The theory of the isotopic enrichment factor is extended to include hyperfine splitting and the nuclear field shift. It is shown that hyperfine splitting is an order of magnitude too small to explain the anomaly in the U-238/U-235 separation in the U(III)-U(VI) exchange reaction. The "anomalous mass effect" in this reaction and the related U(IV)-U(VI) exchange reactions are shown to be related to the nuclear field shift of the electron energy levels. Calculations of the effects of these shifts exactly reproduce the odd-even staggering in the U(IV)-U(VI) exchange reaction and the separation factors for the even-even nuclei. In the U(IV)-U(VI) exchange reactions the nuclear field effect is three times as large as the absolute value and of opposite sign to the vibrational energy term. It is the nuclear field shift which leads to a preference of the U(IV) for the heavy isotope in each of these exchange reactions. A revision of the reduced partition function ratios of uranium ions in solution, which takes into account the nuclear field shift, is presented.