Paramagnetic Resonance in Gases at Low Fields

A classical analysis has been made of the paramagnetic resonance of a gas composed of a collection of magnetic dipoles in an external static magnetic field $H_0$ for both circularly and linearly polarized radio-frequency fields at right angles to $H_0$. Assuming that during collisions the dipoles have components only along the $H_0$ direction one obtains for the circularly polarized case equations similar to those of Bloch with the single parameter $\tau$, the mean time between collisions. The expression for paramagnetic absorption thus obtained suffers from the defect that at zero external field it does not reduce to the Debye formula, as it should. If a Boltzmann distribution of the $x$ and $y$ components of the magnetization is assumed during collisions, the absorption formula is modified and correctly reduces to the Debye formula. For a linearly polarized radiofrequency field, one obtains as the absorption formula the sum of two terms [Eq. (17)]. This again does not reduce to the Debye formula. Introducing a Boltzmann distribution of magnetization during collisions one obtains a corrected formula in which absorption does not vanish at low fields.