NuclearForces

This site contains all teaching material for PHY989: Nuclear forces

The teaching material gives a survey of our present understanding of nuclear forces, from phenomenological models and one-boson exchange models to effective field theory and the fundamental theory of the strong force, quantum chromodynamics. The course contains several hands-on exercises and projects, ranging from the solution of the Lippman-Schwinger equation to the derivation of three-body forces in chiral perturbation theory. The course covers

1. Introduction to nuclear forces, functional expressions based on experimental information
2. Relativistic quantum mechanics and elements of quantum field theory, Dirac's equation and computation of one-boson exchange contributions.
3. Derivation of non-relativistic expressions of nuclear forces from one-boson exchange models
4. Elements of scattering theory and the non-relativistic Lippmann-Schwinger equation
5. Symmetries of nuclear forces, chiral symmetry, PCAC, pion decay constant, Goldstone bosons and links with QCD
6. Effective field theory and nuclear forces, two-, three- and many-nucleon forces, how and why
7. (Time Permitting) From Lattice QCD to effective field theory, how do we link them?
8. (Time Permitting) Connections with nuclear few- and many-body theories and implications for nuclear structure and reaction studies

Learning outcomes

The course aims at giving a basic overview of central aspects of nuclear forces and in particular how we can establish functional expressions for these based on effective field theories. The participants will get an overview of the basic phenomenology of nuclear forces and how these can be interpreted in terms of effective degrees of freedom based on nucleons and pions as the constituents. The course is project based and taught in an active learning model, with roughly 40-50% of class time devoted to project work and group exercises. Through the 2 course projects (graded) and group exercises (not graded), the participants will be exposed to fundamental research problems in the field of nuclear forces, and will acquire tools needed to reproduce state of the art scientific results. More specifically, after this course you will

• Learn about basic properties of nuclear forces, spanning from fundamental symmetries to understanding how data implies certain features of the forces (e.g., tensor and spin-orbit components, short-range repulsion, etc.);
• Learn how to solve the non-relativistic Lippmann-Schwinger equation to constrain nuclear force parameters to scattering data;
• Use concepts from relativistic quantum mechanics and quantum field theory to derive expressions for the nuclear force based on one-boson exchange models;
• Derive the non-relativistic expressions for the nuclear force from one-boson exchange models and be able to analyze data in terms of components of the nuclear force;
• Learn about the basic concepts of effective field theory and closely related concepts of renormalization group transformations
• Link one-boson exchange models with modern effective field theories and qualitatively understand the role of chiral symmetry breaking;
• Work on numerical projects to illustrate the theory. The projects play a central role and the participants are expected to know modern programming languages like Python or C++, or Fortran.