Department of Applied Mathematics & Theoretical Physics

Module AMA401 - Theoretical Atomic Structure and Collisions

Course Lecturer: Dr H W van der Hart
(room G.031 David Bates Building)
E-mail : h.vanderhart@qub.ac.uk
Telephone : x6048


Class Schedule Aims and Objectives Books
Course Description Examinations Absences
Lecture Notes Tutorials
Assignments  Monitoring

Class Schedule

Formal lectures

The course will consist of approximately 32 lectures and 16 tutorials. Students are expected to attend all tutorials. The module begins with a tutorial revisiting material from previous modules on Monday 15 October 2007 in Lecture Theatre 1.004 of the David Bates Building. Formal lectures are scheduled as follows:

Tuesday: 10.00 - 11.00 in room G.005, David Bates Building
Tuesday: 12.00 - 13.00 in room 2.005, David Bates Building
Friday: 10.00 - 11.00 in room 2.005, David Bates Building
Friday: 12.00 - 13.00 in room 2.005, David Bates Building

Tutorials

Times, dates and places :

Monday: 10.00 - 11.00 in room 1.004, David Bates Building
Thursday: 10.00 - 11.00 in room 101, 7 University Square

The first tutorial is given on Monday 15 October 2007.

Aims and Objectives

The first aim of the course is to provide students with an introduction into theoretical atomic structure and collisions. This module should benefit all students with an interest in atomic physics, and in particular those who will study atomic physics during their Level 4 project or during their further research career.

Course Description

Section 1: Theoretical Atomic Structure

Introduction; States; Operators and their manipulation; Angular momentum; Spin; Radial Wavefunctions; Dirac Hamiltonian Step-up and step-down operators; Relation to rotations Clebsch-Gordan coefficients, orthogonality relations and evaluation; 6-j symbols; 9-j symbols Clebsch-Gordan series; Spherical harmonic addition theorem; D-matrices; Irreducible tensor operators; Wigner-Eckart theorem Slater determinant; Singlet and triplet wavefunctions; Effects on energies; Numerical evaluation of two-electron integrals The Hartree-Fock approach; Configuration Interaction; Hylleraas-Undheim theorem; Variational principles

Section 2: Collisions

Deflection angle; Cross section; Rutherford scattering Continuum functions; Dirac delta-function; Normalisation; Current density; Square barrier; S-matrix and its symmetries Plane waves; Spherical waves; Bessel functions and its properties; Scattering amplitude; Optical theorem; Phase shift; Resonances Integral equations for potential scattering; Born series; First Born approximation Derivation; Scattering from potential of form -c/rn R-matrix theory for potential scattering; Numerical example
 

Books

In spite of all the wonders of the web - there is no substitute for independent study. This is particularly true if you are having trouble understanding the lecture notes! The material covered in these lectures can be studied in more detail throguh the following books:

Recommended Reading

Bransden B.H. & Joachain C.J.
Physics of Atoms and Molecules, 2nd ed., Harlow: Pearson Education, 2002. ISBN 058235692x.
Library Shelf Mark QC173 BRAN

Merzbacher E.
Quantum Mechanics, 3rd ed., Wiley 1998. ISBN 0471887021.
Library Shelf Mark QC174.12 MERZ

Supplementary Reading

Froese Fischer C., Brage T. & Jönsson P.
Computational Atomic Structure, Institute of Physics Publishing, 1997. ISBN 0750303743 (Hbk), 0750304669 (Pbk).
Library Shelf Mark QC173.4.A87 FROE

Notes

The course will be presented using the overhead projector supported by handouts. Despite handouts being made available through Queen's Online, it is important that you attend regularly.


Tutorials

All students are required to attend two tutorial classes each week, due to the difficulty level of Level 4 modules and the shorter timespan for the module. The tutorials will commence on Monday 15 October 2007 with a revision of essential material from previous modules. Tutorials are scheduled for
Monday: 10.00 - 11.00 in room 1.004 David Bates Building
Thursday: 10.00 - 11.00 in room 1.004 David Bates Building

The objective of the tutorials is to enable students to raise questions which could not be easily dealt with fully in the lectures and to encourage students to make the effort to "keep up" with the course by working through additional examples. It is recommended that you do a little preparatory reading before you come to tutorials to ensure you make the best use of the time. A tutorial attendance register will be kept which will be monitored from time to time. Poor attendees will be interviewed and in extreme cases may be reported to the Faculty and/or to your fee paying body.

Assignments (Homework)

During the course you will be given "homework" assignments - approximately one assignment each week. These will be graded if your solutions are submitted on time. Whilst they do not contribute to your final examination mark, you are strongly encouraged to complete these assignments as they provide examples of the type of questions you may encounter at the exam. They also allow you to keep up with the module and assess your own progress. Assignments are posted on Queen's Online, and solutions will also be placed there.

Monitoring

We  record  tutorial attendance and home assignment marks. Assignment marks only count in a qualitative (formative) sense in the final examination, and then only if you are on the pass/fail borderline. However, this information is also used to assess how you are progressing with the course and how I am doing in terms of my teaching ! If you do not seem to be progressing reasonably well, I will want to see you to find out why, and where possible provide help and guidance.

In addition to the regular monitoring of your progress on this course, the department will from time to time make a more formal review of the progress of all students taking its courses. The first of these will consider your work during the first six weeks of this semester. Normally the work of most students is very satisfactory. However, those students who are not progressing well (evidenced by inadequate attendance or unexpectedly poor work) will be called to a meeting of the review group so that any problems can be sorted out before they become too serious.

Absences

If you are absent through illness, you should complete a self-certificate form (or, in the case of more serious or prolonged illness, you should obtain a doctor's certificate) and forward it to the School of Mathematics and Physics office. If your reasons for absence are of a personal nature, you should confide in your adviser of studies or faculty tutor, at least so that they have some awareness of your problems. You may wish to confide further in one of the doctors at Student Health, in the Student Counsellor, or in one of the university chaplains. In the case of absence for more than 4 weeks, the university has to inform your Area Board. The Board could cancel your grant if they aren't satisfied with your reasons for absence.

Examinations

The examination for the course consists of a module examination which takes place in January 2008. The exam consists of two sections: section A is theoretical atomic structure, and section B is collisions. Each section contains three questions, and you need to answer two questions from each section. Normally, the exam lasts for 3 hours.


H W van der Hart
31 January 2008