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The densities and form factors of the proton andthe Roper monopole excitedstate resonance are calculatedusing a relativistic three-quark model. Small currentquark masses are used with the three-body Dirac equation solved in hypercentralapproximation. A QCD-based three-body potential,proportional to a minimum string length between thethree quarks, is used for confinement. The calculatedelectric form factor for the proton reproduces closelya dipole fit to the data. The proton density is morecompact than is the Roper resonance density. The centraldensity of the proton is about five times that for the Roper resonance. The hyperradial nodein the Roper resonance composite three-quark wavefunction shows up as a node in the transition densitybetween the proton and the Roper resonance. This node also causes the calculated transition formfactor to be larger than either the proton or Roperresonance form factors, all evaluated at the same valueof momentum transfer. The Roper resonance form factor is smaller than the proton form factor, asexpected, indicative of the Roper resonance being a morediffuse system than the proton. |
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