experimental procedure

[JRomans]

I would measure the a1 and a2 values of both isotopes. What is important to consider is that this setup allows to measure free atoms – no perturbation phenomenon.

From the first isotope nuclear spin I1 and magnetic moment u1 and the hyperfine coupling constant the ratio of magnetic hyperfyne field and total angular momentum J can be extracted: Bj1/J1 = a1*I1/u1.

The orientations of electron cloud with respect to the nucleus from one isotope to another doesn’t change (orbital angular L momentum and electron spin S is not influenced – I assume this due to unperturbed system, but this is not clear to me fully). So if Bj/J is constant ratio, from knowing a2 & I2 I can obtain u2.

[JRomans]

after listening to the lecture again:
unperturbed system – no interaction between I and J -> J is not influenced (and thus Bj) by the change in I (and thus u) from one isotop to the next

[Author]

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