case studies / symmetry

In courses about hyperfine interactions, one often “defines” the hyperfine interaction by an energy level splitting scheme. In this course, this topic has been postponed until now. For a good reason: now you have the background to understand what this level splitting scheme means. Additionally, we’ll examine the impact of symmetry on a level scheme.

After this video, you will understand how the eigenvalues of the quadrupole hamiltonian lead to an energy level scheme, and you will understand the role of such a level scheme within the framework of interactions (cfr. Very Important Picture 1). You understand how the point symmetry at the site of the nucleus that feels the hyperfine interaction determines particular features of the level splitting scheme.

In case you would not be familiar with the concept of (for instance) a 3-fold rotation axis, then you can look at slide 9 and following of this slide deck, prior to watching the video.

download printable slides (3)
download printable slides (6)

Optional resource for digging deeper: here is a paper by L.H. Menke, which gives a list of all exactly solvable quadrupole hamiltonians and their eigenvalues, including pictures. This is a generalization of the low-spin cases that are discussed in the video.

Two tasks related to this video:

1. In the video, you get a quantum picture (I=1) as well as a classical picture (toy model) for the effect of a quadrupole interaction. Describe qualitativey what you would need to change in the quantum situation to evolve to a classical one (= find a quantum situation that is such that if you would search the corresponding levels, you would find something that is almost indistingusable from the classical result). Report your answer in this ‘post first’ forum:

Home › Forums › case studies / symmetry – task 1

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2. Find for both Fe-sites in Fe4N (Fe-I and Fe-II) the relevant rotation axes, and determine as much information about the PAS for both sites as you can.

Home › Forums › case studies / symmetry – task 1

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Expected time: 45 minutes (report)

A05-03

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