Experimental procedure

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    Brent Van Neste

    For isotope 1, we know spin I1 and nuclear magnetic moment u1. Then we find the corresponding operators and calculate the perturbing hamiltonian with those operators. The elements of that hamiltonian are proportional to a * C (with C dependent on F, I and J). We can measure the hyperfine coupling constant a, and we know the hamiltonian, so we can find C.
    For isotope 2, we know I2. We also know C and can measure a so we can calculate the matrix elements. The magnetic hyperfine field operator is the same for isotope 2, as the electron cloud has not changed. We can now find the nuclear magnetic moment operator and deduce u2 from this as we know I2.

    This explanation was done in a rather “hand-waving” way so I am not sure it is correct.

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