On the elusive ninth vibrational state of the argon dimer

An unresolved discrepancy between high-accuracy potential energy curves for the argon dimer (Ar_2), which support different numbers of bound vibrational states and profoundly different scattering lengths for Ar_2, is probed by morphing these curves to available spectral data within the reduced potential energy curve approach. Although the morphed curves studied closely coincide, they still afford different numbers of bound vibrational states and produce disparate scattering lengths. Resolving these discrepancies therefore remains a challenge. Nevertheless, solving vibrational Schroedinger equations with suitably scaled potential energy curves or reduced masses provides a closely matching relationship between the binding energy (D_o) of the highest vibrational state s-wave scattering length (a), thus enabling the reliable determination of D_o directly from experimental s-wave scattering lengths. Importantly, moreover, a is extremely sensitive to reduced molecular mass and can therefore serve as a fairly sensitive probe of the constancy of the electron-to-proton mass ratio.