Elucidating the origin of magic numbers: Trends in the relative binding energies of xenon cluster ions and their implications

Abstract

Metastable decay fractions of Xe<lu>n<bu>+<lux>, n=5–39, are measured using a reflectron time-of-flight mass spectrometry technique. Employing these data, the relative binding energies of Xe<lu>n<bu>+<lux>, n=12–39, are deduced by applying the latest evaporative ensemble model. An excellent correlation is found between the relative binding energies and the intensity anomalies observed in the mass spectrum. Importantly, however, are findings that magic numbers of size n are related to the ratio of the cluster-ion band energies ΔEn/ΔEn+1, and hence are not only influenced by the bonding of this size, but also of n+1 and even n+2! Our results show that magic numbers in the mass spectra alone do not conclusively lead to knowledge of the stabilities and structures of the cluster ions, but consideration of the relative bond energies which can be derived from the new approach are required.