Tri-axial Octupole Deformations and Shell Structure

The remarkable regularity of rotational spectra of superdeformed nuclei has prompted many investigations into the contribution of higher multipoles on the formation of shell structure [1]. Related questions have arisen for other mesoscopic systems. In particular, it appears that octupole deformation has the same importance for two-dimensional systems like quantum dots and surface clusters [2] as for three-dimensional systems like nuclei [3] and metallic clusters [4]. Semi-classical analysis based on periodic orbit theory [5–7] provides substantial insight into the role of the octupole deformation for axially symmetric systems [8–10]. Axially symmetric octupole deformation which leads to soft chaos in the classical case produces short periodic orbits at particular parameter strengths, and, correspondingly, pronounced shell effects arise in the quantum spectrum [8,9]. Conservation of angular momentum may increase the regular region for a non-integrable problem with axial symmetry (see for example [11]). The situation becomes more complicated for nonaxial systems with three degrees of freedom, since angular momentum is no longer a constant of motion and the classical dynamics may lead to a stronger degree of chaos [12]. Inclusion of exotic, i.e. nonaxial, octupole deformations renders the finding of