Magnetoresistance Anisotropy in Metals due to Anisotropic Scattering of Electrons

The elementary algebraic solution of the Boltzmann equation in the theory of metals, for the case where the kernel is of finite rank, is extended to the case where an external magnetic field of arbitrary strength is present. A closed expression is derived for the magnetoresistance tensor which is valid for arbitrary form of the energy surfaces and which does not depend on the relaxation-time approximation. As an illustrative study of the effects of scattering anisotropy, the high-field longitudinal magnetoresistance is calculated for cubic metals with spherical Fermi surfaces, when fourth-order terms are kept in the expansion of the scattering probability in powers of the wave-vector components. The results suggest that experiments on magnetoresistance in single crystals of the alkali metals may give information on the form of the scattering probability.