# Hyperfine interactions

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# Examenvragen

## 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 ${\displaystyle a}$ and ${\displaystyle b}$. Calculate (and draw) the corrections for the ${\displaystyle S_{1/2}}$ ground state and the ${\displaystyle P_{3/2}}$ excited state for ${\displaystyle ^{??}Mg}$, 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, ...