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 providing 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, including continuum contributions and resonances. 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.
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 on github.
As with previous TALENT courses, we envision the following features for the afternoon sessions:
The local organizers are
Thomas Papenbrock and Morten Hjorth-Jensen will also function as student advisors and coordinators.
The teachers are
Lectures are approximately 45 min each with a small break between each lecture. The morning sessions are scheduled to end around 1230pm. Every Friday we will have presentations from each group, where a summary of what has been achieved is presented.
Lectures and preparatory material on second quantization are all available at the Github address of the course, or go to URL: https://nucleartalent.github.io/ManyBody2018/doc/web/course.html"" for an easier read.
Furthermore, we strongly recommend that you read chapter 8 and 10 of Lecture Notes in Physics 936. This text contains also links to all codes we will discuss, in addition to the codes we have placed in the program folder of the course. If you cannot access the pdf file of the above text, you can reach chapters 8 and 10 via their respective arXiv versions, click here for chapter 8 and here for chapter 10.
Furthermore, for Coupled Cluster theory the review of Crawford and Schaefer III, An Introduction to Coupled Cluster Theory for Computational Chemists is highly recommended.
For nuclear structure problems, the book of Rick Casten is a highly recommended read. Similarly, Alex Brown's text on Nuclear Structure is a good companion read. The text of Jouni Suhonen is also an excellent read.
The acronyms here stand for the different teachers:
| Day | Lecture Topics and lecturer | Projects and exercises | |
|---|---|---|---|
| Monday | 830am-1230pm | Welcome and introduction (Organizers) | |
| Second quantization and Hamiltonians (MHJ) | |||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Getting started with Pairing Hamiltonian | Additional analytical exercises | |
| Tuesday | 9am-11am | Full configuration interaction theory (MHJ) | |
| 1130am-1230pm | Pairing in Nuclear Physics (YMZ) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Analytical exercises and start with coding pairing Hamiltonian | ||
| Wednesday | 9am-1230am | Full configuration interaction theory and the pairing model problem (MHJ) | |
| 11am-1230pm | Pairing in Nuclear Physics (YMZ) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Writing a shell-model code for the pairing problem | ||
| Thursday | 9am-11pm | Full configuration interaction theory (MHJ) | |
| Hartree-Fock theory and links to Coupled Cluster theory | |||
| 1130am-1230pm | Pairing in Nuclear Physics (YMZ) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Writing a shell-model code for the pairing problem | ||
| Friday | 9am-1230pm | Pairing in nuclear physics and summary of 1st week (YMZ) | |
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Group presentations of weekly work |
| Day | Lecture Topics and lecturer | Projects and exercises | |
|---|---|---|---|
| Monday | 9am-1230pm | Introduction to Coupled Cluster (CC) theory (TP) | |
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Pairing model: MBPT and begin CC theory | ||
| Tuesday | 9am-1230pm | Developing a CC code for the pairing model (TP) | |
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Start writing a CC code for the pairing model | ||
| Wednesday | 9am-11am | CC theory and Infinite Matter (TP) | |
| 1130am-1230pm | Computational CC theory for closed and open shell nuclei (ZS) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Finalize CC code for the pairing model | ||
| Thursday | 9am-1030am | Summary of CC theory and infinite matter (TP) | |
| 11am-1230pm | Machine learning applied to CC theory (WJ) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Start writing CC code for infinite matter | ||
| Friday | 9am-11am | From structure to reaction theory (TP) | |
| 1130am-1230pm | Summary of second week and links to IMSRG (TP) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Group presentations of weekly work |
| Day | Lecture Topics and lecturer | Projects and exercises | |
|---|---|---|---|
| Sunday | 9am-1230pm | SRG theory (RS) | |
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Continue work on CC code for infinite matter | ||
| Monday | 9am-12:30pm | IMSRG and infinite matter (RS) | |
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Start coding IMSRG for infinite matter and the pairing model | ||
| Tuesday | 9am-1100am | Nuclei as (many-body) open quantum systems (KF) | |
| 1130am-1230pm | Many-body perturbation theory calculations (BH) | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Continue work on code for infinite matter | ||
| Wednesday | 9am-1230pm | Quasi-stationary formalism and Berggren basis (KF) | |
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Continue work on code for infinite matter | ||
| Thursday | 9am-1030am | Many-body methods for nuclear open quantum systems (KF) | |
| Renormalization group approaches for continuum couplings (KF) | |||
| 11am-1230pm | Summary of school | ||
| 1230pm-230pm | Lunch + own activities | ||
| 230pm-6pm | Final group presentations | ||
| Friday | All day | Workshop, see own program | |
| Saturday | All day | Workshop, see own program |
The course will be taught as an intensive course of duration of three weeks, with a total time of 45 h of lectures, 45 h of exercises, with the possibility to complete a final assignment if credits are needed.
The organization of a typical course day is as follows:
| Time | Activity |
|---|---|
| 9am-1230pm | Lectures, project relevant information and directed exercises |
| 1230pm-230pm | Lunch |
| 230pm-6pm | Computational projects, exercises and hands-on sessions |
| 6pm-7pm | Wrap-up of the day and eventual student presentations |
You are expected to have operating programming skills in in compiled programming languages like Fortran or C++ or alternatively an interpreted language like Python and knowledge of quantum mechanics at an intermediate level. Preparatory modules on second quantization, Wick's theorem, representation of Hamiltonians and calculations of Hamiltonian matrix elements, independent particle models and Hartree-Fock theory are provided at the website of the course. Students who have not studied the above topics are expected to gain this knowledge prior to attendance. Additional modules for self-teaching on Fortran and/or C++ or Python are also provided.