  Neutral fermions of spin $\frac 12$ with magnetic moment can interact with
electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation
for such a fermion coupled to a spherically symmetric or central electric field
can be reduced to two simultaneous ordinary differential equations by
separation of variables in spherical coordinates. For a wide variety of central
electric fields, bound-state solutions of critical energy values can be found
analytically. The degeneracy of these energy levels turns out to be numerably
infinite. This reveals the possibility of condensing infinitely many fermions
into a single energy level. For radially constant and radially linear electric
fields, the system of ordinary differential equations can be completely solved,
and all bound-state solutions are obtained in closed forms. The radially
constant field supports scattering solutions as well. For radially linear
fields, more energy levels (in addition to the critical one) are infinitely
degenerate. The simultaneous presence of central magnetic and electric fields
is discussed.
