  Large scale shell model calculations, with dimensions reaching 10**9, are
carried out to describe the recently observed deformed (ND) and superdeformed
(SD) bands based on the first and second excited 0+ states of 40-Ca at 3.35-MeV
and 5.21-MeV respectively. A valence space comprising two major oscillator
shells, sd and pf, can accommodate most of the relevant degrees of freedom of
this problem. The ND band is dominated by configurations with four particles
promoted to the pf-shell (4p-4h in short). The SD band by 8p-8h configurations.
The ground state of 40-Ca is strongly correlated, but the closed shell still
amounts to 65%. The energies of the bands are very well reproduced by the
calculations. The out-band transitions connecting the SD band with other states
are very small and depend on the details of the mixing among the different
np-nh configurations, in spite of that, the calculation describes them
reasonably. For the in-band transition probabilities along the SD band, we
predict a fairly constant transition quadrupole moment Q_0(t)~170 e fm**2 up to
J=10, that decreases toward the higher spins. We submit also that the J=8
states of the deformed and superdeformed band are maximally mixed.
