Microscopic origin of reflection-asymmetric nuclear shapes

Background: The presence of nuclear ground states with stable reflection-asymmetric shapes is supported by rich experimental evidence. Theoretical surveys of odd-multipolarity deformations predict the existence of pear-shaped isotopes in several fairly localized regions of the nuclear landscape in the vicinity of near-lying single-particle shells with $\mathrm{\ensuremath{\Delta}}\ensuremath{\ell}=\mathrm{\ensuremath{\Delta}}j=3$.Purpose: We analyze the role of isoscalar, isovector, neutron-proton, neutron-neutron, and proton-proton multipole interaction energies in inducing the onset of reflection-asymmetric ground-state deformations.Methods: The calculations are performed in the framework of axial reflection-asymmetric Hartree-Fock-Bogoliubov theory using two Skyrme energy-density functionals and density-dependent pairing force.Results: We show that reflection-asymmetric ground-state shapes of atomic nuclei are driven by the odd-multipolarity neutron-proton (or isoscalar) part of the nuclear interaction energy. This result is consistent with the particle-vibration picture, in which the main driver of octupole instability is the isoscalar octupole-octupole interaction giving rise to large $E3$ polarizability.Conclusions: The necessary condition for the appearance of localized regions of pear-shaped nuclei in the nuclear landscape is the presence of parity doublets involving $\mathrm{\ensuremath{\Delta}}\ensuremath{\ell}=\mathrm{\ensuremath{\Delta}}j=3$ proton or neutron single-particle shells. This condition alone is, however, not sufficient to determine whether pear shapes actually appear, and, if so, what the corresponding reflection-asymmetric deformation energies are. The predicted small reflection-asymmetric deformation energies result from dramatic cancellations between even- and odd-multipolarity components of the nuclear binding energy.