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Abstract The longitudinal magnetoresistance is easier to analyse than the transverse magnetoresistance, and it is used here to study how the theoretically predicted behaviour depends on the details of the model chosen. It is found that for a multiply-connected Fermi surface like that of copper there is a large difference according as the scattering is through large or small angles, and that a very small amount of small angle scattering imposed on predominantly isotropic scattering can have a powerful influence in increasing the difference between zero-field and high-field conductivity. The effects discussed arise from those orbits which pass through Brillouin zone boundaries and which in a high field greatly accelerate the relaxation process by connecting opposite sides of the Fermi surface. A detailed calculation is carried out for the longitudinal magnetoresistance of aluminium with the field along a cube axis, and it is found that except in very strong fields the observed behaviour is well accounted for by the nearly-free. electron model and a constant relaxation time.
A. B. Pippard (1964) studied this question.