We present a spin-temperature model, valid at low temperature, of nuclear dynamic polarization using electronic spin systems with ^-factor anisotropy and hyperfine structure. Predictions for the maximum polarization corresponding to some free radicals are compared with experiment.Sizable dynamic polarizations of protons have recently been obtained in solid samples containing free radicals as paramagnetic centers/"" Although the g tensors of these radicals have small anisotropics by current standards, for example,^ ^j^^x~^min~-'^^~^"-'-^""^> ^^^ corresponding frequency spread in the high fields used for such dynamic polarizations, for example 25 kG, is not at all negligible compared with the other sources of broadening of their resonance line. Furthermore, these radicals exhibit often quite important hyperfine structures,^ and the over-all linewidth is not smaller than the resonance frequency of the nuclei which are polarized. In order to predict the maximum polarizations that can be expected from a given radical species, as defined by the parameters of its spin Hamiltonian, some previous considerations,^ which assumed a narrow line, are thus no longer applicable.We present here a model of saturation and dynamic polarization which takes into account anisotropy and hyperfine structure, and which is valid at low temperatures.We consider a dielectric solid, at a temperature TQ, containing diluted unpaired electronic spins Sj, with S = i, located in a strong magnetic field HQ ^^^ i^ 3. high-frequency field if ^ of frequency co, withHJ^«HQ.We assume first that there are no nuclei other than those which interact by hyperfine coupling with the spins S. The spin Hamiltonian of the system reads, by neglecting the small Zeeman and quadrupolar contributions from the "hyperfine nuclei'' HK g.^ 0 '-'i] I g/-H. A..-K. 13 3 cosa)^+3C SS'where g^-and A^j are, respectively, the g tensor and the hyperfine tensors relative to spin Si\ 3C55 are the spin-spin interactions among spins S. We shall consider cases where the broaden-ing of the electronic resonance line due to ^55 is much smaller than its broadening coming from anisotropy and hyperfine interactions. This allows one to avoid using the "high-temperature approximation'*,^ and thus to evaluate realistic upper limits for the nuclear polarization in strong fields at low temperatures; besides this, such a condition is satisfied in many experimental situations. We shall be concerned here only with the limiting case of saturating hf fields. It can be shown by extending Provotorov's quantum-mechanical derivation of cross relaxation'^ that, in the high-temperature approximation and in the limit of strong hf field, the spin system can be described as having a single temperature in a suitable reference frame, when cross relaxation is fast.Here we want to draw some conclusions from the assumption that this remains valid even at low temperatures. In other words, we apply Redfield's spin-temperature hypothesis^ to the case of spin systems with spectral distributions, by assuming that the c...
