Approximate Solutions of the Modified Bloch Equations for Low Magnetic Fields

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Abstract
A set of modified Bloch equations proposed by Torrey, Olds, and Codrington for the description of the time dependence of the magnetic moment expectation value in low magnetic fields, is solved using two approximate methods. The equations are solved approximately for the steady state with a constant field and linearly polarized radio-frequency field applied and an error analysis of the approximate solution is given. A low-harmonic solution is developed and alternative numerical integration techniques are given. Results are exhibited for the low-field electron paramagnetic resonance in anthracene negative ion solution and asphaltene. The methods developed are applicable to a wide range of frequencies, applied field strengths, and ratios of transverse to longitudinal relaxation times.

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