Microscopic derivation of the octupole magic numbers from symmetry considerations

Abstract The valence shells of medium mass and heavy nuclei consist of the normal and the intruder parity orbitals; therefore the Shell Model SU(3) symmetry of Elliott cannot have a straightforward application on them. The proxy-SU(3) can be applied instead, since it uses a unitary transformation, meant to act on the intruder orbitals to alter their parity and transform them to their proxy orbitals. The inverse unitary operator transforms the proxy orbitals back to the intruder ones. The highest weight proxy-SU(3) irreducible representations (irreps) allows one to determine the corresponding number of occupied intruder orbitals. In this way we obtain the so-called ‘octupole magic numbers’ 32 , 56 , 90 , 134 and 194 without any parameter. Moreover, the proxy (unitary) mapping and its inverse transformation make the proxy space eligible for the calculation of observables associated with octupole deformation and the relevant treatment of mixed parity states. The implemented study validates the proxy-SU(3) approach with respect to the octupole deformation and suggests its full applicability in the corresponding mass regions.