J.Wiley&Sons, Ltd)
- B. Povh, K. Rith, C. Scholz, F. Zetsche: Particelle e nuclei. Un' introduzione ai concetti fisici (Bollati Boringhieri)
- W .S.C. Williams: Nuclear and Particle Physics, (Claredon Press, Oxford)

## Course Planning

Subjects | Text References | |

1 | 1. The atomic nucleus (4 hours) | 1 Cap 1; 2 Cap 1.3; 3 Cap 2.3 |

2 | 2. Radioactive decay (4 hours) | 1 Cap 8; 2 Cap 1.5; 3 Cap 3; 4 Cap 2 |

3 | 3. Alpha decay (4 hours) | 1 Cap 10; 2 Cap 3.4; 4 Cap 6 |

4 | 4.Nuclear model (8 hours) | 1 Cap 6, 2 Cap 2.3 2.4 2.5; 4 Cap 8; 3 Cap 17.3 |

5 | 5.Nuclear momenta (8 hours) | 1 Cap 5; 3 Cap 17.3; 4 Cap 4 |

6 | 6. Beta decay (4 hours) | 1 Cap 11; 2 Cap 3.3; 3 Cap 17.3; 4 Cap 12.5-12.7 |

7 | 7. Gamma decay (8 hours) | 1 Cap 9; 2 Cap 3.2; 4 Cap 11.6-11.9 |

8 | 8. Nuclear collisions (4 hours) | 1 Cap 13; 2 Cap 1.6 |

## Learning Assessment Procedures

The exam consists of an oral discussion that focuses on the topics covered in the course.

It can also be carried out on-line, should the conditions require it.

N.B .: The exam relating to Nuclear and Subnuclear Physics Institutions Course (Mod.1 + Mod.2; 6 + 3 CFU) is unique for the 2 Modules and takes place simultaneously in the presence of the 2 Teachers. The final evaluation for 9 CFU, is also unique.

It is possible to consult the exams calendar on the website of the L30-Physics degree course.

## Examples of frequently asked questions and / or exercises

The following list is not exhaustive, just a few examples are reported:

Main models for the atomic nucleus.

Energetics of alpha, beta decay and spontaneous fission.

Electric and magnetic moments of the nucleon and of the nucleus.

Alpha decay.

Beta decay.

Gamma decay.

Nuclear reactions: exoenergetic and endoenergetic.

Kinematics of nuclear reactions