LAUSR

Dynamic Nuclear Polarization (DNP) via the mechanism of thermal mixing has proven itself most powerful for the orientation of nuclear spins in polarized targets and hyperpolarization for magnetic resonance imaging (MRI). Unfortunately, theoretical descriptions of this mechanism have been limited to using-at least partially-the high temperature approximation, in which Boltzmann factors are expanded linearly. However, the high nuclear spin polarization required and obtained for these applications does not justify such approximations. This article extends the description of thermal mixing beyond the high temperature approximation, so Boltzmann factors are not expanded. It applies for DNP in samples doped with paramagnetic centres, for which the electron spin resonance spectrum is mainly inhomogeneously broadened by g-value anisotropy. It verifies Provotorov's hypothesis that fast spectral diffusion leads to a density matrix containing two inverse spin temperatures: the inverse electron Zeeman temperature and the inverse electron non-Zeeman temperature, while thermal mixing equalizes the nuclear Zeeman temperature and the electron non-Zeeman temperature. Equations are derived for the evolution of these temperatures and the energy flows between the spins and the lattice. Solutions are given for DNP of proton spins in samples doped with the radical TEMPO.