Description of the superdeformed rotational band in Ca40 with a shell-model-like approach

Abstract

The superdeformed rotational band in $^{40}\mathrm{Ca}$ is investigated in the framework of a shell-model-like approach based on cranking covariant density functional theory, in which the pairing correlations are treated with conserved particle number. A superdeformed state is obtained at the deformation $(\ensuremath{\beta},\phantom{\rule{0.16em}{0ex}}\ensuremath{\gamma})=(0.70,\phantom{\rule{0.16em}{0ex}}{9}^{\ensuremath{\circ}})$ even though the depth of the superdeformation minimum is only about 0.2 MeV. With increasing rotational frequency, the potential around the superdeformed minimum becomes deeper. This indicates that the superdeformed state becomes more stable with increasing rotational frequency. Besides, the experimental data are well reproduced by the theoretical calculations with pairing correlations. Pairing correlations are important for the states with $I\ensuremath{\le}10\ensuremath{\hbar}$ in the superdeformed rotational band of $^{40}\mathrm{Ca}$ in reproducing the experimental energy spectrum and transition quadrupole moments.