Academic Year 2022/2023 - Teacher: MARIA COLONNA

Expected Learning Outcomes

The course aims to provide the basic elements of scattering theory applied to collisions between nucleons and to nuclear reactions. We also want to introduce the student to the treatment and phenomenology of heavy ion reactions at intermediate energies, from fusion and deep-inelastic reactions to the liquid-gas phase transition in nuclear matter. The approach followed is theoretical-phenomenological.

Knowledge and understanding. 

Critical understanding of the most advanced developments of Modern Physics, both theoretical and experimental, and their interrelations, also across different subjects. Remarkable acquaintance with the scientific method, understanding of nature, and of the research in Physics. During the course the student will understand the main nuclear reaction mechanisms, from low to intermediate energies, framing them in the current context of research in nuclear physics, and will acquire the main theoretical tools for the description of such processes.

Applying knowledge and understanding.

Ability to identify the essential elements in a phenomenon (concerning nuclear reactions and the behavior of nuclear matter), in terms of orders of magnitude and approximation level, and being able to perform the required approximations. Ability to use analogy as a tool to apply known solutions to new problems, related to the description of new nuclear processes of present  interest (problem solving).

Communication skills.

Ability to discuss about advanced physical concepts, both in Italian and in English. These skills will be developed in the context of the communication of issues related to the dynamics of nuclear reactions and the properties of nuclear matter.

Learning skills.

Ability to acquire adequate tools for the continuous update of one's knowledge. Ability to access to specialized literature both in the specific field of nuclear reactions, and in closely related fields.

Course Structure

The course includes lectures (5 CFU = 35 hours), mainly on the blackboard, and some hours of classroom exercises (1 CFU = 15 hours), with student involvement. 

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 programme planned and outlined in the syllabus.

Learning assessment may also be carried out on line, should the conditions require it.

Required Prerequisites

Essential knowledge: basic notions of general physics and quantum mechanics.

Attendance of Lessons

Attendance to the course is usually compulsory (consult the Academic Regulations of the Course of Studies).

Detailed Course Content

SCATTERING THEORY AND NUCLEAR REACTIONS - Elastic and inelastic reactions. Kinematics of nuclear reactions. Classical scattering theory. Qualitative characteristics of nuclear reactions. Quantum scattering theory. Description in partial waves: phase shifts and interference. Hard-Sphere Scattering. Low energy scattering. Bound states and scattering resonances. Scattering length, effective range and nuclear interaction. Born approximation for elastic and inelastic reactions. Double potential model and Born approximation in distorted waves (DWBA). Optical theorem and absorption cross section. Black sphere, Direct reactions: stripping, pick-up and knock-out. Description of the pick-up reaction (p, d). Impulse approximation. Eikonal approximation. Charge exchange reactions and connections with beta decay. Compound nucleus reactions. Empirical theory of optical potentials.

NUCLEAR COLLISIONS AT INTERMEDIATE ENERGY - Nuclear matter Equation of State (EoS). Isospin and symmetry energy. Nuclear dynamics in phase space. Wigner's transform and its properties. Semi-classical approximation. Boltzmann-Nordheim-Vlasov transport equation. Zero and First sound in nuclear matters. From incomplete fusion to multifragmentation: the spinodal mechanism for the dynamics of liquid-gas transition in nuclear matter. Deep-inelastic reactions and neck formation mechanism. Some notions about collective, radial, transverse and elliptic flows in heavy ion reactions.

Textbook Information

1) J.J. Sakurai,  Meccanica Quantistica Moderna, Ed. Zanichelli, 1990 - Capitolo 7

2) G.R. Satchler,  Introduction to Nuclear Reaction, Macmillian Education, 1990

3) C.A. Bertulani, P. Danielewicz, Introduction to Nuclear Reactions, IOP Publishing, London, 2004

Course Planning

 SubjectsText References
1Teoria classica dello scattering: grazing e rainbow nucleare3)
2Formulazione dello scattering in meccanica quantistica1)
3Scattering in onde parziali e phase shift3)
4Approssimazione di Born per lo studio di reazioni dirette2), 3)
5Approssimazione DWBA, approssimazione iconale2)
6Caratteristiche dell'interazione nucleare3)
7Teoria dei canali accoppiati per reazioni dirette2) + materiale fornito dal docente
8Reazioni di transfer e di scambio di carica2) + materiale fornito dal docente
9Equazione di stato della materia nucleareMateriale didattico fornito dal docente
10Equazione del trasporto per la dinamica delle collisioni tra ioni pesantiMateriale didattico fornito dal docente
11Modelli teorici per lo studio delle reazioni dirette e delle collisioni fra ioni pesanti2) + materiale fornito dal docente

Learning Assessment

Learning Assessment Procedures


The learning test is given to a final oral exam, with questions relating to qualifying points of the various parts of the program (classical scattering theory, elastic and / or inelastic quantum scattering, direct nuclear reactions, collisions between heavy ions and equation of state of nuclear matter). In this way we intend to ascertain the level of overall knowledge acquired by the candidate, his ability to critically address the topics studied and to correlate the various parts of the program. The ability to know how to carry out the essential steps that lead to the various basic formulas of the theory of nuclear reactions is also required.

Learning assessment may also be carried out on line, should the conditions require it.

Criteria for awarding the final grade:

The mastery shown in the qualitative and quantitative arguments, the critical vision of the topics addressed during the course and the ability to correlate the various parts of the program will contribute in equal measure to the formulation of the final grade.


Consult the Exam Calendar for the Master's Degree Course in Physics:


Not provided.


See exam methods and dates.

Examples of frequently asked questions and / or exercises

The questions below are not an exhaustive list but are just a few examples

Frequent questions:

- Concept of cross section

- Rainbow and orbiting effects

- Lippmann-Schwinger equation

- Born DWBA approximation

- Elastic and absorption cross section

- Examples of direct reactions

- Compound nucleus reactions

- Equation of state of nuclear matter

- Concept of medium field

- Landau-Vlasov kinetic theory

- Collective modes and instability

- Main characteristics of collisions between heavy ions.