field, F, known in atomic physics as a Stark shift, Depending on the sign of the projection of the dipole moment onto the local electric field vector, a state may have energy that increases or decreases with field strength (low-field and high-field seeking states respectively). The narrow spacing between adjacent n-levels in the Rydberg series means that states can approach degeneracy even for relatively modest field strengths. The theoretical field strength at which a crossing would occur assuming no coupling between the states is given by the Inglis–Teller limit, In the hydrogen atom, the pure 1/r Coulomb potential does not couple Stark states from adjacent n-manifolds resulting in real crossings as shown in figure 5. The presence of additional terms in the potential energy can lead to coupling resulting in avoided crossings as shown for lithium in figure 6. Applications and further research Precision measurements of trapped Rydberg atoms The radiative decay lifetimes of atoms in metastable states to the ground state are important to understanding astrophysics observations and tests of the standard model. Investigating diamagnetic effects The large sizes and low binding energies of Rydberg atoms lead to a high magnetic susceptibility, . As diamagnetic effects scale with the area of the orbit and the area is proportional to the radius squared (A ∝ n4), effects impossible to detect in ground state atoms become obvious in Rydberg atoms, which demonstrate very large diamagnetic shifts. Rydberg atoms exhibit strong electric-dipole coupling of the atoms to electromagnetic fields and has been used to detect radio communications. In plasmas Rydberg atoms form commonly in plasmas due to the recombination of electrons and positive ions; low energy recombination results in fairly stable Rydberg atoms, while recombination of electrons and positive ions with high kinetic energy often form autoionising Rydberg states. Rydberg atoms’ large sizes and susceptibility to perturbation and ionisation by electric and magnetic fields, are an important factor determining the properties of plasmas. Condensation of Rydberg atoms forms Rydberg matter, most often observed in form of long-lived clusters. The de-excitation is significantly impeded in Rydberg matter by exchange-correlation effects in the non-uniform electron liquid formed on condensation by the collective valence electrons, which causes extended lifetime of clusters. In astrophysics It has been suggested that Rydberg atoms are common in interstellar space and could be observed from earth. Since the density within interstellar gas clouds is many orders of magnitude lower than