Influence of the nuclear Zeeman term on anisotropic hyperfine patterns in electron spin resonance

Abstract

The spin Hamiltonian for the two spin system S = 1 2 , I = 1 2 was solved taking into account the electronic Zeeman, nuclear Zeeman and hyperfine interactions. The two Zeeman terms were assumed to be isotropic and the hyperfine interaction was completely anisotropic. The spectrum is a symmetric quartet with the splitting of the outer pair T 0 related to that of the inner pair T i through the relations T 0 2+T i 2=T 2+(2g nβ nH) 2 , T 0T i=|2g nβ nHT 22| , where T is the true hyperfine coupling constant and T zz is its zz component. The two doublets have the respective intensities. I 0= T 0 2−(2g nβ nH) 2 T 0 2−T t 2 , I t= (2g nβ nH)−T i 2 T 0 2−T t 2 At X-band twice the nuclear Zeeman term 2 g n β n H amounts to eleven gauss, so for typical irradiated organic single crystals the outside doublet is strongest. In such samples the weak doublet is ordinarily only observed at particular orientations. An analysis was made of the errors that arise when the nuclear Zeeman term is neglected. For typical irradiated organic single crystals at X-band the errors in many hitherto reported coupling constants amount to several percent.