Large-scale shell-model calculations for deformed states around ⁴⁰Ca

The deformed band in ⁴⁰Ca is one of the classical examples of shape coexistence studied more than half a century. This band is considered as states associated with 4p-4h excitation across the N=Z=20 shell gap. In the last decades, while a number of similar 4p-4h (or 4ħω) states are observed around ⁴⁰Ca, including ^36,38,40Ar, ⁴²Ca, and ⁴⁴Ti, by the state-of-the-art γ-ray spectroscopy, successful systematic calculations for these deformed bands are still missing. In this study, we carry out systematic large-scale shell-model calculations for these 4ħω states. The valence shell consists of the full sd shell plus f_7/2+p_3/2 orbitals, and the model space is truncated to cover the configurations up to 6ħω excitations. The SDPF-M interaction is used for the initial choice of the effective interaction, and it is modified so that one-neutron separation energies of ^40,41Ca and α separation energies of ⁴⁴Ti and ⁴⁰Ca are reproduced. This is based on a natural requirement that the N=Z=20 gap and correlation energies within the major shells are preserved in theory. It is shown that the resulting 4ħω states are well reproduced.