9.1 Introduction

In Section 6.7, the discovery of the magnetic isotope effect (MIE) of 13C was introduced. In this Chapter, a more detailed review of MIEs will be given. Because the chemical isotope effects (CEs) of hydrogen is much larger than those of heavier elements, their MIEs will be dealt with in this Chapter. Let us consider the following reactions from a starting molecule (A) through a radical pair (RP):

Here, N represents escaped products. We can see from the radical pair theory that reactions (9-1) and (9-2) are independent on nuclear spins inside the RP, but that reaction (9-3) is dependent on the nuclear spins. If a starting molecule contains a magnetic isotope such as ¹³C, it will be represented as A ^#. On the other hand, if A contains no such magnetic isotope, it will be represented by A.

In this case, the isotope ratio ( ?) is given by

When ? ₀ and ? are the ratios measured before and after an enrichment reaction, respectively, the isotope enrichment ( S) in the starting molecule is represented as follows:

The rates of the decreases of [ A] and [ A ^#] can be represented by

Here, P and P ^# are the probabilities of regeneration of A and A ^#, respectively, through reaction (9-3). Thus, the one-step enrichment coefficient ( ?) is defined as follows:

If P ^# is larger than P, ?