The spin -spin mass splitting of light, heavy and mixed mesons are described within a good accuracy in the potential model with screened potential. We conclude that the long -distance part of the potential cannot be pure scalar and that a vector -scalar mixture is favoured. With the same parameters which gives correct average mass spectrum excellent spin -spin splittings of heavy quarkonia is obtained. The results are obtained by going beyond usually used perturbation method, namely using configuration interaction approach.

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Based on the numeric solution of a system of coupled channels for vector mesons ($S$- and $D$-waves mixing) and for tensor mesons ($P$- and $F$-waves mixing) mass spectrum and wave functions of a family of vector mesons $q\bar{q}$ in triplet states are obtained. The calculations are performed using a well known Cornell potential with a mixed Lorentz-structure of the confinement term. The spin-dependent part of the potential is taken from the Breit-Fermi approach. The effect of singular terms of potential is considered in the framework of the perturbation theory and by a configuration interaction approach (CIA), modified for a system of coupled equations. It is shown that even a small contribution of the $D$-wave to be very important at the calculation of certain characteristics of the meson states.Comment: 12 pages, LaTe

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