Magnetic breakdown in real metals

The treatment of magnetic breakdown given by Pippard in 1964 is extended to apply to real metals, in which the lattice potential is not negligibly small. It is shown that for a hexagonal metal Pippard's results remain applicable, if suitably re-interpreted. An expression is given for the probability of breakdown, in terms of the geometry of the orbits at the breakdown point. The effect of breakdown on the de Haas-van Alphen effect is discussed, and a simple expression is given for estimating the signal amplitudes in the presence of breakdown.