Spectra of Pairs

Abstract

The spin hamiltonian appropriate to describe the EPR spectra of interacting pairs can be written as the sum of the spin hamiltonians appropriate for the interpretation of the EPR spectra of the individual spin centers and the spin hamiltonian describing the exchange interaction outlined in the previous chapter. A convenient form of this hamiltonian is:

$$H = {\mu _B}B \cdot {g_A} \cdot {S_A} + {\Sigma _k}{I^k} \cdot A_A^k \cdot {S_A} + {S_A} \cdot {D_A} \cdot {S_A} + $$

(3.1)

$$ + {\mu _B}B \cdot {g_B} \cdot {S_B} + {\Sigma _k}{I^k} \cdot A_B^k \cdot {S_B} + {S_B} \cdot {D_B} \cdot {S_B} + $$

(3.2)

$$ + {J_{AB}}{S_A}\cdot{S_B} + {S_A}\cdot{D_{AB}}\cdot{S_B} + {d_{AB}}\cdot{S_A} \times {S_B}$$

(3.3)

where g_I, ${\text{A}}_{\text{I}}^{\text{k}}$ and D_I are the Zeeman, hyperfine (superhyperfine), and zero field splitting tensors of spin center I (the other symbols have been defined in the previous chapters). The sums over k extend to all the nuclei:a given nucleus k will therefore appear both in (3.1) and (3.2), although in general the hyperfine interaction will be described by different tensors.