Knowledge Bank

The $\ell$-doubling in the degenerate sode $\nu t$ of a linear molecule is of the form $$\Delta F=q_{t}J(J+1) + q^{J}_{t}J^{2}(J+1)^{2}+\ldots.$$ The $qtJ$ term is simpler than other $H~24$ terms of the effective Hamiltonian and is round to be independent of the quartic potential constants and to depend only linearly on the cubic potential constants. A theoretical formula for $qtJ$ is obtained and compared with experimental measurements. The high-J limiting behavior of the energy levels with $\nu t>1$ is also discussed.