Supersymmetry Aspects of Nuclear Cluster Systems

A supersymmetry scheme is proposed for core+α-type nuclear cluster systems in which the core cluster is a p-shell nucleus. The bosonic sector describes the relative motion of the clusters, while the fermionic one is associated with the internal structure of the core cluster. The underlying superalgebra is found to be U(4|12). We interpret correlations between the spectroscopic properties (energy spectrum, band structure, E2 transitions, one-nucleon transfer amplitudes) of the ¹⁶O + α and ¹⁵N + α systems in terms of this supersymmetry scheme.