  Under a few mild assumptions, N=1 supersymmetry in four dimensions is shown
to be spontaneously broken in a self-consistent Hartree-Fock approximation of
BCS/NJL type to one-loop off-shell, in the gauge theory specified by the gauge
kinetic function and the superpotential of adjoint chiral superfields, in
particular, that possesses N=2 extended supersymmetry spontaneously broken to
N=1 at tree level. The N=2 gauginos receive mixed Majorana-Dirac masses and are
split. We derive an explicit form of the gap equation, showing the existence of
a nontrivial solution.
