Analysis of bound-state spectra near the threshold of neutral particle interaction potentials

It is understood that conventional semiclassical approximations deteriorate towards threshold in a typical neutral particle interaction potential which is important for the study of ultra-cold atoms and molecules. In this Letter we give an example of the Lennard-Jones potential with tuning of the strength parameter on the basis of the analytical transfer matrix (ATM) method. Highly accurate quantum mechanical results, such as number of the bound states, energy level density and the eigenvalues with extremely low energies have been derived.