Cranked Skyrme–Hartree–Fock calculation for superdeformed and hyperdeformed rotational bands in N=Z nuclei from S to Cr

With the use of the symmetry-unrestricted cranked Skyrme–Hartree–Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30–50 region. Along the N=Z line, we have found superdeformed solutions in ³²S, ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, and hyperdeformed solutions in ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, ⁴⁸Cr. The superdeformed band in ⁴⁰Ca is found to be extremely soft against both the axially symmetric (Y₃₀) and asymmetric (Y₃₁) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.