Muonium

In this chapter we discuss the spectroscopy of the muonium atom, the bound state between a positive muon and an electron formed during the thermalization process in semiconducting and insulating materials. Muonium is a light hydrogen isotope, and its spectroscopy allows the study of the electronic states and behavior of an isolated hydrogen impurity in solids. Starting with the Hamiltonian of muonium in a magnetic field, we first derive the energy eigenvalues and eigenstates of free (isotropic) muonium (Breit-Rabi diagram). We then work out the time evolution of the muon spin polarization in bound muonium in the presence of transverse and longitudinal fields and its limiting cases for low and high fields. We discuss and present experimental examples of special hydrogen-like states found in some semiconductors, such as anisotropic and shallow muonium and related muon-polaron complexes. The nuclear hyperfine interaction as a source of muonium depolarization in matter is introduced.