Coexistence of spherical states with deformed and superdeformed bands in doubly magicCa40: A shell-model challenge

Abstract

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 $^{40}\mathrm{Ca}$ at 3.35 and 5.21 MeV, respectively. A valence space comprising two major oscillator shells, $\mathit{sd}$ and $\mathit{pf}$, 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 $\mathit{pf}$ shell (4p-4h in short). The SD band by 8p-8h configurations. The ground state of $^{40}\mathrm{Ca}$ 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 $n\mathrm{p}\text{\ensuremath{-}}n\mathrm{h}$ 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 ${Q}_{0}(t)~170\phantom{\rule{0.3em}{0ex}}e$ 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 bands are maximally mixed.