Quantitative Aspects of To-S Mixing

Quantitative Aspects of Tq-S Mixing 1. The spin Hamiltonian and Tq-S mixing A basic problem in quantum mechanics is to relate the probability of an ensemble of particles being in one particular state at a particular time to the probability of their being in another state at some time later. The ensemble in this case is the population distribution of nuclear spin states. The time-dependent Schrodinger equation (14) allows such a calculation to be carried out. In equation (14) (S,i) denotes the total 

It is necessary to substitute a phenomenological equation for which in this case involves only spin variables. 

The spin Hamiltonian is thus generated. In particular it can be used to examine the Tq-S mixing of electron spin states and its relationship to the distributions of jiopulations of nuclear spin states. The total spin Hamiltonian is given in equation (16) which contains both electron and nuclear terms. 

The first term is the electronic part of the Hamiltonian and this can be expanded as shown in equation (16). 

Here Hg and H describe radicals A and B of the radical pair and the interaction of their electrons. The other terms in equation (15) are Hls, the spin orbit coupling term, Hgg and Hgi, representing the interaction of the externally applied magnetic field with the electron spin and nuclear spin, respectively Hgg is the electron spin-spin interaction and Hgi the electron-nuclear hyperfine interaction. 

---