An accurate potential model for the a³Σ_u⁺ state of the alkali dimers Na₂, K₂, Rb₂, and Cs₂

A modified semi-empirical Tang-Toennies potential model is used to describe the a³Σ_u⁺ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth D_e, well location R_e, and the harmonic vibrational frequency ω_e of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na₂, K₂, Rb₂, and Cs₂, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li₂ and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li₂ less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.