Program for Nuclear Talent course on Many-body methods for nuclear physics, from Structure to Reactions at Henan Normal University, P.R. China, July 16-August 5 2018

Kevin Fossez [1]
Morten Hjorth-Jensen [2]
Baishan Hu [3]
Weiguang Jiang [4]
Thomas Papenbrock [4]
Ragnar Stroberg [5]
Zhonghao Sun [4]
Yu-Min Zhao [6]

[1] National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA
[2] National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
[3] School of Physics, Peking University, Beijing 100871, P.R. China
[4] Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA and Oak Ridge National Laboratory, Oak Ridge, TN, USA
[5] Departmentof Physics, Reed College, Portland, OR, 97202 and Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
[6] School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, P.R. China

Aug 2, 2018












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 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.

Aims and Learning Outcomes

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 on github.

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

Objectives and learning outcomes:

At the end of the course the students should have a basic understanding of









Teachers and organizers

The local organizers are

  1. Chun-Wang Ma at Henan Normal University, Xinxiang, Henan 453007, P.R. China
  2. Furong Xu at School of Physics, Peking University, Beijing 100871, P.R. China
  3. Shan-Gui Zhou at the Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100864, P.R. China
In addition Qiao Chunyuan will help with administrative matters. You can reach her at the email address qiaochunyuan919@126.com.

Thomas Papenbrock and Morten Hjorth-Jensen will also function as student advisors and coordinators.

The teachers are

  1. Kevin Fossez at National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA
  2. Morten Hjorth-Jensen at National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USA
  3. Baishan Hu at School of Physics, Peking University, Beijing 100871, P.R. China
  4. Weiguang Jiang at Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA and Oak Ridge National Laboratory, Oak Ridge, TN, USA
  5. Thomas Papenbrock at Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA and Oak Ridge National Laboratory, Oak Ridge, TN, USA
  6. Ragnar Stroberg at Departmentof Physics, Reed College, Portland, OR, 97202 and Department of Physics, University of Washington, Seattle, WA 98195-1560, USA
  7. Zhonghao Sun at Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA and Oak Ridge National Laboratory, Oak Ridge, TN, USA
  8. Yu-Min Zhao at School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, P.R. China










Course Content and detailed plan

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:

  1. BH: Baishan Hu
  2. KF: Kevin Fossez
  3. MHJ: Morten Hjorth-Jensen
  4. WJ: Weiguang Jiang
  5. TP: Thomas Papenbrock
  6. RS: Ragnar Stroberg
  7. ZS: Zhonghao Sun
  8. YMZ: Yu-Min Zhao
There is a bus transportation from the hotel to the auditorium at Henan Normal University. Note that we start 830am on Monday July 16.











Week 1

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











Week 2

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











Week 3

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











Teaching and projects

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











Audience and Prerequisites

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.