We’ll examine an example from the research literature where PAC has been used (and was crucial). After this video, you will understand better which features of hyperfine interaction methods (here PAC) make them sometimes the only tools available to obtain particular information.
In hyperfinecourse A, you learned how the hyperfine level scheme of a nucleus with spin I=5/2 subject to an electric-field gradient looks like :
With the knowledge you have, you can even prove that — provided the electric-field gradient has axial symmetry — these relations hold: ω2=2ω1 and ω3=3ω1 (just accept that for know, keep the challenge for proving this for later).
You may take it for granted that the oscillating function in a PAC experiment for this situation will be a superposition of three cosine functions, with these arguments ω1t, ω2t and ω3t. Make a plot of such a superposition (using a spreadsheet or your favourite plotting tool). Make a plot as well for a case where there is no axial symmetry. Make a pdf with both plots, and add a discussion about how you can visually determine from a PAC experiment whether or not an electric field gradient in your sample has axial symmetry.
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