Muon capture in atoms, crystals and molecules

The slowing down and capture of negative muons in solids is discussed on the basis of classical equations of motion where the energy dissipation is described in terms of frictional forces. Transport equations determining the energy distribution of the muons in the target are formulated and solved for various models. Using a statistical model of the atom it is shown that the muons are captured typically at energies of a few tens of electron volts, that the angular momentum distribution of the muons at capture is almost statistical, and that this distribution is not expected to be qualitatively changed by the subsequent cascade to the tightly bound orbits. In mixtures of atoms with atomic numbers Z1 and Z2 the capture ratio is to a good approximation proportional to the atomic concentration and, in the statistical model, proportional to (Z1/Z2)sup(7/6). Calculations are also performed with more accurate atomic models, and it is shown that capture ratios as well as angular momentum distributions are influenced by the ionicity of the atomic bonds and the atomic shell structure. No systematic study of these effects has been made but the few results obtained seem to be in reasonable agreement with experiments. (Auth.)