Abstract
A mass formula relating the $\ensuremath{\Delta}\ensuremath{-}N$ and $\ensuremath{\rho}\ensuremath{-}\ensuremath{\pi}$ hyperfine splittings is derived within the context of the relativistic harmonic-oscillator quark model. The spring constant, determined from the Regge trajectories, adjusts the wave-function overlap integrals so that reasonable agreement with experiment is obtained. The formula involves the square of the hadron masses and clearly indicates factors due to color, SU(6), and internal quark motion.
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