Spacings of Quarkonium Levels with the Same Principal Quantum Number

Physics – High Energy Physics – High Energy Physics - Phenomenology

Scientific paper

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20 pages, latex, 3 uuencoded figures submitted separately (process using psfig.sty)

Scientific paper

10.1103/PhysRevD.53.2742

The spacings between bound-state levels of the Schr\"odinger 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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