Overview of course material: PHY981 Nuclear Structure

Morten Hjorth-Jensen (hjensen at nscl.msu.edu)

The teaching material is produced in various formats for printing and on-screen reading.

The PDF files are based on LaTeX and have seldom technical failures that cannot be easily corrected. The HTML-based files, called "HTML" and "ipynb" below, apply MathJax for rendering LaTeX formulas and sometimes this technology gives rise to unexpected failures (e.g., incorrect rendering in a web page despite correct LaTeX syntax in the formula). Consult the corresponding PDF files if you find missing or incorrectly rendered formulas in HTML or ipython notebook files.

PHY 981: Nuclear Structure notes

Introduction to nuclear structure

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Single-particle data, experimental information and simple models

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Mean-field theories

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Second quantization

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Angular momentum algebra

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Models for nuclear forces

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The nuclear shell model and full configuration interaction theory

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Nuclear decays

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Pairing, random-phase approximation and simple models

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Effective interactions for the nuclear shell-model

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Coupled cluster theory and nuclear structure

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Similarity transformation methods

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Green function theory based methods

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Monte Carlo methods

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From nuclei to stars, properties of infinite nuclear matter, symmetric and neutron rich

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Schedule Spring 2016

All lectures are in the main conference room of the theory trailer.

Week and days Topics to be covered Exercises and projects Reading assignments Additional activities

Week 2 January 11-15 Introduction Exercise set 1 Chapters 1-4 of Brown

Observables, masses, radii and definitions Lecture notes

Week 3 January 18-22 Single particle properties Exercise 1

Definitions, basis sets and begin Hartree-Fock Lecture notes

Week 4 January 25-29 Hartree-Fock Exercise set 2

Single-particle quantum numbers, second quantization

Week 5 February 1-5 Second quantization Exercise set 3

Hartree-Fock final

Week 6 February 8-12 Second quantization Project 1

Week 7 February 15-19 Second quantization Work on project 1

Week 8 February 22-26 Second quantization Work on project 1

Angular momentum algebra Lecture notes

Week 9 February 29 -March 4 Nuclear shell model Work on project 1 Lecture notes Deadline for project 1 is March 4

Angular momentum algebra Lecture notes

Week 10 March 7-11 Spring break

Week 11 March 14-18 Nuclear shell model Presentation of project 2

Week 12 March 21-25 Nuclear shell model Work on project 2

Nuclear forces

Week 13 March 28 -April 1 Effective Hamiltonians and operators Work on project 2

Nuclear decays

Week 14 April 4-8 Nuclear decays Work on project 2 Deadline for project 2 April 8

Electromagnetic decays

Week 15 April 11-15 Nuclear decays Exercise set 4

Electromagnetic and Electroweak decays

Week 16 April 18-22 Nuclear decays Exercise set 5

Electroweak decays Presentation of projects for final oral exam

Week 17 April 25-29 Nuclear decays Work on final oral exam project

Summary of course

Week 18 May 2-6 Finals week Time and schedule TBA

Basic Syllabus

Syllabus: Lecture notes, exercises and projects. Relevant chapters of Suhonen's text that cover parts of the material are chapters 3-9 and 11. Chapters 1-2 on angular momentum will be used as references for various derivations and only parts of these two chapters will be used. Alex Brown's lecture notes from 2011 can also be used, and the relevant chapters are 1-4, 6-29. Chapter 5 of Brown on angular momentum plays the same role as chapters 1-2 of Suhonen.

Main themes and reading suggestions

The various observables we will discuss in the course are thought to be understood via the following five major topics

Single particle properties and mean-field models, lecture notes, Suhonen chapters 3-5 and Brown chapters 7-10 and 14
Nuclear forces, covered by lecture notes
The nuclear shell-model, lecture notes, Suhonen chapter 8 and Brown chapters 11-22.
Decays and one and two-body transition probabilities, lecture notes, Suhonen chapters 6 and 7, Brown chapters 23-29.
If time allows, Particle-hole excitations, random-phase approximation and pairing (and perhaps something on collective models), lecture notes and Suhonen chapters 9 and 11.

Links to all course material

PHY981 on github

All material is at https://github.com/NuclearStructure/PHY981/
The link http://nuclearstructure.github.io/PHY981/doc/web/course.html gives direct access to html, ipython notebooks and pdf files of the lectures.

Projects, exercises and final oral exam

Projects, weekly exercises, deadlines and final oral exam.

Two projects with a possible numerical content that count 25% each of the final mark, weekly exercises that count 20% and a final oral exam which counts 30% of the final grade.
Project 1 will be available in week 6 (begins with February 8) and to be handed in before spring break (March 4)
Project 2 will be available in week 13 (begins with March 28) with deadline April 18.
For the final oral exam you have to prepare a 25-30 minutes talk based on either a topic chosen by you or a topic defined towards the end of the semester.

Duration of the examination is 45 minutes.

Selected Texts on Nuclear Structure and Many-body theory

Nuclear structure

Heyde, The Nuclear Shell Model, Springer 1990
Lawson, Theory of the Nuclear Shell Model, Oxford 1980
Ring and Schuck, Nuclear Many-Body Theory, Springer 1980
Talmi, Simple Models of Complex Nuclei: The Shell Model and Interacting Boson Model, Harwood Academic Publishers 1993.

Many-body theories

Blaizot and Ripka, Quantum Theory of Finite systems, MIT press 1986
Fetter and Walecka, Quantum Theory of Many-Particle Systems, McGraw-Hill, 1971.
Dickhoff and Van Neck, Many-Body Theory Exposed, World Scientific, 2006.

Links and useful software

Useful links

When I write code in C++ I tend to recommend to use the linear algebra library armadillo.
For OS X users I recommend using brew.
To set up github, use the guides and/or the github link.
An excellent IDE for c++ programmers is Qt Creator

Week and days	Topics to be covered	Exercises and projects	Reading assignments	Additional activities
Week 2 January 11-15	Introduction	Exercise set 1	Chapters 1-4 of Brown
	Observables, masses, radii and definitions		Lecture notes
Week 3 January 18-22	Single particle properties	Exercise 1
	Definitions, basis sets and begin Hartree-Fock		Lecture notes
Week 4 January 25-29	Hartree-Fock	Exercise set 2
	Single-particle quantum numbers, second quantization
Week 5 February 1-5	Second quantization	Exercise set 3
	Hartree-Fock final
Week 6 February 8-12	Second quantization	Project 1

Week 7 February 15-19	Second quantization	Work on project 1

Week 8 February 22-26	Second quantization	Work on project 1
	Angular momentum algebra		Lecture notes
Week 9 February 29 -March 4	Nuclear shell model	Work on project 1	Lecture notes	Deadline for project 1 is March 4
	Angular momentum algebra		Lecture notes
Week 10 March 7-11	Spring break
Week 11 March 14-18	Nuclear shell model	Presentation of project 2

Week 12 March 21-25	Nuclear shell model	Work on project 2
	Nuclear forces
Week 13 March 28 -April 1	Effective Hamiltonians and operators	Work on project 2
	Nuclear decays
Week 14 April 4-8	Nuclear decays	Work on project 2		Deadline for project 2 April 8
	Electromagnetic decays
Week 15 April 11-15	Nuclear decays	Exercise set 4
	Electromagnetic and Electroweak decays
Week 16 April 18-22	Nuclear decays	Exercise set 5
	Electroweak decays			Presentation of projects for final oral exam
Week 17 April 25-29	Nuclear decays	Work on final oral exam project
	Summary of course
Week 18 May 2-6	Finals week	Time and schedule TBA