Spacings of Quarkonium Levels with the Same Principal Quantum Number

Abstract

The spacings between bound-state levels of the Schrödinger equation with the same principal quantum number $N$ but orbital angular momenta $\ell$ differing by unity are found to be nearly equal for a wide range of power potentials $V=\lambda r^{\nu }$, with $E_{N\ell }\approx F(\nu ,N)-G(\nu ,N)\ell$. Semiclassical approximations are in accord with this behavior. The result is applied to estimates of masses for quarkonium levels which have not yet been observed, including the 2P $c\bar{c}$ states and the 1D $b\bar{b}$ states.

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