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Since you’re working with the same isotope, I think you can assume that the electron cloud will somehow behave the same as before. If this assumption is correct, one can measure the perturbed energies and divide by the appropriate C factors (nuclear spin I2 is known and spin electron cloud too by our assumption). This gives the new ‘a’. But the only unknown in a is the magnetic moment of the nucleus, since we assumed to know B.
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