Angular-momentum-insensitive quantum-defect theory for diatomic systems

Abstract

With recent developments such as the analytic solutions of the Schrodinger equation for 1/r 6 and 1/r 3 potentials @1-3#, our understanding of two-atom systems is already conceptually comparable to the quantum-defect theory ~QDT! of atomic Rydberg spectra @4#. Namely, the slow atomic scattering and the rovibrational spectrum of a particu- lar angular momentum can be understood in terms of the long-range solutions and a parameter that is a slowly varying function of energy in the threshold region @5-7,1-3#. In this work, we show that a two-atom system possesses an even greater degree of systematics in the following sense. Unlike the QDT for atomic Rydberg spectra in which different angular-momentum states have different quantum defects with no general relationships among them, a single param- eter is sufficient to characterize slow atomic collisions for practically all angular momenta. The same parameter also characterizes the rovibrational spectra in the threshold re- gion, including states of different angular momenta. In other words, in addition to the relationship between the bound spectrum and scattering, as expected from traditional QDT formulations @4#, a two-atom system has also the unique property that scattering of different angular momenta are re- lated, and so are the bound spectra of different angular mo- menta. The origin of this relationship between different angular- momentum states is not difficult to understand and is due to a combination of the following three properties of a typical molecular system. ~i! Atoms are strongly repulsive at short distances. ~ii! Atoms are heavy compared to electrons. ~iii!