Abstract
The harmonic-oscillator (HO) quark model, wherein Pauli spinors are replaced by Dirac spinors and quark masses are less than $\frac{1}{3}$ of the nucleon mass, is studied in the spirit of the bag model. In particular, we have calculated $\frac{{G}_{A}}{{G}_{V}}$ and the magnetic moment and charge radius of the proton; the variation of these quantities with quark mass and spring constant is also investigated. In the case of the magnetic moment we find that the relativistic correction is of the right order of magnitude, while in the case of charge radius the result is better than the nonrelativistic HO value. For $\frac{{G}_{A}}{{G}_{V}}$ we find that the relativistic corrections bring the nonrelativistic value of 1.667 down to \ensuremath{\sim} 1.50 only; reasons for this less-than-anticipated fall are investigated in detail. Furthermore, we have calculated certain gluon probability integrals; the trend of our results is the same as those of Golowich and of Close and Horgan.
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