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We investigate the stability and softness of nuclei against quadrupole,octupole, and hexadecapole deformation. By applying the spherical Skyrme-forceHartree-Fock Bardeen-Cooper-Schrieffer quasi-particle random phaseapproximation, we diagnose ground-state deformation when imaginary solutionsare obtained, i.e., the spherical ground state {\em collapses}. We alsocalculate the multipole polarizability in spherical nuclei with no collapse, asa measure of softness. This numerically light and theoretically sound method isfound able to capture deformation patterns across the nuclide chart. Theconnection between the intrinsic shape of nuclei and the dynamics of theirlow-lying collective states is established and the role of shell structure isdiscussed.

Landscape of nuclear deformation softness with spherical quasi-particle random phase approximation