The Morse molecular potential is used for the first time as an effective potential for the overall interaction in charmonium. This procedure allows the calculation of the rotational contributions of P states, the radii of five S states, and an absolute threshold for bound states. The calculation of the latter provides important information on the character of the recently found levels X(3915), X(3940), Ψ(4040), X(4050), X(4140), Ψ(4160), X(4160), X(4250), X(4260), X(4350), Ψ(4415), X(4430), and X(4660).
[Article published in January 2016]