Coexistence of spherical states with deformed and superdeformed bands in doubly magic 40Ca; A shell model challenge

Large scale shell model calculations, with dimensions reaching 109, are carried out to describe the recently observed deformed (ND) and superdeformed (SD) bands based on the first and second excited 0+ states of 40Ca 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 40Ca 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 Q0(t) ∼ 70 e fm2 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. (authors)