Long-range states of diatomic molecules have average values of internuclear separations at least one order of magnitude larger than the equilibrium value of R. For example, the helium dimer 4He2 has a single bound state with <R> of about 50 Å. We show that the properties of these states, such as <R>, the dissociation energy, or the s-wave scattering length, can be related by simple, yet very accurate formulas if a potential energy curve is known. By examining a range of ab initio and empirical helium dimer potentials, as well as scaling these potentials, we found that the formulas remain accurate even if very approximate potentials are used. In addition to 4He2, we present results for 9Be2, 20Ne2, and KRb.
Physical Review a (atomic, Molecular and Optical Physics), 2013, Vol 87, Issue 1