The classic theory of stable isotope fractionation in chemical exchange reactions has been established by Bigeleisen, Mayer, and Urey in 1947. The theory was based on the difference of molecular vibrational energies of isotopomers that are proportional to the respective masses, and hence, results in mass-dependent isotope effect only. In 1996, this conventional mass-dependent theory has been expanded by Bigeleisen to include a mass-independent term named the nuclear field shift effect. The nuclear field shift is an isotope shift in orbital electrons, which results from the isotopic difference in nuclear size and shape. The new equation defined by Bigeleisen (at a constant temperature) can be simply expressed as, ln α = δ<r2> A + (δ m/mm') B, where α is the isotope separation factor, δ<r2> isotopic difference in mean-square nuclear charge radius, δm difference between isotopic masses m and m'. A and B are scaling factors of the nuclear field shift effect and the conventional mass effect, respectively. Since this new theory was presented, the mass-independent isotope fractionation of various elements, e.g, Ti, Cr, Ni, Zn, Sr, Zr, Mo, Ru, Cd, Te, Ba, Nd, Sm, Gd, Yb, and U, found in chemical exchange systems has been successfully explained as the nuclear field shift effect. In our most recent studies, the nuclear field shift effect of Cr, Mo, Ru, Cd, and Te isotopes has been found in laboratory scale experiments. The isotopes of these elements were fractionated by using a liquid-liquid extraction system (a ligand exchange system) at room temperature. The isotopic analysis was performed by the multiple-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) with a typical precision of <100 ppm (at ENS Lyon or UC Davis). Isotope enrichment factors did not show mass-dependent trend, but possessed a similar variation of their nuclear charge radii. For Cr, we tested a different chemical exchange system (a redox system): at high temperature (723-1023 K), an eutectic melt was contacted with a liquid metal. In this system, the nuclear field shift effect of Cr was also found. All these experimental results suggest that the nuclear field shift effect may occur in every chemical exchange reaction at various temperatures to various degrees. Therefore, isotopic anomalies found in a natural system might be partly or largely affected by the nuclear field shift effect via chemical reactions occurred in the nature. In order to clarify the degree and significance of its contribution, we may need to pay more attention to the nuclear field shift effect created chemically.