Fermions in scalar and vector potentials

Abstract

This paper investigates the basic physical properties of spin-1/2 bound states, using numerical solutions of the Dirac equation to illustrate the distinctive differences between scalar and vector binding. The results are discussed in relation both to the quark structure of hadrons and to the further possibility that quarks and leptons might themselves be composite. The effect of scalar and vector potential strengths, separately and in combination, on energy levels and magnetic moments is discussed, together with the energy and potential dependence of the wave function parameters 〈1/r〉, 〈p2〉1/2 and ψ2(0), which provide the coefficients in perturbative mass formulae based on the Fermi-Breit Hamiltonian. The results are used to reassess a number of topics, including the ground-state meson and baryon mass spectrum, vector-meson leptonic-decay widths, effective quark mass and the shape of the confining potential.