Shape transitions in exotic Si and S isotopes and tensor-force-driven Jahn-Teller effect

We show how shape transitions in the neutron-rich exotic Si and S isotopes occur in terms of shell-model calculations with a newly constructed Hamiltonian based on ${V}_{\mathrm{MU}}$ interaction. We first compare the calculated spectroscopic-strength distributions for the proton $0{d}_{5/2,3/2}$ and $1{s}_{1/2}$ orbitals with results extracted from a ${}^{48}\mathrm{Ca}(e,{e}^{\ensuremath{'}}p)$ experiment to show the importance of the tensor-force component of the Hamiltonian. Detailed calculations for the excitation energies, $B(E2)$, and two-neutron separation energies for the Si and S isotopes show excellent agreement with experimental data. The potential-energy surface exhibits rapid shape transitions along the isotopic chains towards $N=28$ that are different for Si and S. We explain the results in terms of an intuitive picture by involving a Jahn-Teller-type effect that is sensitive to the tensor-force-driven shell evolution. The closed subshell nucleus ${}^{42}\mathrm{Si}$ is a particularly good example of how the tensor-force-driven Jahn-Teller mechanism leads to a strong oblate rather than a spherical shape.