The density matrix describing a paramagnetic ion subjected to both pump and signal fields is calculated. It is used to determine the fractional population differences, magnetic polarization densities, susceptibility tensors and power dissipation densities at both the pump and signal frequencies. There are six relaxation parameters of prime significance: the spin-spin relaxation times, the spin-lattice relaxation times and the Overhauser parameters for both the pump and signal transitions. The spin-spin relaxation times control the low-level absorption. The spin-lattice relaxation times control the completely saturated absorption. The Overhauser parameters control the absorption by one transition when the other transition is partially or completely saturated.
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