Steady electrically neutral axisymmetric equilibria of an earlier developed extended electromagnetic theory are considered, as being based on a nonzero electric field divergence in the vacuum and combined with the requirement of Lorentz invariance. Thereby the general solutions of these states are given in terms of a generating function. It is found that electrically neutral particle-like states result not only from the convergent generating functions being considered earlier, but also from divergent such functions which are top-bottom antisymmetric with respect to the midplane of the axisymmetric geometry.

The models of the present theory can at least reproduce part of the general features of the neutrino in a state at rest, such as vanishing integrated values of the electric charge and the magnetic moment, angular momentum, and a very small rest mass. The model with a convergent generating function further results in a large effective neutrino radius as compared to that of a nucleon, whereas a divergent function leads to a very small such radius. Both cases and their combination may become reconcilable with the extremely long observed mean free path of neutrinos in solid matter, but this requires further consideration.