Rest frame properties of the proton

The proton is modeled as three quarks of small current quark mass. The three-body Dirac equation is solved with spin-independent central diagonal linear confining potentials with an attractive Coulombic term in a relativistic three-quark model. Hyperspherical coordinates are used, and the bound state is found analytically. After integrating over the hyperangles, the Hamiltonian is an 8 by 8 matrix of coupled first-order differential equations in one variable, the hyperradius. These are analytically solved in hypercentral approximation. For the (1/2+)3 ground-state configuration in the nonrelativistic large-quark-mass limit, there are no nodes in the wave function. However, in the extreme relativistic limit of small current quark masses of a few MeV, the expectation value of the number of nodes is about 1.30 when the potential parameters are chosen to reproduce the proton rms charge radius. The quarks are assumed to possess a Pauli anomalous magnetic moment, like that of the electron and muon of (α/2π)(e/m). Assuming all three quarks have equal mass, one can fit the rest energy, magnetic moment, rms charge radius, and axial charge of the proton with this relativistic three-body Dirac equation model. The solution found shows the necessity of including all components of the composite three-quark wave function, as the upper component contributes only 0.585 to the norm