Influence of Collisions on the Magnetic Susceptibility of an Electron Gas. I

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Abstract
Using a simple model, a determination is made of the influence of collisions on the magnetic susceptibility of an electron gas without assuming the existence of a relaxation time. The model consists of noninteracting free electrons being elastically scattered by randomly distributed impurity centers in the presence of a strong uniform magnetic field. The free energy for this simple system is expanded in ascending powers of the strength of the scattering potential and is evaluated for impurities represented by a screened Coulomb potential. The result for the oscillatory part of the magnetic susceptibility is in agreement with that obtained by Dingle to the order considered and provides an explicit expression for the collision relaxation time and the corresponding Dingle temperature.

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