We present an experimental and computational study of the photoabsorption line shape of Xe+N clusters. Positively charged xenon clusters have a unique feature not seen in lighter rare gas cation clusters: there are two families of isomers whose ground states consist of neutral atoms surrounding either a linear trimer ion core or a linear tetramer ion core. Interconversion of these two isomers is possible at temperatures as low as 60 K. The combination of simulation and experiment demonstrates the existence of these two families of isomers and their manifestation in the photoabsorption spectra. Clusters present, in general, either of the two cores depending on the number of atoms along the axis that contains the ion core.