  The theory of interactions between lasers and cold trapped ions as it
pertains to the design of Cirac-Zoller quantum computers is discussed. The mean
positions of the trapped ions, the eigenvalues and eigenmodes of the ions'
oscillations, the magnitude of the Rabi frequencies for both allowed and
forbidden internal transitions of the ions and the validity criterion for the
required Hamiltonian are calculated. Energy level data for a variety of ion
species is also presented.
