Hyperfine interactions
Overview
This course is on hyperfine interactions in atoms and nuclei and taught by Stefaan Cottenier from UGent. It is relevant for both nuclear physicists as well as physicists interested in condensed matter. The course is taught via lecture videos at a separate website, namely https://www.hyperfinecourse.org/. All material is always available there, and can be watched whenever you like.
Evaluation
During the semester, Leuven students have to watch one chapter from the website each week and submit answers to small tasks related to the video lectures, with a certain deadline. Your grade starts off with 4/20, but if you don't complete these assignments before their deadline, you get -1 each time this happens (but you cannot go lower than 0 of course). Note that this is only for part A of the website: this does not hold for part B. Moreover, you keep these points if you submit answers to the assignments, even if your answers are wrong. You just have to show that you thought about the exercises. Stefaan is friendly about this and said that if he sees a student did not submit all his or her or their assignments for a certain week, he will first enquire whether or not you had some technical difficulties.
For part B (experimental methods on hyperfine interactions), you have to choose one topic (the full list is given on the hyperfinecourse.org website) and make a paper of around 7 pages about that topic and a specific application. This counts for 6/20. The remaining 10 points are graded during an exam in the examination period, which mostly involves part A of the course (theory), although very general and basic questions about part B can appear as well. You are allowed to bring all the slides available on the hyperfinecourse website to the exam, with your own annotations next to them, so it is advised to print all the slides before watching the videos (a compilation of all slides is given in the summaries below) and make notes on those slides, since this will save you a lot of time in the exam period.
Summaries
Klik hier om de samenvattingen te bekijken
A long and detailed summary is written by a former student, Jeffrey De Rycke: Media:Full_Summary_Jeffrey.pdf.
Another, short and more sloppy summary can be found here: Media:Notes_HFI.pdf.
All the slides for part A of the website in one PDF can be found here: Media:HFI_all_slides.pdf (note that they are without the additional lines to write stuff whenever it was possible, to reduce the number of pages. Because you know "there is no planet B" etc etc).
Exam questions
15/06/2015
1. What causes the fine structure in atoms?
2. Give expresiions for the hyperfine splitting in funciton of the parameter a and b.
3. Calculate the energy splitting of the ground state 2s_(1/2} and the excited states 2p_(1/2) and 2p_(3/2) of ^{9}Be which has a nuclear spin of I=1/2.
4. Discuss the different contributions to the monopole correction. What causes these different contributions? Give an expression. Which of these correction terms is related to the isotope shift.
5. The monopole interaciton consist of different contributions. Which ones depend on the fine structure? Why?
The next two questions involve the articles of the experimental techniques and were discussed orally.
6. The article mentions c.g. (centre of gravity) and \Delta\nu_{fs} (fine structure splitting). Define these in the context of the article.
7. Why doesn't ^{10}Be show any additional splitting?
8. What is SIS (splitting isotope shift)? How is it different from the Isotope shift?
17/06/2013
There were three questions, each one to be discussed orally.
1. What correction needs to be added if the nucleus has a finite mass? Is this correction applied at the fine or hyperfine levels? This leads to difference in energy levels for different isotopes, what is this difference called? Sketch this for two isotopes (essentially the same as last year).
2. What corrections are needed if the electrons and protons have a charge distribution? Consider the mass of the nucleus to be infinite, and without overlap with the electron cloud. Give the expressions in function of the hyperfine parameters and . Calculate (and draw) the corrections for the ground state and the excited state for , which has a nuclear spin of 1/2.
3. Discuss your favorite method for measuring the magnetic moment of radioactive nuclei. Also consider the limits of its applicability.
18/06/2012
1. (oral) What correction needs to be added if the nucleus is not infinitely massive. What is this correction called? Sketch the energy difference between two isotopes of the same element. (This question was essentially the same as the first question last year).
2. You have two charge distributions; one is a point charge, the other some general distribution. Does it matter whether or not you take the origin of you axis system in the point charge? Explain why (not).
3. Calculate the hyperfine energies for an atom with I=1, J=1/2. Sketch them. Prove that the energy difference between the hyperfine levels is a(I+1/2). (hint: use the relation between F1 and F2 for this specific case.)
4. (Oral) Give the Hamiltonian for the interaction of a nucleus implanted in a solid. The nucleus has no magnetic hyperfine field, and its electric field gradient is axially symmetric. There is an external magnetic field applied along the axial symmetry axis.
Draw the energy spectrum as function of the external magnetic field. At what field do the levels cross?
24/06/2011
1.
- Welke correctie moet je in rekening brengen als de kern niet infinitly massive is
- Vergelijk de grootorde van de correctie met andere mogelijke correcties
- Er is een andere correctie voor een andere isotoop, hoe noemt dit?
- Teken een spectrum voor twee verschillende isotopen
2. Oefening
- Hyperfijnopsplitsing: Wat zijn de bijdragen, oorsprong
- Bepaalde kern met wat eigenschappen gegeven, bereken die bijdrages (-1/2 AC, ..)
- Teken spectrum
3. Bespreek een methode waarop het magnetisch moment van een exotische kern kan worden gemeten, denk ook aan productieproces, limieten van halfwaardetijd, ...