**Code documentation****Excercies****Projects**

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**About this Course**

**Questionnaire**(download here)

Motivation and introduction

To understand why matter is stable, and thereby shed light on the limits of nuclear stability, is one of the overarching aims and intellectual challenges of basic research in nuclear physics. To relate the stability of matter to the underlying fundamental forces and particles of nature as manifested in nuclear matter, is central to present and planned rare isotope facilities.

Important properties of nuclear systems which can reveal information about these topics are for example masses, and thereby binding energies, and density distributions of nuclei. These are quantities which convey important information on the shell structure of nuclei, with their pertinent magic numbers and shell closures or the eventual disappearence of the latter away from the valley of stability.

During the last decade, the study of nuclear structure and the models used to describe atomic nuclei are experiencing a renaissance. This is driven by three technological revolutions: accelerators capable of producing and accelerating exotic nuclei far from stability; instrumentation capable of detecting the resulting reaction products and gamma radiation, often on an event-by-event basis, in situations where data rates may be many orders of magnitude less than has been traditional; and computing power adequate to analyze the resulting data, often on-line, and to carry out sophisticated theoretical calculations to understand these nuclei at the limits of stability and to unravel what they tell us about nuclei and their structural evolution.

The nuclear shell model plays a central role in guiding our analysis of this wealth of experimental data. The shell model provides an excellent link to the underlying nuclear forces and the pertinent laws of motion, allowing nuclear physicists to interpret complicated experiments in terms of various components of the nuclear Hamiltonian and to understand a swath of nuclei by following chains of isotopes and isotoones over wide ranges of nucleon numbers. The nuclear shell model allows us to see how the structure of nuclei changes and how the occupation of specific nucleonic orbits affects the interplay of residual interactions and configuration mixing. The computed expectation values and transition probabilities can be directly linked to experiment, with the potential to single out new phenomena and guide future experiments. Large-scale shell- model calculations represent also challenging computational and theoretical topics, spanning from efficient usage of high-performance computing facilities to consistent theories for deriving effective Hamiltonians and operators. Alltogether, these various facets of nuclear theory represent important elements in our endeavors to understand nuclei and their limits of stability.

However, the dimensionalities of interest for shell-model studies exceed quickly present computational capabilities of eigensystem solvers. In order to be able to describe nuclear systems with many more degrees of freedom as well as pro- viding better effective operators, approximative many-body methods like Coupled Cluster (CC) theory or the In-Medium Similarity Renormalization Group (IMSRG) approach have lately gained wide interest and applicabilities in the nuclear many-body community.

It is the goal and motivation of this course to introduce and develop the nuclear structure tools needed to carry out forefront research using the shell model and many-body methods like CC theory and the IMSRG method as central tools, with applications to both structure and reaction theory studies. After completion, it is our hope that the participants have understood the overarching ideas behind central theoretical tools used to analyse nuclear structure experiments.

This three-week TALENT course on nuclear theory will focus on the Many- body methods for nuclear structure and reactions, focusing on nuclear shell model and/or coupled cluster theory and in-medium SRG with applications to structure and reactions. Via hands-on projects and series of exercise, the participants will have been exposed to the necessary tools and theoretical models used in modern nuclear theory.

Format: We propose approximately forty-five hours of lectures over three weeks and a comparable amount of practical computer and exercise sessions, including the setting of individual problems and the organization of various individual projects. The course starts July 16 (with arrival on July 15) and ends (the course) on August 3. A three days workshop will be organized from August 4 to August 6. The mornings will consist of lectures and the afternoons will be devoted to exercises meant to shed light on the exposed theory, and the computational projects. These components will be coordinated to foster student engagement, maximize learning and create lasting value for the students. For the benefit of the TALENT series and of the community, material (courses, slides, problems and solutions, reports on students’ projects) will be made publicly available using version control software like git and posted electronically ongithub.

As with previous TALENT courses, we envision the following features for the afternoon sessions:

We will use both individual and group work to carry out tasks that are very specific in technical instructions, but leave freedom for creativity.

Groups will be carefully put together to maximize diversity of backgrounds.

Results will be presented in a conference-like setting to create accountability.

We will organize events where individuals and groups exchange their experiences, difficulties and successes to foster interaction.

During the school, on-line and lecture-based training tailored to technical issues will be provided. Students will learn to use and interpret the results of computer-based and hand calculations of nuclear models. The lectures will be aligned with the practical computational projects and exercises and the lecturers will be available to help students and work with them during the exercise sessions.

These interactions will raise topics not originally envisioned for the course but which are recognized to be valuable for the students. There will be flexibility to organize mini-lectures and discussion sessions on an ad-hoc basis in such cases.

Each group of students will maintain an online logbook of their activities and results.

Training modules, codes, lectures, practical exercise instructions, online log- books, instructions and information created by participants will be merged into a comprehensive website that will be available to the community and the public for self-guided training or for use in various educational settings (for example, a graduate course at a university could assign some of the projects as homework or an extra credit project, etc).

Objectives and learning outcomes: At the end of the course the students should have a basic understanding of

Configuration interaction methods (nuclear shell-model here) as a central tool to interpret nuclear structure experiment

Central many-body methods like Coupled Cluster theory and the In- Medium Similarity Renormalization Group approach

How to compute nuclear structure properties with these methods

Have an understanding of single-particle basis functions and the construc- tion of many-body basis states built thereupon. Examples are basis states from a Woods-Saxon potential, harmonic oscillator states and mean-field based states from a Hartree-Fock calculation. The single-particle basis states are orthonormal and are used to construct a corresponding orthonor- mal basis set of Slater determinants.

Develop an understanding of what defines an observable.

Understand how theory can be used to interpret experimental quantities

(separation energies and shell gaps for example).

Understand how second-quantization is used to represent states and com- pute expectation values and transition probabilities of operators

Understand how the Hamiltonian matrix is constructed from this orthonor- mal basis set of many-body states (linear expansion of Slater determinants)

The students will also learn to understand the basic elements of effective shell-model Hamiltonians and how to interpret the calculated properties in terms of various components of the nuclear forces (spin-orbit force, tensor force, central force etc). We will provide the students with the necessary tools to perform such analyses.

Develop a critical understanding of the limits of many-body studies and how these can be related to interpretations of data such as results from in-beam and decay experiments.