A new analytic function method is utilized to study self-consistent vector interactions in the non-relativistic case. A mass formula is obtained as a function of the current and charge densities and found to yield particle radii near the Compton lengths for a number of elementary particles. With spin-current interactions included, the mass formula gives the baryon masses within 10% at densities corresponding to the Compton lengths. The results lead to definite conclusions regarding the nature of strong forces.