orbital with higher energy and lower binding energy. In hydrogen the binding energy is given by: , where Ry = 13.6 eV is the Rydberg constant. The low binding energy at high values of n explains why Rydberg states are susceptible to ionization. Additional terms in the potential energy expression for a Rydberg state, on top of the hydrogenic Coulomb potential energy require the introduction of a quantum defect, δl, into the expression for the binding energy: . Electron wavefunctions The long lifetimes of Rydberg states with high orbital angular momentum can be explained in terms of the overlapping of wavefunctions. The wavefunction of an electron in a high l state (high angular momentum, “circular orbit”) has very little overlap with the wavefunctions of the inner electrons and hence remains relatively unperturbed. The three exceptions to the definition of a Rydberg atom as an atom with a hydrogenic potential, have an alternative, quantum mechanical description that can be characterized by the additional term(s) in the atomic Hamiltonian: If a second electron is excited into a state ni, energetically close to the state of the outer electron no, then its wavefunction becomes almost as large as the first (a double Rydberg state). This occurs as ni approaches no and leads to a condition where the size of the two electron’s orbits are related; a condition sometimes referred to as radial correlation. An electron-electron repulsion term must be included in the atomic Hamiltonian. Polarization of the ion core produces an anisotropic potential that causes an angular correlation between the motions of the two outermost electrons. This can be thought of as a tidal locking effect due to a non-spherically symmetric potential. A core polarization term must be included in the atomic Hamiltonian. The wavefunction of the outer electron in states with low orbital angular momentum l, is periodically localised within the shells of inner electrons and interacts with the full charge of the nucleus. Figure 4 shows a semi-classical interpretation of angular momentum states in an electron orbital, illustrating that low-l states pass closer to the nucleus potentially penetrating the ion core. A core penetration term must be added to the atomic Hamiltonian. In external fields The large separation between the electron and ion-core in a Rydberg atom makes possible an extremely large electric dipole moment, d. There is an energy associated with the presence of an electric dipole in an electric