Long-range interaction between polar Rydberg atoms

The most attractive and the most repulsive potential-energy curves for interaction between two Rydberg atoms in a broad superposition of internal angular momentum states are studied. The extreme Stark states have the largest dipole moments and provide the dominant contribution to the interaction which is then expressed as a long-range expansion involving the permanent multipole moments Q(j) of each polar atom. Analytical expressions are obtained for all Q(j) associated with principal quantum number n of H(n) and permit the long-range expansion for the H(n)-H(n') first-order interaction to be explicitly expressed analytically in terms of n, n' and internuclear distance R. Possible quasi-molecular formation is investigated. Direct calculations show that the H(n = 2)-H(n' = 2) interaction is capable of supporting 47 bound vibrational levels. As n increases, the long-range interaction becomes increasingly attractive so that molecular formation at large internuclear distances is expected to be scarcely possible for these extreme Stark levels.