LOW-TEMPERATURE QUANTUM DIFFUSION OF LIGHT PARTICLES - THE DOMAINS OFTHE VARIOUS MECHANISMS IN THE STATIC-ENERGY-ASYMMETRY-TEMPERATURE PLANE

The motion of a light particle in a solid coupled to conduction electr ons and/or phonons is investigated within the framework of a two-state model, which may be taken as representing the particle ground states in two neighbouring potential wells. With regard to the coupling of th e particle to phonons, an important distinction arises between (i) spe cial two-phonon processes, termed diphonon processes, which result fro m nonlinear particle-lattice coupling and which may give rise to qunsi elastic phase-destroying scattering and (ii) essentially inelastic pro cesses which may arise from linear as well as from nonlinear particle- lattice coupling. An important parameter affecting particle motion is the static energy shift epsilon between the particle ground states in the two wells. Under favourable conditions it may be experimentally co ntrolled within certain limits. The two-state model allows us to estim ate reliably the boundary in the E-T plane separating the regimes of i ncoherent hopping from that of coherent bandlike motion, and to discus s its dependence on the particle mass and the coupling parameters. Wit hin the regime of incoherent motion a number of subregimes may exist. The situation becomes particularly interesting if a condensation of th e electron system takes place, as in the case of a Bardeen-Copper-Schr iefer superconductor. Then domains have to be distinguished in which t he hopping rates are dominated by either quasiparticle coupling, dipho non processes, one-phonon processes, Cooper-pair breaking, coupling to normal-conducting electrons, or multiphonon-assisted processes. In th e series of light particles carrying one positive elementary charge, w hich includes the positive muon (mu(+)) and the nuclei of the hydrogen isotopes, the range of validity,of the two-state description extends to rather high temperatures for the mu(+) but only to considerably low er temperatures for the heavier particles. Nevertheless, for protons t he limiting temperature can be almost as high as the Debye temperature . Towards low temperatures the validity of the two-well description of unrestricted particle motion in a crystal is limited by the onset of coherent motion.