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Phonon-induced decay rates for quasiparticle cyclotron orbits in simple metals: analytical approximations and models

A formalism is developed for studying the temperature dependence of phonon-induced quasiparticle scattering rates averaged over cyclotron orbits in simple metals. The underlying model is expressed in terms of analytic forms for the spectral distribution alpha 2F( omega ), from which the scattering rate tau -1(T) is easily computed. The material-dependent parameters upon which the results depend are the inter-sheet threshold wavevector Q1, orbit caliper Q2, transverse and longitudinal sound velocities cT and cL, and a parameter R expressing the importance of the momentum dependence of the pseudopotential form factor, all of which are known in many cases. The orbitally averaged scattering rates exhibit a regime of T2 dependence that is not associated with individual point rates, above a characteristic temperature T1 approximately Q1cT.