  The nuclear equation of state is explored with the constrained HFB approach
for self conjugate nuclei. It is found that beyond a certain low, more or less
universal density, those nuclei spontaneously cluster into A/4 alpha particles
with A the nucleon number. The energy at the threshold density increases
linearly with the number of alpha particles as does the experimental threshold
energy. Taking off the spurious c.o.m. energy of each alpha particle almost
gives agreement between theory and experiment. The implications of these
results with respect to alpha clustering and the nuclear EOS at low density are
discussed.
